THE SPECTROPHOTOMETER

THE SPECTROPHOTOMETERA Module on the Spectral Properties of Light

l€KCRobert F. Tinker, Springfield Technical Community College

John W. McWane, Technical Education Research Centers

John W. McWane, Project Director

NEW YORKST. LOUIS

DALLASSAN FRANCISCO

AUCKLANDDUSSELDORF

JOHANNESBURGKUALA WMPUR

LONDONMEXICO

MONTREALNEW DELHI

PANAMAPARIS

sAO PAULOSINGAPORE

SYDNEYTOKYO

TORONTO

The Physics of Technology modules were produced by the Tech Physics Project, whichwas funded by grants from the National Science Foundation. The work was coordinated bythe American Institute of Physics. In the early planning stages, the Tech Physics Projectreceived a grant for exploratory work from the Exxon Educational Foundation.

The modules were coordinated, edited, and printed copy produced by the staff at IndianaState University at Terre Haute. The staff involved in the project included:

Philip DiLavoreJulius Sigler . .Mary Lu McFallB. W. Barricklow.Stacy Garrett. . .Elsie GreenDonald Emmons.

. . . . . . . . . . . Editor

. . . . . . Rewrite EditorCopy and Layout Editor

. Illustrator· . . . . . Compositor· . . . . . CompositorTechnical Proofreader

In the early days of the Tech Physics Project A. A. Strassenburg, then Director of the AlPOffice of Education, coordinated the module quality-control and advisory functions of theNational Steering Committee. In 1972 Philip DiLavore became Project Coordinator andalso assumed the responsibilities of editing and producing the final page copy for themodules.

The National Steering Committee appointed by the American Institute of Physics hasplayed an important role in the development and review of these modules. Members ofthis committee are:

J. David Gavenda, Chairman, University of Texas, AustinD. Murray Alexander, DeAnza CollegeLewis Fibel, Virginia Polytechnic Institute & State UniversityKenneth Ford, University of Massachusetts, BostonJames Heinselman, Los Angeles City CollegeAlan Holden, Bell Telephone LabsGeorge Kesler, Engineering ConsultantTheodore Pohrte, Dallas County Community College DistrictCharles Shoup, Cabot CorporationLouis Wertman, New York City Community College

This module was written and tested at the Curriculum Development Laboratory of theTechnical Education Research Centers, Inc.

The authors wish to express their appreciation for the help of many people in bringingthis module to final form. The criticisms of various reviewers and the cooperation of field-test teachers have been most helpful. Several members of the staff of the TechnicalEducation Research Centers also deserve special recognition for their contributions. Theyare:

Richard R. LewisMary A. HeffernanJohn W. Saalfield .

· .. Apparatus DesignGraphic Composition

· .... ' Illustration

Nathaniel H. Frank, Massachusetts Institute of TechnologyErnest D. Klema, Tufts University

Copyright © 1975 by Technical Education Research Centers. AU rights reserved. Printedin the United States of America. No part of this pUblication may be reproduced, stored in aretrieval system, or transmitted, in any form or by any means, electronic, mechanical,photocopying, recording or otherwise, without the prior written permission of thepUblisher.

Except for the rights to material reserved by others, the publisher and copyright ownerhereby grant permission to domestic persons of the United States and Canada for use ofthis work without charge in the English language in the United States and Canada afterJanuary I, 1982. For conditions of use and permission to use materials contained hereinfor foreign publication or publications in other than the English language, apply to theAmerican Institute of Physics, 335 East 45th Street, New York, N.Y. 10017

The purpose of the Physics of Technologyprogram is to giveyou an insight into some ofthe physical principles that are the basis oftechnology. To do this you are asked to studyvarious technological devices. These deviceshave been cho~:en because their operationdepends on or illustrates some importantphysical phenomenon. In this module thedevice is the spectrophotometer. Its designand use are based on the spectral properties oflight.

The PoT program has adopted a modularformat with each module focusing on a singledevice. Thus yOl can select those modulesthat relate to your own interests or areas ofspecialty. This preface highlights some of thefeatures of the modular approach so that youmay use it efficiently and effectively.

Introduction ~Section ~ _

Section B

The module design is illustrated below. TheIntroduction explains why we have selectedthe spectrophotometer to study and whatphysical principles will be illustrated in itsbehavior. Learning Goals are given, as well asPrerequisite skills and knowledge you shouldhave before beginning. The three Sections ofthe module treat different aspects of thedevice. They are of increasing difficulty buteach can be completed in about one week.

Each section begins with a brief Introductionto the topics treated and how they relate tothe behavior of the device. The Experimentsfollow and take about two to three hours.Tear-out Data Pages are provided to recordyour data. The body of the section thendescribes the method of Data Analysis includ-ing a Discussion of the physical principleswhich explain your results. A Summary endsthe section with Problems and Questions youcan do to test your understanding.

Data Analysisand Discussion

Summary,

IProblems,Questions

This module has been written so that it can bequickly and easily scanned. That is, you canget the gist of the ideas and experiments bysimply flipping from page to page, readingonly the headings and italicized words, andlooking at the illustrations. We suggest beforeyou begin a section or an experiment that youscan through it in this way so that you willknow where you are going.

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The heart of the Physics of Technologymodules is the experimental studies of thedevice behavior. These will often involvelearning to use a new measuring device orinstrument. Since your observations and datamay not be analyzed until after you leave thelaboratory, it is important that you do theexperiments carefully and take accurate data.A scan of the Data Analysis and Discussionbefore you begin the experiment will helpyou to know what aspects of the experimentand data are important.

The data you take will generally have to begraphed before they can be analyzed. Graphingand graphical analysis are essential parts ofexperimental science. And understandinggraphs is important for technology sincetechnical information is often presentedgraphically. For these reasons, and since thediscussion of your results wlll be centeredaround your graphs, it is important that youprepare them clearly and accurately.

When you finish a section ~ou should againscan it to be sure you understand how theideas were developed. Reading the Summarywill also help. Then you should try to answerthe Problems and QuestiOils to test yourunderstanding and to be sure that you haveachieved the Goals for that sl~ction. When youhave completed the module, you may want totear out certain pages for future reference; forexample, conversion tables, methods of cali-brating instruments, explanations of physicalterms and so on.

Introduction: Why Study Spectrophotometers? .The Phyfics Has Many Applications . .Spectrophotometers Are Widely Used .What Will You Learn?Goals .

Section A. M~:asuringLight AbsorptionWhat Is a Spectrophotometer? ...Experiment A-I. The Light SourceExperiment A-2. A Simple SpectrophotometerSetting Up a Grating Spectrophotometer .Setting Up a Prism Spectrophotometer . . . . . .Transmission and Absorption .Analysis of Your Transmission Spectrum . . . .The Electromagnetic SpectrumReview ,Questions . . . . . . . . . . . .

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10· 12· 14· 14· 16.20.20

Section B. The Dispersion of LightWhat Is Dispersion? .Dispersive Elements .Experiment B-1. The Spectrum from a Diffraction GratingExperiment B-2. The Spectrum from a Prism .....Experiment B-3. Comparing the Prism and Grating .,Experiment B-4. Building a Better SpectrophotometerLight as Wave Motion .....How Do We Describe a Wave?Wavelength Scales for LightThe Frequency Scale for LightAnalyzing Your Curves by WavelengthsThe Physics of Prisms .The Physics of GratingsReview .QuestionsProblems

· 23.23.24.26.29.30· 31.34.36.37.39.40.42.44.46.46.47

Section C. Spectrophotometer AnalysisExperiment C-I. Measuring Transmission SpectraAnalyzing Your Data .Applications of SpectrophotometersSpectrophotometer Quality .....Spectrophctometer Specifications ..Other Spectrophotometer SystemsReview .Questions . . . . . . . . . . . . . . .

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The Spectrophotometer

INTRODUCTION: Why Study Spcctrophotometcrs?

In order to really understand how a spectro-photometer works and is used, you will haveto learn about light-how it is produced,measured, controlled, and detected-and aboutcolor. One frequently comes in contact withthe principles involved and in applicationsquite different fr:>m spectrophotometers.

The light that we see with our eyes, visiblelight, is only a small part of a more generalkind of radiation called electromagnetic radia-tion. Other types of electromagnetic radiationinclude radio waves, microwaves, x-rays,gamma rays, infrared, and ultraviolet radia-tion.

The spectrophotometer you will use can makeuse of not only visible light but also the twotypes of electromagnetic radiation-infraredand ultraviolet-thilt you cannot see.

Visible light, ultraviolet, and infrared radia-tion are all present in common sources oflight: flames, light bulbs, fluorescent lamps,and the sun. However, if one wishes toseparate out the different kinds of radiationfrom a light source, a prism or other separatoris required. Such separators are called disper-sive elements and they are the key compo-nents in spectrophotometer design.

Other instruments, called spectrometers, areused to study the other types of electro-magnetic radiation (gamma-ray spectrometers,x-ray spectrometers, etc.). These other spec-trometers have most of the same basic compo-nents that you will study here. Thus, theprinciples that you will learn in your study ofthe spectrophotometer are useful for manyother applications.

SPECTROPHOTOMETERS ARE WIDELYUSED

There are many areas in industry, medicineand science where spectrophotometers, ordevices which work on the same principles,

are used. The following examples indicate thewidespread use of such instruments.

