JOHNS HOPKINS UNIVERSITY, PHYSICS AND ASTRONOMYAS.173.112 – GENERAL PHYSICS LABORATORY II
Diffraction by Biological Specimens
1 INTRODUCTION
The purpose of this experiment is to study diffraction.
2 LEARNING OBJECTIVES
At the conclusion of this activity you should be able to:
• Define diffraction.
• Describe the interference pattern of light that passes through a diffraction grating.
• Design experiments, that use diffraction, to study biological systems.
3 BACKGROUND
Henry A. Rowland[1] – for whom the Johns Hopkins Physics department is named – was the first chair ofthe department when the university opened its doors in 1876. Rowland’s career was highlighted by manycontributions in the areas of magnetism and thermodynamics.
Perhaps his most important contribution was the diffraction grating – that now bears his name – that hedescribed in 1882. A diffraction grating consists of a plate – that is either reflective or transparent – thathas been engraved with a large number of fine parallel lines. Rowland invented a ruling engine that wasable to engrave lines in a diffraction plate with unprecedented accuracy. “Rowland gratings” have beenused extensively in observational astronomy applications as spectrum analyzers.
One of Rowland’s ruling machines, similar to the one shown in Figure 3.1, is on display on the Northside of the second floor of the Bloomberg building along with several examples of his early gratings.The sculpture in the grass courtyard outside the Bloomberg building is a model of the Rowland CircleSpectrograph that made use of his gratings. Much of the early work in diffraction was done here, in theJohns Hopkins Physics Department.
3.1 DIFFRACTION BY A GRATING
A diffraction grating can either be a reflective surface or a transparent material with finely ruled parallellines. Diffraction is an interference process that occurs because of the difference in path length for lightthat is either reflected or transmitted from, or through, each of the lines or slits[2][3].
When light of a single wavelength illuminates a diffraction grating, constructive interference occurs whenthe difference in path length, for light passing through the various slits, is equal to an integer number ofthe wavelength.
Figure 3.1: Henry Rowland’s second ruling engine. Image Source: “PSM V49 D127 Dividing engine for
ruling gratings for spectrum analyzers 1895” by Unknown - Popular Science Monthly Volume 49. Licensed under
Public domain via Wikimedia Commons - http://commons.wikimedia.org/link.
The equation that describes the interference pattern is:
d sinθ = nλ (3.1)
where d is the distance between lines of the grating and λ is the wavelength of the light. n is an integerthat describes the order of the maxima line that is observed. For example, n = 0 is the “zeroth order”maximum line and is directly in line with the incident light – with an angle θ = 0. Higher order maxima(i.e. |n| > 0 will be found with some opening angle θ relative to the zeroth order maximum.
3.2 STRUCTURE OF MUSCLE TISSUE
All muscles are composed of fibers, which may be single cells or syncytia*. The classification of differenttypes of muscle fiber is based primarily on the presence of absence of regular cross-striation, which maybe observed by ordinary light microscopy, along the length of the fibers. In vertebrates, the cardiac andskeletal muscles are striated; non-striated muscles are used for the control of the gut, viscera, and bloodvessels.
Striated muscle is composed of small subunits as shown in Figure 3.2. Each muscle fiber is a cylindricalstructure which may be many centimeters long and approximately 100 microns (100 µm) in diameter.The muscle fiber is a collection of myofibrils encased by the sarcolemma. The muscle tissue exhibitsregular striation that extend along the length of the fibers, dividing them into sarcomere. These are thestructures in the tissue that actually contract. Between the myofibrils, in the sarcoplasm, are other struc-tures of importance, including mitochondria.
Figure 3.2: A cartoon illustrating the structure of striated muscle tissue. Image Source: OpenStaxCollege - Anatomy & Physiology, Connexions Web site. http://cnx.org/content/col11496/1.6/, Jun 19,2013.
The fibril or myofibril is a rod of contractive protein that runs from one end of the fiber to the other. Thefibril is divided into segments by thin partitions called Z-lines or Z-discs. These partitions also run fromfibril to fibril across the sarcomeres[5]. In the middle of the sarcomere is the A-band with a high refractiveindex, with a less refractive central H-zone. The rest of the sarcomere is occupied by the I-band.
The length of the sarcomere varies from species to species, but it is generally in the range from 2.05 µmto 2.60 µm, from end to end, including the Z-region. In our experiment, the dark bands in the sarcomereact as the parallel lines in a diffraction grating. The grating spacing corresponds to the length of thesarcomere.
3.3 STRUCTURE OF A COMPOUND EYE
The eye of many insects, such as the butterfly, is a compound eye made of a large number of cells calledommatidia[6], which are conical in shape and are arranged on the surface of a hemisphere on the outsideof the insect’s head (see Figure 3.3). The approximately hexagonal arrangement of such a compound eyeis shown in Figure 3.4.
The arrangement of the ommatidia in a compound eye results in three axes of symmetry that correspondto the symmetry of a hexagon. The diffraction pattern of the compound eye then is expected to be asuperposition of three “gratings”. The center-to-center spacing of the apertures in an insect’s compound
Figure 3.3: A portrait of a fly. The ommatidia of the compound eye are clearly visible. ImageSource: JJ Harrison ([email protected]) (Own work) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons.