Spectrophotometers are routinely used toanalyze body fluids to help spot diseasebefore it becomes serious. For example, astandard test for diabetes uses a spectro-photometer to measure th~ sugar level inurine.

The widespread use of powerful insecticidesand pesticides creates an increasing threat ofpoisoning ourselves and oUI water. Scientistsuse spectrophotometers to find trace amountsof these toxic compounds before they causeharm.

Brewers use spectrophotometers instead oftasters to monitor the color and flavor of beercoming off the production line.

Before helium had been found on earth,astronomers using spectrophotometers hadlocated it on the sun. S!)ectrophotometershave been essential in determining the speed,size, and age of thousands (If stars.

Police laboratories use spedrophotometers toidentify poisons which are difficult or impos-sible to tag any other way. Narcotics andsleeping pills are exampks. Race tracks runroutine tests with spectrophotometers tocheck whether horses have been drugged.

In the first part of the module you will puttogether a very simple spectrophotometerusing your eye to detect the light. You willsee how various materials absorb visible lightdifferently, and l:hat two materials that maylook alike to the I~yehave quite different lighttransmission (or absorption) properties. Youwill learn that transmission spectra are centralto the way in which spectrophotometers areused in analysis.

Visible light is only one type of a broad classof electromagnetic radiation. Two othertypes, ultraviolet and infrared, are also usedby spectrophotometers. Since these types ofradiation cannot be seen, a method other than"color" is required to specify them. You willlearn about wavelength specification for elec-tromagnetic radiation.

In the second part of the module you willstudy the components used to separate, ordisperse, white light into its various colors.Prisms and gratings are the components,called dispersive elements, that will bestudied.

These components depend on different opti-cal principles to disperse the light and there-fore they act differently. You will observe thebehavior of the dispersive elements and seetheir differences. You also will learn todescribe and explain their behaviors in termsof the wavelike properties of light.

Finally, you will assemble a good qualityspectrophotometer system that will let youdetect non visible ultraviolet and infrared radi-ation.

In the third part of the module you will usethe spectrophotometer you assembled in Sec-tion B to measure accurately the transmissionspectrum of a didymium (di-dim'-e-um) glassfilter. This will introduce you to the tech-niques of spectrophotometric analysis and, atthe same time, show you how spectrophotom-eters are calibrated. Didymium is a substancewhose transmission spectrum is well known.It is commonly used for spectrophotometercalibration.

From your data you will also be able todetermine the resolution of your instrument.This and other spectrophotometer specifica-tions will be described and discussed.

The general goals of this module are to giveyou an understanding of the nature of light,and a knowledge I)f how the properties oflight are used in the design and operation ofspectrophotometen.

Achieving these goals will involve a knowledgeof:

I. The wave description of light and itsapplication to infrared, visible, and ultra-violet radiation.

2. The term used to describe colors oflight (wavelength).

3. The graphs used to display the transmis-sion of colors by various materials (trans-mission spectra).

4. The devices used to disperse light into itscomponent wavelengths (prisms, grat-ings), and the physical processes (refrac-tion, diffraction) on which each depends.

5. The operating principles of spectro-photometers, including the purpose ofeach of its basic components, themethods used for calibration, and theprocedures for making qualitativeanalyses.

Measuring Light Absorption

The light from an ordinary light bulb isactually a mixture of many colors. Whenwhite light is separated into its componentcolors the result is called a spectrum. This iswhere the "spectro" part of the name spectro-photometer comt::sfrom.

Photometer mea:ns light meter or light-measuring device. Thus, a spectrophotometeris a device which measures the light spectrumof something.

A spectrophotometer is used to answer ques-tions about how light is affected by sub-stances. Light can be reflected from, absorbed

REFLECTED TRANSMITTED

--~- 111/RED LIGHT

II.

--~IBLUE LIGHT

IAB$ORBED

Figure 4. In the sam", liquid in a test tube, theamounts of reflected, llbsorbed and transmitted lightdiffer for different colcrs.

by, or transmitted through materials. But thefraction of the light reflected, absorbed, ortransmitted by a particular material dependson the color of the light.

Different chemical substances have uniquepatterns of absorption and reflection. Thesepatterns are like fingerprints, since they canbe used for identification. To do this identifi-cation a spectrophotometer can measure theamount of each color of light which isreflected, transmitted, or absorbed by asample.

Thus, with a spectrophotometer you can findout what substances are present in a sample ofmaterial (qualitative analysis) and how much(quantitative analysis), just by passing lightthrough it.

There are five major parts to every spectro-photometer:

1. The light source, which produces lightwith many colors in it

2. A monochromator, which selects onecolor from the source

3. A sample, where part of the light isabsorbed

4. A detector, which converts the trans-mitted light into an electrical signal

5. A display unit, which records the lightlevel

The figure on the next two pages shows eachof these components in the student spectro-photometer that you will use.

which is spread into a spuctrum of colors. Aslit passesone color only. , .

Most sources of light produce light containingmany colors. An ordinary incandescent lightbulb, for example, produces light containingvisible colors. Special bulbs are needed ifmeasurements are to be extended to non-visible infrared and ultraviolet light.

With a monochromator you can pick onecolor out of the many produced by thesource. This is done by bl1~akingthe light intoits spectrum with a prism or diffractiongrating, which we shall discuss later. Thenonly one color from the spectrum is allowedto pass through a narrow slit. A dial permitsyou to select over a wide range the color oflight coming out.

II

//

/

LIGHTBULB

FILTERSLOT

CONDENSINGLENS

which strike:; a sample. Aportion of the light pas-sesthrough the sample...

Each element or com-pound absorbs only cer-tain colors. The patternof absorption is uniqueto the particular com-pound and serves to iden-tify it. If a 4;ertain com-pound is p:resent in asample of material beinganalyzed, its absorptionpattern will show up andthe operator will know itis there.

and strikes the detector.The amount of lightstriking the detector ...

The detector generates anelectrical signal whenlight falls on it. The sizeof the signal is propor-tional to the intensity oflight. For example, abright light causes a largeelectrical signal andmeans a low absorption.Different types of detec-tors are used, dependingon the range of colorsbeing used.

SAMPLE HOLDER AND.".SHUTTER

PHOTODETECTOR

is electronically mea-sured, and displayed on ameter.

The signal from the de-tector in a spectropho-tometer is rarely largeenough to move the me-ter needle, so an electron-ic amplifier, similar tothose in radios, is needed.Actually, a meter is onlythe simplest form of dis-play. Commercial unitsoften automaticallygraph the absorption on achart recorder.

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0 lI I I I \\ \: \ \i i I I I I

A basic part of any spectrophotometer is thesource of light. The light produced should bevery bright and include a broad range ofcolors. In your spectrophotometer, the sourceis a high-intensity incandescent lamp, similarto those used in automobile tail lights. Thewhite light it produces includes all of thevisible colors.

In order to increase the brightness, a lens isused to gather as much of the output of thebulb as possible and concentrate it on theentrance slit. This means that one must focusthe light to form an image of the bulbfilament. The image should just fill the slitthrough which the light enters the main partof the spectrophotometer (entrance slit).

1. Inspect the light-source box. Open it upand observe the arrangement of the bulband the lens. Note in particular the bulbfilament. It should be long and straight.

2. Attach the light-source box securely tothe monochromator table so that the

light shines through the entrance holenearest you on the left.

3. Turn on the light source.CAUTION: Do not look directly at thefilament; the light is extremely intense.

1. Place the entrance slit on the mono-chromator table with the black sidetoward the light.

2. Move the slit around (back and forth andside to side) until you get the sharpestpossible image of the filament centeredon and passing through the slit. If it isnot centered vertically, ask your instruc-tor for help to make a further adjust-ment.

3. Place the white card after the entranceslit and observe the light coming throughthe slit. Make fine adjustments of the slituntil the light is centered and uniformlybright on the card.

ENTRANCE SLITFOCUSFILAMENTIMAGEHERE

You can now make a simple spectropho-tometer with your laboratory apparatus. Fora first attempt you will make one whichillustrates the principles, but is too inaccuratefor practical use, That is because you will useyour eye in place of the detector and meter.You will simply look at a spectrum andestimate how much of each different color isin the spectrum. You may be surprised howwell you can esti::nate with practice.

CAUTION: Thrc~ Things toWatch Out For

I. Front surfa,~e mirrors. Common mirrorshave silver behind glass to protect thesilver. But the mirrors in this apparatushave silver in front of the glass toimprove their quality. It is very easy to

LIGHTSOURCE

scratch off the thin layer of silver. Don'tput them face down and don't touch themirror surface. If you see that a mirror isdirty don't try to clean it. Impropercleaning can scratch the surface badly.

2. Diffraction grating. A diffraction gratingalso has a delicate front surface. Thesame precautions apply to gratings as tomirrors. Those precautions are evenmore important because some gratingsare extremely expensive.

3. General care. This experiment uses deli-cate scientific equipment. Treat it allwith care. The prisms can chip and themirrors can break. The lamp and detec-tor are both fragile and can break orbecome misaligned. Please be careful.

LENSF= 87 mm

3x5 CARDSCREEN

Figure 7. A spectrophotometer using only a slit, lens, and grating. It spreads the light from the source into aspectrum on a 3 X 5 index card.

SETTING UP A GRATINGSPECTROPHOTOMETER

1. Place the template titled A SIMPLESPECTROPHOTOMETER securely onthe base, centered on the turntable.

2. Place the components on the base asshown in Figure 7 and the plan below.When you do this, you should seethe colors of the rainbow in a spectrumon the white 3 X 5 index card. You mayhave to make some adjustments to makeit work best. This procedure is calledalignment.

1. Follow the checklist on this page for thedetails of aligning the other components.Every time you set up the optical systemyou have to fuss with it to make it workwell. The general idea is to start at thesource and adjust (slide, tilt, and rotate)the components until the maximumamount of light goes squarely throughthe center of each component. Thecircles on the template are only approxi-mate positions, so you may have tomove components slightly off the circlesto get the best alignment.

A. You want as much light as possible topass through the first Hlit. Move the slitaround until the brightest and smallestpossible line of light from the sourcepasses through the center of the slit as inthe previous experiment.

B. You also want the 1t:ns to focus themost light possible. Find the beam oflight coming from the slit by letting ithit another 3 X 5 indl~x card you hold.See Figure 9. Make sure that the lens isin the center of this beam. If it isn't,slide it sideways into the center, but donot move it any closer to the slit.

C. Slide the grating so that it also is in thecenter of the light beam, but do notmove it any closer to the lens.

D. Turn and tilt the grating so that aspectrum falls squarely on the whitecard. Note that there are several spectra.Choose the brightest spectrum which hasthe blue on the left.

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Figure 8. The layout of the grating spectrophotometer, showing the light path to use. When setting up theexperiment, it is important to use approximately the angles and distances shown.

Before using your )pectrophotometer, be sureyou know where the light is going. The lightstarts in the sourc€~ box. It then goes throughthe slit, the lens, and strikes the grating. Thelight leaves the gmting in several beams. Onebeam is reflected ;IS white light, but each ofthe others is broken into a spectrum of colors.These spectra decr'~ase in brightness the great-er the angle they make with the whiterefe1ction. You should have one of the twobrightest ones on the screen.

Figure 9. The beam (an be followed from source toscreen using this method. The maximum amount oflight should be transmitted by each component.

2. Light some incense, place it on theincense holder, put it in the box, and puton the clear plastic cover to get a view ofthe light path. The smoke from theincense will kt you "see" the paths oflight going thr,)ugh the system.

Observe all of the light paths. Note thatthe light paths appear more brilliantwhen the light is coming toward you. Doyou have the light going through thecenter of each component? Make anynecessary cOffl~ctions by using the smoketo show where the light is going.

Now that you haye set up the instrument,what can you do with it? One use is to look atthe effects of colored filters on the spectrum.

You should have a pack of plastic filters withyour equipment.

1. Find out the effects of various filters onlight by placing them one at a time, inthe light path near the slit. You will findthat the darker filters have more notice-able effects. Does it matter where youplace the filter in the light path? Do youget the same result by looking throughthe filter at the spectrum? Why?

2. Try the didymium filter, a pale-blue glassfilter. This filter fits into a slot in thesource box.

Notice that the didymium filter removesalmost all of the yellow light from thespectrum. We say that this filter absorbsyellow. On the other hand, the filterdoes almost nothing to the blue. In otherwords, it transmits the blue. A spectro-photometer is used to determine exactlyhow much of each color is absorbed ortransmitted by various substances.

1. Place filter number 821, a red filter, infront of the entrance slit, as illustrated inFigure 10. The filter should be close tothe slit, and cover only the lower half ofthe slit. Then you will be able tocompare light which has passed throughthe filter with light which has not.

2. Estimate by eye the spectrum passed bythe filter. Judge the amount of light ateach color using a scale with four values.You should be able to decide whetherthe light of each color coming throughthe filter is:

3- Very Bright-As bright as with nofilter. No light is absorbed by thefilter.

2-Bright-Most of the light getsthrough the filter. Some of the light isabsorbed.

I-Dim-Most of the light is stoppedby the filter. Only some is trans-mitted.

O-Dark-All of the light is stopped bythe filter. None is transmitted.

3. Record your results on a graph likeFigure 11.

v G=-

Figure 11. A sample transmission spectrum. Thecolors are violet, blue, green, yellow, orange, and red.

By connecting the dots you make acrude version of what is called a trans-mission spectrum, a graph of the amountof light transmitted for each color.

4. Draw a transmission spectrum for eachof the following filters:

5. Repeat your meaSU1ements for eachfilter, using double thicknesses. Eitheruse two filter books Jr fold each filterover.

6. Explore the transmission spectra of someof the other filters. ~:ee if you can findthe filter which produces the spectrumgiven in Figure 11. Also try combina-tions of filters.

SETTING UP A PRISMSPECTROPHOTOMETER1. Set up a different ;;pectrophotometer

using a prism instead of a grating tobreak up the light. Use the same tem-plate but place the components as shownin Figure 12.

Figure 12. This spectrophotometer uses a prism tobreak up the light. It is simili.r in many respects tothe grating spectrophotometer.

2. Run through the Alignment Checklist onpage 10. To ,~et the best spectrum, rotatethe prism so that the spectrum is as farto the right en the card as it will go.

What differences do you notice between thespectrum madelere by a prism and thespectrum made!Jefore by a grating? Forconvenience in comparing, the distance fromthe prism to the 3 X 5 index card has beenmade the same a~: the distance was from thegrating to the 3 >< 5 index card. Likewise, thedistance from len s to prism equals the dis-tance we had from lens to grating. Essentially,the grating has been replaced by a prism andno other changes tave been made.

I. Repeat your experiment with the didym-ium filter to get a better idea of thedifference between the prism and grat-ing. Estimate the transmission of each ofthe colors:or the didymium filter.Graph the didymium transmission spec-trum.

A SIMPlE SPECTROPHOTOMETERrSCREEN

(PRISM SPECTRUM)

Figure 13. The layout showing the paths to use forthe prism spectrophotometer.

2. Compare the didymium spectra taken bythe grating and by the prism. Whatdifference do you see? How do youaccount for it?

In Experiment B-3, you will compare in amore quantitative manner the spectra pro-duced by a grating and a prism.

For many materials we are interested in, suchas filters, the fraction of the light which isreflected is small. If one neglects the lightwhich is reflected from a substance, then theincoming light is either absorbed or trans-mitted. The fraction transmitted is oftenexpressed in terms of percent transmission.Likewise, the fraction absorbed can be expres-sed in terms of percent absorption. The sumof these two must be 100%. See Figure 14.

INCOMING

LIGHT100%

z0enen:Eenz

a. exactly the sameb. quit~ similar but differentc. quite different

_ 3. Which of the following colors wasabsorbed most by the didymiumfilter?

a. redb. orangec. yellc,wd. greene. blue

_ 4. What color was absorbed most byyour yellow filter?

a. redb. orangec. yellowd. greene. blue

__ 5. Which 0' the following colors wasabsorbed most by the blue filter,number ~56?

a. redb. yellowc. greend. bluee. viole1

__ 6. From this information, what colordo you guess can be removed fromwhite light to make blue light?

a. redb. yellowc. greend. bluee. violet

__ 7. From the facts above, can you guesswhat color would be transmittedbest by a yellow filter?

b. orangec. yellowd. greene. blue

_ 8. Which color would be transmittedmost by a green filter?

a. redb. orangec. yellowd. greene. blue

__ 9. Compared to the grating, the prismspreads the colors out more. True orFalse?

10. Compared to the grating spectrum,the prism spectrum is brighter. Trueor False?

II. The didymium spectrum transmittedby the grating is the same as thattransmitted by the prism. True orFalse?

12. A major difference between the grat-ing and the prism is

a. noneb. the prism absorbs more lightc. the grating spreads out the col-

ors mored. the prism focuses the light bet-

tere. the grating absorbs light of some

wavelengths

13. It is possible to find two filters thatlook alike and that would result inthe same graph in this experiment.True or False?

Pretend you forgot to label your eight graphs.Can you figure out the color of each filter bylooking at its graph? Try it.

Can you now predict the effect of combiningtwo filters? For example, suppose each trans-mits 60% of the light of a particular color.The second filter "sees" only 60% of theincoming light. Therefore only 60% of this60% gets through the second filter. Thus, 36%is transmitted by the two filters together.

I IINCOMING 60%LIGHT100%

In general, the fractions transmitted by eachfilter are multiplied together to obtain the netfraction transmitted. In this case the calcula-tion was

The fraction of light transmitted is thereforerelated to the amount of absorbing material.This relation is discussed further in Section C.It is the basis for the use of spectrophotom-eters in quantitative analysis-determininghow much of a substance is present in a givensample.

If you can, compare your spectra with afriend's. You will probably find that yougenerally agree. Your spectra have roughly thesame ups and downs as his. However, if youcompare them carefully, you probably dis-agree with the exact position of some of thedots.

These disagreements are largely the fault ofthe light-detecting instrument-you. Theywould be expected even from the mostcareful experimenters. We need instrumentsthat can measure light intensity with moreaccuracy than your eye.

You also need a more precise way of specify-ing colors. Red, orange, yellow, etc., are onlygeneral terms. Exactly where in the spectrumone color ends and the next begins can onlybe estimated. And the estimate will vary fromperson to person.

In the following pages we will describe colormore precisely by introducing the term wave-length as a specification for color. In SectionB we will show how color is related to ourunderstanding of the wave nature of light. Wewill also extend the notion of wavelength toregions of the spectrum that our eye cannotsee.