Figure 3.4: A scanning electron microscope image of the lens tissue of an insect’s com-pound eye. The approximate hexagonal shape of the ommatidia is clearly seen along withthe resulting three-fold symmetry of the lens arrangement.
"FLY EYE" by Nation kingdom - Own work. Licensed under Creative Commons Attribution-Share Alike 3.0 via WikimediaCommons - http://commons.wikimedia.org/wiki/File:FLY_EYE.jpg#mediaviewer/File:FLY_EYE.jpg
The distance between the laser and sample should be kept relatively short. The distance between thesample and the screen will have to be adjusted for each sample. To determine the angle θn , the sample-screen distance x and the distance between adjacent maxima in the diffraction pattern measured on thescreen yn should be measured. Trigonometry can be used to find sinθn from x and yn (see the PrelabQuiz).
4.1 MEASURE THE WAVELENGTH OF A LASER
laser grating
n = 2
n = 1
n = 0
n =−1
n =−2
x
yn
screen
θn
Figure 4.1: Geometry of the laser and diffraction grating system. The distance from thediffraction grating to the viewing screen is given by x. The distance along the screen fromthe centerline (n = 0) to the nth point of constructive interference is given by yn .
Using Equation 3.1 and the results from the Prelab Quiz, develop an experiment to measure the wave-length λ of a laser.
• An expression for sinθn , in terms of the observable distances x and yn (see Figure 4.1) was derivedin the Prelab Quiz. The uncertainty in the sine of the angle δ(sinθn) is given by:
δ(sinθn) =(
x
(x2 + y2n)3/2
)√(xδyn)2 + (ynδx)2. (4.1)
• Be sure to report the measured wavelength with an uncertainty estimate δλ.
4.2 MEASURE THE STRUCTURE OF MUSCLE TISSUE
The diffraction pattern that you will observe from the muscle sample is determined by the sarcomerespacing; the distance between Z-bands. The Z-band “grating” runs perpendicular to the direction of themuscle fiber. Because the Z-bands are not all aligned in a muscle tissue sample, the observed pattern willbe smeared and will appear as a much wider band than what was observed for the man-made grating.
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Use the observed diffraction pattern to estimate the distance between Z-disks (sarcomere length) in themuscle sample.
4.3 MEASURE THE STRUCTURE OF A COMPOUND EYE
It is possible to simulate the hexagonal diffraction pattern of the compound bug eye by stacking severaldiffraction gratings at 60◦ angles to one another.
By applying Equation 3.1 along each of the axes of symmetry , the dimensions across each of the “grat-ings” – or ommatidia – can be determined.
Prepare the compound eye sample that is to be measured. The eye of the butterfly is first removed witha scalpel. You will see that the cup-shaped eye is filled inside with opaque nerve tissue. This must becarefully pulled away from the lens tissue with the dissecting needles until only the transparent shellremains (see Figure 4.2). Care should be taken to not pierce the lens with the dissecting needle. Once thenerve tissue has been removed make a radial cut from the center of the lens to the periphery, to allow thehemisphere to lay flat on the microscope slide without breaking. Secure the sample to the slide with adrop of glycerin and a slide cover.
Use the observed diffraction pattern to estimate the dimensions of the approximately hexagonal omma-tidia.
Figure 4.2: The compound eye lens (red) with the optical nerve tissue (blue) removed.
5 LAB REFLECTION
Write a brief reflection to document and summarize your lab work.
Your work will be evaluated using the following rubric:
• Data Analysis & Plots (4 points)
– State what you intend to accomplish with your experiment. What are you trying to measure?
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– Briefly describe how the apparatus will be used to make the measurement. A well-labeledphotograph or diagram is an efficient way to explain the details of the experimental setup.
– Analyze your data using well-formatted plot(s).
– Describe the models that were used to make sense of your data.
• Result(s) and Comparison (4 points)
– Clearly state the final result(s) of your experiment with an associated uncertainty estimate.
– Report your result with measurement units and the appropriate significant digits.
– Compare your result to another relevant quantity. For example, you might compare yourmeasurement to an accepted value or another another group’s value.
– Choose the best tools available to make the comparison meaningful.
• Dominant Source of Uncertainty (4 points)
– Identify and discuss the dominant source(s) of uncertainty in your result.
– Use error propagation calculations (as appropriate) to support your explanation.
• Experiment Reflection (4 points)
– Interpret the evidence (plots, results, calculations, error estimates, etc) that you have pre-sented.
– Explain how your experimental findings relate to the underlying physical principles.
– Emphasize interesting features of your experiment and/or highlight unanswered questionsthat you identified in the course of the experiment.
– Remember that we are interested in the details of your experiment and not vague theoreticalstatements.
REFERENCES
[1] See the Wikipedia entry on Henry A. Rowland: https://en.wikipedia.org/wiki/Henry_Augustus_Rowland.
[2] Wikipedia entry on diffraction gratings: https://en.wikipedia.org/wiki/Diffraction_grating.
[3] Hyper-physics information explaining the fundamental physics behind the interference caused bypassing or reflecting light through a grating. http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/grating.html.
[4] Wikipedia entry on Skeletal Muscle: https://en.wikipedia.org/wiki/Skeletal_muscle.
[5] Wikipedia entry on muscle Sarcomere: https://en.wikipedia.org/wiki/Sarcomere.
[6] Wikipedia entry on an Ommatidium: https://en.wikipedia.org/wiki/Ommatidium.