In Sections Band C of this module you willuse these ideas to build a more accuratespectrophotometer. The spectrophotometerthat you will build will be accurate enoughfor many useful laboratory measurements.

As you have seen, white light is a mixture ofmany colors. A prism or a diffraction gratingis able to spread this mixture into its compo-nent colors to form what is called a spectrum.

Figure 17. The emission spectrum of a "white light"lamp.

Figure 18. The emission spectrum of a "black light"lamp.

forming the different spectra produced bytwo different sources of light. Emission spec-tra show the intensity of the light a sourceemits for each color. Shown in Figure 19 isthe relative sensitivity of the human eye; thisshows that the eye is most sensitive to yellowlight.

Note that the emission spectra extend beyondthe red and violet ends of the spectrum. Butthe human-eye sensitivity does not. Your eyeis not sensitive to light outside of the narrowrange from what we call red to what we callviolet.

The colors we see are visible only becausecertain molecules in the retinas of our eyesare sensitive to light in this range. When lightstrikes these molecules, they relay the infor-mation to our brains and we say the light isvisible. If we had different sensitive moleculesin our retinas, we might call light of someother range visible.

Visible light is only a small part of a vastrange of radiation called electromagnetic radi-ation. This radiation includes radio waves,microwaves, x-rays, and gamma rays (seeFigure 20). The radiation just below the redend of the spectrum is called infrared, whichmeans "below the red." Similarly ultravioletis the name for radiation "beyond the violet."

All electromagnetic radiation has essentiallythe same properties as light. For example,every type of electromagnetic radiation trav-els through a vacuum at the same speed,300,000,000 meters per second (m/s). Buteach type interacts with matter differently,and it is these different interactions thattechnology exploits for various purposes.

Spectrophotometers are used for measure-ments in three regions of the electromagneticspectrum: the infrared, the visible, and the

SPECTROPHOTOMETERRANGE

VIOLET

ULTRAVIOLET

Figure 20. The electromagnetic spectrum, showing the range in which spectrophotometer~-f'e used for analysisand the region of visible radiation. The numbers given are the wavelengths in nanometers (10m).

ultraviolet. Measurements in each of theseregions present particular design problems, sothat a single instrument rarely can cover morethan one region without modifications.

The spectrophotometer that you are using isdesigned for the visible region. However, withsuitable light sources and detectors, it can beused in the regions which are "close" to thevisible region on either end. These regions arecalled the near infrared and near ultraviolet.

Wavelength Specification forRadiation

Since the eye is an imperfect instrument, weneed a better method of specifying electro-magnetic radiation than color. The term usedis wavelength. In the visible light region, thewavelength of a given radiation is measured innanometers (nan'-o-me-ter), abbreviated nm.

-9(1 nm is equal to 10m.) The term wave-length derives from the wavelike character-

istics of light. TIlis is discussed in some detailin Section B, but for the moment simplythink of wavelengths as numbers which spec-ify radiation in the electromagnetic spectrum.

Light that we can see has wavelengths be-tween 400 nm and 700 nm. Table I shows theapproximate wavelength of each of the visiblecolors.

ApproximateWavelength

(nm)

Ultraviolet/violet edgeViolet center

Blue/violet edgeBlue center

Green/blue edgl~Green center

Yellow/green edgeYellow center

Orange/yellow edgeOrange center

Red/orange edgeRed center

Red/infrared edge

400410425470491520575580585616647690730

It is difficult to say exactly what wavelengtheach color is because the colors in thespectrum merge slowly from one to another.The table shows the accepted ranges of thecolors of the spectrum, but it should not betaken too seriously. First, as you have seen,there is no sharp boundary between colors.Secondly, within each color range there are anumber of hues. The information in Table Icomes from the R'Indbook of Chemistry andPhysics (Chemical Rubber Co.), and it is fairlyarbitrary. Other handbooks give slightly dif-ferent values.

It is also interesting to note how uneven thecolor widths are. In particular, note hownarrow yellow is compared to green or red.Did you notice this in your laboratory obser-vations?

Wavelengths are also assigned to the electro-magnetic radiation that we cannot see. Radia-tion with wavelengths greater than the largestred wavelength is called infrared (IR). Radia-tion with wavelengths less than the smallestviolet wavelength is called ultraviolet (UV).The chart below gives the approximate wave-lengths for the IR and UV parts of theelectromagnetic spectrum.

The wavelengths for each of these ranges thatare close to the visible are often referred to asnear. For example, wavelengths of about730-5,000 nm are near infrared. Those wave-lengths farther away are called far.

WavelengthRadiation Range (nm)

The energy carried by electromagnetic radia-tion depends on wavelength. The greater thewavelength, the less the energy. Thus, infraredradiation with large wavelengths has lowenergy. It is called heat radiation since it isemitted by any hot or even warm object.Ultraviolet radiation, on the other hand, hassmall wavelengths which means high energy.Ultraviolet is responsible for suntan and sun-burn and it can cause eye damage if looked atdirectly. Therefore be extremely careful withultraviolet light sources.

Light shining on a substance is either re-flected, absorbed, or transmitted by it. Aspectrophotometer is used to measure theamount of each color of light which istransmitted (or absorbed). Since each sub-stance has a unique absorption pattern, spec-trophotometer analysis can identify whatsubstances are present in a sample.

The five major parts of all spectrophotom-eters are: a light source which produces lightof many colors, and a monochromator whichselects out one of the colors to pass to thesample to be analyzed. The amount of lighttransmitted strikes a detector whose output isamplified so that it can be registered on adisplay device.

The object of Experiment A-2 was to build asimple spectrophotometer using a diffractiongrating to separate the light into a spectrum,and using your eyes as the detector. With thissetup you could estimate the absorptionpatterns of various colored filters. From thedata obtained you drew transmission spectra.You also repeated one of your measurementswith a prism in place of the grating.

Transmission and absorption spectra for asample are "mirror images" of each other.The light absorbed plus the light transmittedat each color must add to 100% of theincident light. Graphs of such spectra are thebasis of qualitative analysis, determining whatmaterials are present in a sample.

When the thickness of the sample is increased,the amount of light transmitted decreases.This is the basis for quantitative analysis,determining how much of each material ispresent.

Visible light is only a very small part ofthe electromagnetic spectrum, which includesradio waves, microwaves, x-rays, gamma rays,and infrared and ultraviolet radiation. Spec-

trophotometers are used for analysis in thevisible, the near infrared, and the near ultra-violet portions of this spectrum.

A more accurate designation of radiation thancolor is wavelength. It is commonly expressedin nanometers (nm). The range of visible lightis from about 385-730 nm, but it is impos-sible to assign exact numbers to visible colorssince individuals perceive colors differently.

1. Which colors are left in light by thefollowing filters?

What is the color of the filter whichwould give each of the following trans-mission spectra?

3. Which of the following transmissionspectra is that of a filter which stopsinfrared radiation?

I400 700WAVEL.ENGTH (nm)

400WAVELENGTH (nm)

4. Which of the colors in the spectrumcovers the largest range of wavelengths?Which covers the smallest wavelengthrange?

5. What are the five basic components inevery spectrophotometer?

6. Describe each of the spectrophotometercomponents used in the first experiment.

7. Draw a diagram of the electromagneticspectrum showing the wavelengths forthe infrared, visible, and ultravioletranges.

The Dispersion of Light

The word disperse means "break up and causeto go in different directions." In the news, forexample, you sometimes hear of police dis-persing a crowd. Applied to light the word hasessentially the same meaning. White light iscomposed of all the visible colors as well asultraviolet and infrared radiation. In spectro-photometry we want to "break up" the whitelight (or separate it) by causing its componentcolors "to go in different directions." Thenwe can block out all the colors except the onewe want to pass through the sample beinganalyzed.

The problem then is how to break light up.When light strikes an object it is eitherreflected, transmitt~:d, or absorbed. Thereforewe must reflect, transmit, or absorb light insuch a way that the colors separate.

The simplest solution has probably alreadyoccured to you. Why not use light absorp-tion? That is, one could use a lot of filters,like those in the pack provided, each of whichabsorbs all but one color. Then you simplydrop the filters in one at a time and measurethe amount of light of each color that getsthrough the sample: to obtain transmissionspectra. While this solution is used in someinstances, the problem is that filters whichtransmit only a single color, or a narrow bandof colors, are expensive. And, to provide afilter for every wavelength would be quiteexpensive.

The other two solutions are by reflection andtransmission. You have already seen that areflection type diffraction grating can disperse

the colors. You have also seen that a prism,which transmits light, also produces dis-persion. In this section of the module we willexplore these dispersive elements in somedetail. You will see how the light reflectionand transmission properties of materialsdepend on wavelength, and you will see howgratings and prisms have been cleverly de-signed to use these properties to disperselight.

Another type of dispersive element, the trans-mission type diffraction grating, is also pro-vided with your laboratory apparatus. Itscharacteristics are essentially the same asthose of the reflection type grating, andtherefore they are not discussed in detail.However, you may want to observe its be-havior.

REFLECTIONGRATING

Figure 22. The two dispersive elements you will usein your experiment.

A prism is a wedge of transparent materialwhich "bends" light beams. For complicatedreasons, violet light is more sharply bent byglass than is red light.

A prism works best only for certain colors,leaving the rest still rather closely bunchedtogether. For example, in Figure 24, violet iswidely spread out while orange and red arequite compressed.

To surmount this problem, prisms for work-ing in different parts of the spectrum aremade of different materials. For example,prisms made of common table salt are usedfor the infrared part of the spectrum. Figure

2S shows the useful ranges of various prismmaterials. Note that the wavelength scale islogarithmic, so that a wide range of wave-lengths can be conveniently covered.

Common materialsfor the visible andthe near infrared.

A reflection grating is a front-surface mirrorwith thousands of fine, parallel scratches onit. A grating reflects. light in several ways:

Zeroth (Oth) order: Simple white lightreflection, like- a mirror, with no disper-sion. See Figure 26.

First (lst) order: On both sides of thezeroth order a bright spectrum appears.The spectrum on one side can be mademuch brighter than that on the otherside by blazing.

Higher orders: Broader but weaker addi-tional spectra appear. Sometimes thesehigher order spectra overlap.

1stORDER

1stORDER

.... , ............. ............ . . .\;:;:;:;:1(:::;:::;

The point of this investigation is to observeexperimentally what a dispersive element doesand in what ways this is done differently by aprism and by a grating. The spirit of this lab isexploratory: you should observe what hap-pens when you change things around. Thisprocess will raise questions which will beanswered later in this module.

The setup we will use first is illustrated inFigure 29. It is quite similar to the previousexperimental arrangement. The only change isthat there is a longer light path from thedispersive element to the card where thespectrum is viewed. This is accomplished byreflecting the light once from a mirror. Theresult is that the spectrum is fainter but largerand easier to measure.

1. Place the paper template titled COM-PARING A PRISM AND A GRATINGsecurely on the base and centered on thecenter hole (see Figure 30).

2. Attach the light-source box and adjustthe entrance slit, as in Section A, to getthe maximum amount of light to passthrough.

3. Place the optical components in theindicated positions. You may have tomove your components somewhataround these positions to get the maxi-mum amount of light squarely througheach element.

3" X 5"Ct~RDSCREEN

Figure 29. System for obtaining the diffraction grating spectrum. The light should he centered on each com-ponent both v~rtically and horizontally to maximize the intensity.

COMPARING A PRISMAND A GRATING

ACHROMATIC LENSf=87mm

WHITE CARD(FOR GRATING) ""'+

~~

DIFFRACTIONGRATING --.

4. Properly align the components. To focusthe lens turn the grating so that itprovides a white image of the slit (thezeroth order) on the white card. Thenmove the leni; back and forth to makethe width of this image as small aspossible. Bemre that the white lightstrikes each element (lens, mirror, etc.)at its center, both horizontally andvertically. This may require some tiltingof the elements on their bases.

When you think the system is properlyaligned, check the system by followingthe beam with a white card or by puttingsome incense smoke into the box.

1. Turn the grating (without changing itsposition) to get the spectrum on thecard.

a. How many orders can you see oneither sid~:of the white image?

b. Are the same orders on either sideidentical?

c. How does the first-order spectrumcompare to the second-order spec-trum on the same side with regardto width and intensity?

2. Look carefully at the first-order spec-trum. The colors are the pure spectralcolors. In particular, note the narrowpure yellow and the beautiful emeraldgreen.

The spectrum is as interesting for what colorsare missing as it is for the colors present.There is no brown, black, white, or any of thepastel colors like pink; all these are mixturesof spectral colors, and they are called non-spectral colors.

It is interesting that colors which appear thesame to the eye, as some spectral colors, can

be made by mixmg two or more spectralcolors. For instance green can be made bymixing spectral blue and yellow, but there isalso a pure spectral green. Other colors likebrown and purple can only be made bymixing spectral colors (red and blue forpurple). Mixing spectral colors to get newcolors is called additive color mixing. How-ever, when one mixes paints it is the colorswhich are subtracted (absorbed) from thelight reflected by the paint which are impor-tant. This is called subtractive color mixing.The two kinds of color mixing yield ratherdifferent results. For example, a proper com-bination of the spectral colors can producewhite light, whereas an analogous combina-tion of paints produces black. Similarly, lightpassing through two color filters, one afterthe other, also undergoes a subtractiveprocess.

3. Explore the effects of removing the slitand the lens, separately. Also try mis-alignment of each of the elements, side-ways, and back and forth. Try this withincense smoke in the box so that youcan see the effects more clearly. Youshould be able to determine the reasonsfor having these elements where theyare.

4. Return the elements to their properpositions and refocus the system. Usethe first-order spectrum for which red isat the right side of the card. Get thebrightest possible spectrum centered onthe white card.

5. Adjust the white card so that it is atright angles to the incident light.

1. Make a clear, neat table of colors andcolor boundaries as shown in the sample.Use the designated space on the datapage at the end of the module for yourdata table.

C0/0"bll. tA"~" (fill.)G".tl~ 1>"'''111

'R.el cc4,e. 0 0c.".,.,~ l2 '"

0•.4M5' e.J~&. ~:ll VceMt.~ .~9

" •. /Ill!> .Hdtf.". ••••••••••••••• -----2. Place a millimeter scale so that its zero is

at the red edge of the spectrum (asshown in Figure 31).

3. Record the location on the ruler of thecenters of each of the following col-ors: red, orange, ydlow, green, blue,and violet. Even though it is difficult todo, try to estimate where the boundariesare between colors and record these also.Also record the location of the violetend of the spectrum" Your distances canonly be estimates, using your eye. Youwill be surprised to see, later in themodule, how well you have done.

This experiment is essentially the same as theprevious one, except that the dispersive ele-ment to be used is a prism. Follow theprocedure below to get your data.

1. Replace the grating with a prism, asshown in Figures 32 and 33.

2. Align the system, following the properalignment procedure. NOTE: Do notmove the lens or the slit. Adjust only themirror at 3 and the card at 2.

3. Rotate the prism (without changing itsposition). What happens to the spec-trum? As you turn the prism in onedirection, you will see that the spectrummoves to the left, stops, then movesback. Adjust the prism until the red partof the spectrum reaches its maximumleft position. llhis position is called the

COMPARING A PRISMAND A GRATING

®~WHITEIFORPRtU

Figure 33. The layout of components. The distancefrom the dispersive element to the card is identical tothe previous experiment, so that the two spectra canbe compared exactly.

angle of minimum deviation and givesthe least mixing of colors.

4. Put incense smoke in the box andobserve the light paths. Note that, at theangle of minimum deviation, the anglethe light makes with the side of theprism it enters is the same as the angle itmakes with the side from which it exits.

5. Adjust the white card so that it is atright angles to the light striking it.

1. Placea millimeter scale so that its zero isat the red edge of the prism spectrum, asyou did for the grating spectrum.

2. Measure the distances to the color cen-ters and boundaries as you did before,and record them in your table.

You now have some data on the dispersiveproperties of a prism and of a diffractiongrating. But there are additional character-istics that must be considered in comparingthese two dispersive elements.

In this experiment you will make someadditional observations of the two spectra.These observations, like the previous ones,will be based on your best judgment of whatyou see. Follow the guide below to makeyour comparisons of the prism and grating.Later we will explain the principles behindthese observations.

Some of the characteristics that you cancompare for the two elements are:

Brightness: Which element produces thebrighter spectrum? That is, which spectrumhas the higher intensity of light in each color?Why is it brighter? (Hint: How many spectraare produced by each element?)

Purity: Which of the elements producescolors which may be a slight mixture? Why doyou think this happens?

Dispersion: Which element spreads out thecolors more?

Uniformity: Which element spreads thecolors out more uniformly, so that each bandof color is more nearly the same width?

I. Compare the spectra obtained for theprism and for the grating. You may wantto set one system up on your spectro-photometer and the other on your neigh-bor's. Or you might see if you canproduce both at the same time on onesetup. If you do the latter, be sure thatthe total distance along the light pathfrom dispersive element to white card isidentical for each system.

To help in some of your comparisons,put an exit slit in place of the white cardand put the white card behind the slit.Then scan the spectrum across the slit byrotating the flat mirror. Observe thebeam of light that gets. through the slit.How pure is each color for the prism?For the grating? What influence do youthink the width of the slit makes oncolor purity? On intemity?

2. Fill in the table on th~ data page in theback of the module with your estimatesof the brightness, purity, dispersion, anduniformity of the two elements.

As a final experiment in this section, you willassemble a good quality monochromatorsystem using the diffraction grating. You willthen add the light detector, amplifier, anddisplay parts to make a complete spectropho-tometer. This instrument will be comparablein quality to many commercial units.

Once your instrument has been constructed,you will use it to observe that there is indeedradiation "below the red" and "beyond theviolet." In Section C you will use it to makean accurate tran:~mission spectrum of thedidymium filter.

The purpose of the monochromator is todisperse the white light from the source intoits component colors in such a way that theoperator can select anyone of them to passthrough the sample:.

A REFLECl'IONGRATING

SPECTROPHOfOMETER

\\

~ \ Ql: I~\ i!llo 1l I"t \ ,; I•• \ I

\ I

" I\ I

\ I\ I

\ I

\ I\ I

\ I

~DIFFRACTIONGRATING

1. Fasten the template for the REFLEC-TION GRATING SPECTROPHOTOM-ETER to the monochromator table.Your instructor may prefer you to set upa different monochromator system. Ifso, he will provide you with the propertemplate. While this discussion describesthe reflection grating monochromator,most of the steps apply also to othermonochromator systems.

2. Place the components in their properpositions on the monochromator table.The mirrors (flat and spherical) are usedto concentrate the pure colors on theexit slit. Have the white side of the exitslit facing inward. Each component canbe rotated to direct the light to the nextcomponent and tilted to be sure the lighttravels parallel to the base.

SPHERICAL MIRRORf=300mm

Figure 34. The layout of components for the reflection grating spectrophotometer. An illustration of thissystem is shown on the bottom of page 6.

to achieve the proper mirror alignment isto replace the diffraction grating with aflat mirror. Then the goal is to form animage of the entrance slit on the exit slit.When you have accomplished this andrepositioned the grating, the opticsshould be in good alignment.

For aligning the components use a whitecard to trace the light path. Be sure thelight beam is centered, both horizontallyand vertically, at each step.

First, place the card in front of thespherical mirror M2 (centered on thelight-path line), and rotate and tilt M1until the light spot is centered on thecard.

Next, place the card in front of M3 andadjust spherical mirror M2• Continue thisprocess from component to componentuntil an image of the entrance slitappears on the exit slit. Be sure eachcomponent remains near its designatedspot.

Figure 35. Aligning the monochromator. Slit Slshould have its black side toward the source. Thewhite side of slit S2 should serve as a screen forviewingthe spectrum.

4. Make a fine adjustment of the system bymoving the exit slit back and forth untilthe smallest (and brightest) image

appears on the exit slit. If the system isperfectly aligned, the image of the en-trance slit should exactly match the sizeand shape of the exit slit, and all thelight will pass through.

5. Replace the mirror M" with the diffrac-tion grating. Rotate it so that the zerothorder (white light) ::alls on M4 andproduces an image of the entrance slit onthe exit slit. If necessary, tilt the gratinguntil the image is centered on the exitslit. Again, make a fine adjustment toproduce the best image by moving S2back and forth.

6. Rotate the grating counter-clockwiseuntil the first-order spectrum falls on theexit slit. As you scan the colors, be surethat each fully illuminates the exit slit.

SAMPLEHOLDERANDSHUTTER

PHOTO-DETECTOR

LMONOC~ROMATOR DIAL

smoke into the chamber. How well areyour components aligned?

8. Measure the ~pectrum of this gratingsystem as yOlI did in Experiment B-2.

Now that you have the optical components inthe spectrophotom~ter, the next step is toadd the photometer. Your strategy here is toget the maximum Fraction of the light thatcomes through the exit slit to fall on thephotodetector.

1. Inspect the photometer box. Observe thearrangement of the sample holder/shutter and photodetector. If yourinstructor permits, open the box toobserve the parts more clearly.

2. Attach the ph'Jtodetector box securelyto the monochromator table at the holethe light comes through.

3. Remove the sample holder/shutter sothat you can see the photodetector.Does the light~oming from the exit slitfall squarely on the detector? If not,then you must rotate mirrors M4 and Mstogether, chang:.ngthe angle at which thebeam hits the exit slit, until the detectoris uniformly lighted.

4. Replace the sample holder. Rotate it andnote how it acts as a shutter. With theshutter open, the detector inside thehousing should be brightly lighted.

It is important that the electronics operateproperly and that th.e system has sufficientwavelength range fDr your measurements.Your objective here is to test the amplifierand meter and to check the range of wave-

POWER@ @lQ\

RANGEaGAIN

lengths over which the system will detectlight.

1. Plug the meter into the terminals of thedetector box marked METER, beingcareful not to bump the mono-chromator.

2. Close the shutter, turn on the amplifier,put the RANGE SWITCH on 1000, andturn the GAIN all the way up (clock-wise). Put the meter on the O.l-V scale.If the meter does not read zero, see yourinstructor.

3. Open the shutter. The needle shouldfully deflect to 100%. If it goes in thewrong direction, reverse the connectionsto the meter.

4. Check the range of your system. Use thedigital dial on the front panel to rotatethe turntable on which the grating rests.Scan the spectrum completely across theexit slit. The meter should stay fully de-flected over the whole visible range. If itdoesn't, have your instructor check thesystem out with you.

Does your detector register radiationbeyond both ends of the visible? Inter-rupt the light coming from the source toverify that this radiation is coming fromthe source.

The range of your instrument is deter-mined by the range of wavelengths overwhich your detection system will register100% of full scale.

Your observations of the effects of the prismand diffraction grating on light should haveraised some questions: What are the princi-ples behind this behavior? How does it relateto the properties of light? What factors affectthe ability of prisms and gratings to disperselight?

Before these questions can be answered, youmust learn a bit more about light and itscharacteristics. One crucial point is that lightacts in many ways like a "wave. " In thefollowing pages we discuss the wave proper-ties of light and see how prisms and gratings

OCEANWAVES

WAVES ONA ROPE

WAVES ONA POND

SOUNDWAVES

use them to disperse light into its componentcolors.

Ocean waves, ripples on a pond, a wave on arope, sound, and light have one thing incommon-they are all waves.

By a "wave" we mean a moving disturbancethat produces an oscillation or vibration ofsome quantity as it passes. In ocean waves andripples it is the height of the water whichoscillates up and down; for waves on a rope,the position of the rope oscillates; for soundwaves, the air pressure oscillates.

For light, the "electric and magnetic fields"oscillate. It is hard to vimalize electric andmagnetic fields, but if you were an electron,you would know all about them. Electricfields exert a force on e:.ectrons (and otherelectrically charged matter) that is just as realas the force an ocean wave exerts on afloating object. Whenever a light wave passesnear an electron, it drives it up and down at afantastic rate.

Since we cannot see the oscillating electricand magnetic fields of a light wave, nor canwe directly see its effects on an electron, howcan we say that light is a wave? The reason isthat light behaves in many ways just likewaves that we can see.

The illustration on the next page showssimilar properties of light and of ripples inwater. The light wave illustrations can bereproduced using your spectrophotometerapparatus. The water wave illustrations can bereproduced by a device ~alled a ripple tank.This device is specifically designed to demon-strate the properties of waves. In the photo-graphs the waves move in the directions of thearrows.

It is because of these similar properties thatwe say light is a wave.

COMPARING THE PROPERTIES OFAND

Reflection is the bouncing of wavesoff barriers. At the left, the wavescannot penetrate the block in thewater. As a result, they bounce offin another direction. At the right asilvered mirror forms a similar bar-rier for the light.

Refraction is the bending of waveswhen they change speed. In eachillustration there are two regions inwhich the wave speeds are differ-ent. At the left the ripples travelfrom deep water to shallow water,where the speed is reduced. At theright, light enters water where itsspeed is about 7S percent of itsspeed in air.

In terference occurs when twowaves interact. At left, water wavesradiate from two arms bobbing atthe same frequency. This gives re-gions of no water motion (destruc-tive interference) separating regionswhere the waves are twice as high(constructive interference). Similar-ly two light sources of the samewavelength give alternating lightand dark patterns.

Diffraction is the bending of wavesproduced by obstructions. Here itis produced by regularly placed ob-structions. At the left the obstruc-tions are pegs in the water. Thesecause incoming waves to go off inparticular directions. At the right,the pegs are replaced by thousandsof regular scratches on a transmis-sion grating. Similar beams result.

Figure 39.

IDIFFRACTIONGRATING

Three important quantities come up wheneverwe talk about a periodic wave: its wave-length, speed, and frequency.

Wavelength: A periodic wave is a sequence ofregular, repeating cycles. The distance be-tween identical points of two neighboringcycles is the wavelength. The Greek letter i\(lambda) is usually used for wavelength.

Speed: As time passes, the whole sequencemoves. The distance moved divided by thetime required is the wave speed. The symbol cis often used for wave speed. For light in avacuum,

Frequency: If you stand still as a wave movespast you and count the number of completecycles that pass, the number per second is thefrequency. It is often given the symbol f.Frequency is measured in cycles per second.This unit used to be abbreviated as cps,

-1cycles, or s . Now the units are called Hertz(Hz), which simply means cycles per second.

Since light exhibits wavelike properties, it isnatural to measure it by its wavelength. Eachpure color corresponds to an electromagneticwave of a certain wavelength. Thus, thespectral colors can be classified and specifiedby their wavelengths.

The wavelength numbers we gave in Section Afor. the electromagnetic spectrum representthe wavelengths of the waves of the varioustypes of radiation. For visible light this isextremely small, about 500 nm, or about1I50,000 of an inch.

The speed of light waves, however, is extreme-ly high, about 3 X 108 mis, or 186,000 milesper second (mils). That is 7.5 times around

Figure 40. The distance between two adjacent crestsis called wavelength. For light, each color is a differ-ent wavelength.

WAVESPEED C'-"I \I \, \, \,, \ ,

, \ I

" \\,/INITIAL \1" SECOND

Figure 41. The distance a Wllvecrest travels in onesecond is its speed.

WAVE FREQUENCY fI

Figure 42. The number of Clests that pass a point inone second is the frequency. For light, frequency(like wavelength) is different for different colors.

the earth in one sfcond. This speed is thespeed of light in a vacuum. It is slightly lessthan this in air, ani much less in glass andmost other transparent materials.

In a vacuum, light (,f all wavelengths has thesame speed. But in transparent materials thespeed is different f,Jr different wavelengths.The variation of speed with wavelength ac-counts for the dispenion by a prism.

Frequency can also be used to specify lightcolors. Wavelength h much easier to measure,so it is more often used. The frequency oflight is around five hundred million million

14cycles per second (5 X 10 Hz). At present,this is impossible to measure directly.

Wavelength, frequen::y, and velocity are notindependent of eacl other. There is a basicwave relationship such that, if two are known,the third can be computed.

To get this relationship we need a new term,the period T. The period is the time inseconds for a compkte cycle to pass a givenpoint. Period and fn~quency are very simplyrelated; they are reciprocals. That is, if thefrequency is x cycles per second the period isIlx seconds per cycle, Put mathematically,

IT= -f

For example, if the frequency is 10Hz, thenthe period for each cycle is I I I0 s.

There is a simple relation between period, T,wavelength, X, and speed, c. Recall that forany uniform motion:

distance coveredSpeed = -------

time required

A wave travels the distance of one completecycle (the wavelength, X) in the time for this

cycle (the period, T). Since it is going at thespeed c, then the basic speed formula gives:

Xc =-T

Now replace the period T with its substituteI If to get the basic wave relationship:

This equation indicates that large frequenciescorrespond to small wavelengths.

According to the wave relationship eitherwavelength or frequency can be used tospecify light. For historic reasons, spectro-photometers generally use wavelength.

Unfortunately, there are about a dozen wave-length scales in common use. For our workhere, we will use the international standard(SI) unit. The SI unit of length is the meterand, since wavelength is a length, it should bemeasured in meters. But, since it is so small, itis generally measured in nanometers. Nano isthe prefix for 10-9• A nanometer (nm) is atiny measure of distance equal to 10-9 m, or10-7 cm.

m = meter

cm = centimeter = 10-2 metermm = millimeter = 10-3 meterfl = micron = 10-6 meter

nm = nanometer = 10-9 metermfl = millimicron = 10-9 meter

A = Angstrom = 10-1 0 meter

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You will almost certainly encounter otherwavelength units. The most common otherunit used is the Angstrom (A), which is

-10one-tenth of a nanometer, or 10m. Youwill also run across the unit millimicron (mil)which is identical to a nmometer. It meansone-thousandth (milli) of a micron, where amicron (Il) is 10-6 m.*

To convert wavelengths in one unit of lengthto wavelengths in other units, use the rules inthe lists below. Since all of the wavelengthscales are in decimal units, the conversionsare relatively simple.

To convert a wavelength in other units to a To convert from a wavelength in nanometerswavelength in nanometers: to a wavelength in other units:

Multiply By To Get Multiply By To Get

meters 109 nanometers nanometers 10-9 meterscentimeters 107 nanometers nanometers 10-7 centimetersmicrons 103 nanometers nanometers 10-3 micronsmillimicrons 1 nanometers nanometers 1 millimicronsAngstroms .1 nanometers nanometers 10 Angstroms

I n applications other than spectropho-tometry, you may tind light specified by itsfrequency. The frequency corresponding to aparticular wavelengtl can be calculated usingthe wave relationship. For example, violetlight is 400 nm. Its frequency is:

3 >< 108 mls= 400 X 10-9m

Figure 44 gives thl~ wavelengths and fre-quencies for some types of electromagneticradiation.

tween the common wavelength units andfrequency can be made quickly without calcu-lations. The only drawback is that it has lessthan two-digit accuracy.

Note that wavelength increases from left toright while frequency increases from right toleft. Do you know why? Also note that thescales are not linear; equal distances along thechart do not represent equal differences inwavelength.

To use the chart, locate the known quantityon one scale, then draw an imaginary verticalline at that location to the scale of the desiredequivalent unit. A clear plastic ruler would bea great help in this.

For example, locate 7.5 X 10· 4 Hz. Tracing avertical line upward shows that this is equiva-lent to violet light of 400 nm, as we cal-culated .

• lIJzOC!)lIJ.JZlIJ .J c( 0It: lIJ It: lIJ IC!) >- 0 It:

II I:6 71

ANALynNG YOUR CURVES BYWAVELENGmSThe data from your experiments can now beanalyzed in terms of wavelengths.The centralquestion is, what is the relation between thelocation in the spectrum of a color and itswavelength, for both the prism and thegrating? Follow the procedure below to findthis relation.

The first step in analyzing your data is tograph it. You will graph the observed loca-tions of each color on one axis and thewavelength of the color on the other. Hope-fully, the resulting curves will reveal somesimple relationship between location andcolor. An example is shown in Figure 45. Thedata are similar to yours, but the dispersiveelements are different.

1. Make a graph like that shown in Figure45. Layout wavelengths at the bottomon an equally spaced (linear) scale. Atthe top, layout the corresponding colorboundaries and centers, as given inFigure 44 or in Table Ion page 19.

2. Graph the colors against the position atwhich each color appeared, as measuredfrom the red/infrared boundary. Putboth sets of data on the same graph, butbe sure to label which is which.

3. Draw the curves for each set of data. Astraight edge or a draftsman's Frenchcurve may help you to obtain smoothcurves. For the best curve, the numberof points that are above the line (andtheir distances) should roughly equal thenumber that are below.

4. Label the axes and place a title on thegraph to remind both yourself andothers what the graph shows.

Figure 45. Typical data foc two dispersive elementsdifferent from those you USt~d.

To analyze this graph it is necessary to moreaccurately define the word dispersion. Disper-sion refers to the amount that the colors arespread out. The more the colors are spreadout, the greater the dispersion.

Two facts about disper:;ionthat relate to yourgraphs are:

1. The dispersion is equal to the slope ofyour graph. For a straight line graph, theslope is the v€:rtical distance betweentwo points on the line divided by thehorizontal distance between the sametwo points. For your graph this will be aratio of distance over wavelength. Asteep slope means that slightly differentwavelengths are found at quite differentpositions; this is what we mean by"spread out." A shallow slope meansthat different colors are found at nearlythe same positions, not spread out. Ahorizontal line, with zero slope, means

Figure 46. The slope of a straight line is the verticaldistance between two points divided by the hori-zontal distance. Thus, slope = dv/dh. Line 2 has agreater slope than line 1.

IJJ

IdYII1- _

dhFigure 47. The slope of a curved line at a point isthe same as the slope:>f a straight line which istangent to the curve at that point.

that the colors are all at the sameposition, and there is no dispersion at all.

2. The dispersion can depend on wave-length. If one of your graphs is a curvedline, then its slope is changing. There-fore, the dispersion is changing. You canfind the slope of a given point of a curveby drawing a straight line tangent to(touching at only one point) the curve,then the measured slope of the tangentline is the slope of the curve at thatpoint. See Figure 47.

Since the slope of your curves can be deter-mined you have a quantitative measure ofdispersion. That is, the slope, and thus thedispersion, can be calculated in millimetersper nanometer. For example in Figure 45, theupper curve is a straight line. In the wave-length interval from 380 nm to 460 nm, themeasured distance interval is from 85 mm to66 mm. Therefore, the slope (and dispersion)is:

D = 85- 66mm380- 460 nm

= .24 mmnm

Note that both units in this ratio are lengths.Therefore you must be careful in your inter-pretation of D. It means the number ofmillimeters on the screen for each nanometerof light wavelength.

1. Find the dispersion of both the gratingsystem and the prism system at wave-lengths of 400 nm, 550 nm, and 700 nm.(First draw the tangent to the curve atthat wavelength and then measure theslope of each tangent line.)

The first question to ask about prisms is whythe path of light bends or refracts when itenters glass. The answer lies in the fact thatthe speed of light is less in glass than in air.You can see this same effect in the followingimaginary experiment. Imagine a line ofmarchers which has been given two orders:

1. March at full speed on the pavement buthalf speed on the grass

2. Always keep your shoulder touchingthat of the man on each side

Look at what happens when the line ap-proaches the edge of the grass at an angle(Figure 48). In the second row, the first twoplayers on the grass lag behind because theyare marching more slowly. To obey order #2,they and the other soldiers must turn andmarch at a slightly different angle.

This illustration is only an analogy, but itdoes show what happens to light. For essen-tially the same reason, the light path bendswhen it enters at an angle* into a region inwhich it goes more slowly. This effect iscalled refraction. The amount of bendingwhich occurs depends on the speed of light inthe material; the slower the speed, the morepronounced the bending.

Figure 48. An analogy. Substitute light waves for therows of marchers, and glass for grass, and you see

42 why light paths bend.

The quantity which expresses the speed oflight in a particular material is the index ofrefraction, n. This is the ratio of the speed oflight in a vacuum, c, to the speed of light inthe material, v.

cn = --

v

Values of n for yellow light in commonmaterials are given in Table III.

RefractiveIndex

(at 589 nm)

Empty SpaceAirIceWaterEthyl AlcoholPlexiglasCrown Glass

1.00001.00281.311.331.361.491.517

When light passes from a material whoseindex of refraction is n1 (air for example),into one for which it is n2 (glass), the amountof bending is given by Srzell's Law:

NORMAL~"81

*In refraction the angles ilfe usually measured fromthe normal, a line which is perpendicular to thesurface, to the light path.

For air, the index of refraction is very close toone, so that n1 = 1 can usually be used. Then,for light passing from air into a materialwhose index of refraction is n2, Snell's Lawbecomes:

This expression can be used to determine theindex of refraction of a material. One simplymeasures 01 and O2 :'or a light beam.

All of this does not explain the way a prismseparates colors, however. The missing key isthe following: In a given material, the speedof light is different for different wavelengths.Therefore the index of refraction depends onthe wavelength-the greater the value of n2,the smaller the angle O2, A smaller O2 meansmore of a bend. (See Figure 49.)

This is the basis of dispersion. Since theamount the light path bends depends on itsspeed, and since different wavelengths travelat different speeds, different wavelengths arebent by different amounts. This results in thecolors dispersing to form a spectrum.

Figure 50 shows how the index of refractionchanges with wavel1mgth for various prism

-c:-x 1.7"-I0Z

"-I 1.6>~0

Gratings disperse light because of a peculiarproperty of waves. On page 35 you saw that,when a wave strikes a large flat surface, itreflects off in a different direction. However,when the size of the reflecting surface de-creases to less than a wavelength, the reflec-tion pattern changes. For example, Figure 52shows what happens when parallel waterwaves strike a post whose width is much lessthan the wavelength. The incoming waves passstraight on, except where they hit the post.These waves are reflected off the post ascircular waves, not simple parallel waves.

This property of waves is called diffraction. Itoccurs for all kinds of waves (water, light,sound, etc.) when they strike objects about thesize of a wavelength or less. Thus Figure 52also illustrates the diffraction pattern for a

Figure 52. Reflection of water waves from a post(or light from a very thin mirror).

When waves strike two such objects, two setsof circular waves are produced. These wavesinteract with each other, producing the vividlight and dark regions of Figure 53.

Look carefully at Figure 53. Assume that theblack rings in the drawing mark the crests orhigh points of the waves, and the spacesbetween mark the valleys or low points. Atthe lighter regions of H.e drawing the blackrings coming from the two mirrors lie on topof each other. Here the crest of a wave fromone mirror adds to a crest from the other.This is called constructive interference andresults in a stronger wave where the drawing islighter.

On the other hand, the darker regions in thedrawing occur when erests are added tovalleys. There the waves cancel (destructiveinterference) and there is no wave (or light).

Figure 53. Reflection from two posts or mirrors. Theincoming waves are omitted for clarity.

To summarize, light reflected from two mir-ror strips produces several strong beams oflight separated by regions of much less light.The beam reflected directly back is called thezeroth-order beam. On either side of thezeroth-order beam are symmetrically placedbeams called first order, second order, and soon.

Look closely at the upper first-order beam inFigure 53. Pick a point in the middle of thatbeam where two rings overlap. If you countcircles, you will see that this point is one ring,or one wavelength, farther from the lowermirror than it is from the upper one. This istrue for every point irl the first-order beam. Asimilar thing is true for the other beams,except that there is a difference of twowavelengths in the second-order beam, threewavelengths in the third-order, and so on.

This fact can be usd to relate the angles ofthe strong beams to the wavelength of theincoming light. If one looks at a point Pwhich is much farthe:r from the mirrors thantheir separation, a, then the paths from thetwo mirrors are very nearly parallel, as shownin Figure 54. The extra distance, A, travelledto P by the lower p~.th is one side of a righttriangle of angle e. Fer this triangle:

For higher-order be:ams, where m is thenumber of the order, similar reasoning showsthe angle to be given by:

mAsin e = --

£!

If one knows the mirror separation, a, one canuse this relation to determine the wavelengthof the light, A, by rreasuring the diffractionangle, e.

Diffraction gratings are essentially many par-allel strip mirrors placed at equal distancesfrom one another. The width of these mirrorsis approximately that of visible light, a fewhundered nanometers (see Problem #3). Thepattern created is similar to that created bytwo mirrors.

Thus, the grating produces beams which obeythe same equation as the beams produced bytwo strip mirrors. The key point, as applied togratings, is that the angle of each order, e,depends on A. Therefore within each orderdifferent wavelength light is diffracted atdifferent angles. This is the basis for disper-sion. The longer the wavelength the greaterthe diffraction angle. Thus, red is diffractedthrough a larger angle than is violet, produc-ing the spectrum you observed.

In this section you built a simple spectro-photometer and used it to study the charac-teristics of two dispersive elements, thediffraction grating and the prism. You foundthat each of them breaks up white light intoits component colors and arranges these inorder of their wavelengths. For the gratingthere is a simple straight-line relationshipbetween wavelength and the location of agiven color. The prism on the other handcompresses the red end of the spectrum.

You learned how to assignnumbers to colors.These numbers are based on the fact that lightacts like waves. Colors, as well as nonvisibleradiation, can be named by wavelength, A.The wavelengths of light are short, so specialunits of length, such as the nanometer and theAngstrom, are used. You learned the waverelationship A= elf, where c is the speed oflight in a vacuum, 3 X 108 mis, and f is thefrequency of the wave. Light waves can alsobe specified by their frequencies.

The term which describes the ability of anelement to separate white light into its com-ponent colors is dispersion. In prisms thisresults from the fact that light bends or isrefracted when it enters a region in which ittravels more slowly. The amount of bending ismeasured by the index of refraction n, whichis the ratio of the speed of light in a vacuum,c, to that in the medium, v.

For most transparent materials the amount ofbending depends on the wavelength of thelight. When the materials are shaped intoprisms, they can produce dispersion.

Gratings also disperse white light, but by adifferent mechanism. They are essentially aseries of closely spaced mirrors. The reflectedlight of each mirror interferes with that from

its neighbors in such a way as to send strongbeams in certain directions. These beams arecalled orders. The angk that the mth ordermakes with the zeroth order (simple reflec-tion) is given by:

where a is the distance separating the mirrors.Since 0 depends on the wavelength, light ofdifferent wavelengths comes off in differentdirections; in other words, the light is dis-persed.

1. Is blue light bent less or more than redby a prism? By a grlting? Why?

2. Does either the pri:;mor the grating haveapproximately constant dispersion?(Look at your data.)

3. What property of a prism causes thespectrum it produces to be spread outdifferently for the red and blue parts ofthe spectrum?

4. Which dispersive element has the greaterover-all dispersion?

5. For what regions of color are the disper-sions of the prism and grating approxi-mately equal?

6. Suppose that there were substances A, B,and C that had a speed-of-light versuswavelength depend,~nceas shown in Fig-ure 55. If prisms were made from eachsubstance, how would they disperse thelight?

7. What are the limits to the wavelengthrange of both prisms and gratings?

8. Describe why each of the importantcharacteristics of light listed below isconsistent with a wave picture for light.

a. reflectionb. refractionc. interferenced. diffraction

1. Convert the following wavelengths tonanometers (nm):

a. 3580 Ab. .64 p.c. 481 mp.d. 4.3 X 10-7 me. 1.7 X 10-5 cmf. 358.41 nm

a. Ab. p.c. cmd. me. mp.

3. Optional Experiment: Using the setupof Experiment B-1, measure (J for yellowlight. Calculate a from the fact that thegrating has 13,400 lines per inch. Thencalculate the wavelength of yellow light.Careful measurements of this sort are agood way to determine wavelengths.

Spectrophotometer Analysis

ELEMENT PURPOSE

Lamp and Condenser Make High-IntensityWhite Light

First Slit and Lens Render the Light(or Spherical Mirror) Parallel

Prism or Grating Disperse the Light

Lens (or Spherical Focus the SpectrumMirror)

Exit Slit PassOne Color toSample

Detector, Amplifier, Measure the Lightand Meter Intensity

Figure 56.49

In the final experiment of Section B you puttogether a good quality spectrophotometer.

But how do you define "quality"? How doyou specify "good"? And what effect did theother elements, slits, lenses, and mirrors haveon both?

Here you will explore your system in detail tolearn about some of these factors. Youranalysis will be focused primarily on thecharacteristics of the monochromator sincethat is the emphasis of this module. Butthe behavior of the other spectrophotometercomponents, particularly the source and thelight detector, is also important in deter-mining the quality of the spectrophotometer.

These devices are treated in other modules ofthe Physics of Technology series, The Incan-descent Lamp and Photodetectors.

DETECTORDISPLAY

Because of effects we have so far ignored,prisms and gratings produce the purest spectrawhen illuminated with "parallel light." (Ifyou divide the beam into a number ofnarrower beams, they will all be parallel, notdiverging.) Therefore, most monochromatorsstart by using a narrow slit and either a lens ora spherical mirror to make parallel light.

When the dispersed light leaves the dispersingelement, a second lens or spherical mirror isused to focus the light at the entrance slit.Thus, at the exit slit, there are multipleimages of the entrance slit, one for each color,but spread out into the spectrum. The exit slitis then placed so that only one color at a timecomes through.

Figure 56 summarizes the components ofspectrophotometers and emphasizes the pur-pose of each element in processing the light.

The block diagram on the previous pageindicates that either a lens or a sphericalmirror can be used to render the light parallelor to focus the spectrum. This is true becauseeither lenses or spherical mirrors can performthe same two tasks:

Collimation: Collimating the light comingfrom the first slit simply means making thelight beam parallel.

Focusing: Focusing the light coming fromthe grating or prism means forming images ofthe entrance slit on the exit slit.

Light diverging from a slit S a distance f behind thelens emerges in parallel beams.

mirror doing each task. The only differenc