Phys 2: Chap. 24, Pg 1 l Waves vs. particles l Some properties of waves: çHuygens’ principle...

Phys 2: Chap. 24, Pg 1

Waves vs. particlesWaves vs. particles

Some properties of waves:Some properties of waves:

Huygens’ principleHuygens’ principle

Superposition — “adding” wavesSuperposition — “adding” waves

CoherenceCoherence

Some observed experimental effects:Some observed experimental effects:

Interference Interference — — doubledouble-slit experiments-slit experiments

DiffractionDiffraction — — singlesingle-slit experiments -slit experiments

PolarizationPolarization


We observe in nature:InterferenceInterferenceDiffractionDiffractionPolarizationPolarization

Light: Waves or Particles?Light: Waves or Particles?

Light carries energy. But how?As a stream of particles travelling in the direction of the light

ray?As a wave that spreads outward from the source?

These are wave phenomena!!

In future chapters we will see light acting as a particle. Wave-particle duality


Question: Suppose light falls onto a screen with two slits.

What would you see on the wall behind the screen?

To understand this, we must understand these principlesHuygens’ PrincipleSuperposition of wavesCoherence

You might expect to see two bright lines on the wall:

But instead you would see many lines on the wall:


Huygens’ PrincipleHuygens’ Principle

All points on a wave front serve as point sources of spherical waves

This also works for plane waves...This also works for plane waves...Apply Huygens’ Principle to a spherical wave...Apply Huygens’ Principle to a spherical wave...

Recall that a point source of light emits a spherical wave

…and that far from the source, the wave is a plane wave


So What?So What?

Waves can bend around corners!

This is a characteristic of all waves:EM wavessound waveswater waves


SuperpositionSuperpositionWhat happens when two particles are in the same place at the same time?

They collide!

Constructive

Interference

Destructive

Interference

+

=

Amplitude = 1

Amplitude = 1

Amplitude = 2

What happens when two waves are in the same place at the same time?

They “superpose”! Their amplitudes add to give one new wave!

+

=

Amplitude = 1

Amplitude = 1

Amplitude = 0


[wavopt1b]

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ConcepTest 1ConcepTest 1(Post) InterferenceInterference

(1)

(2)

(3)

(4)

If waves A and B are superposed (that is, their amplitudes are added)

the resultant wave is


The amplitudes of

waves A and B have to

be added at each

point!

ConcepTest 1ConcepTest 1(ans) InterferenceInterference

(1)

(2)

(3)

(4)

If waves A and B are superposed (that is, their amplitudes are added)

the resultant wave is


PhasePhase Phase refers to the relative position of the wave crests of the two waves

Phase difference180o or ½

“Out of phase”

Phase difference0o

“In phase”


constructiveconstructive interference interference destructivedestructive interference interference

waves are waves are in phasein phase waves are waves are out of phaseout of phase


CoherenceCoherence

Two sources of light are said to be coherent if the phase difference between the

waves emitted is always the same incoherent if the phase difference between the

waves emitted is always changing

Everyday light sources are not coherent

Lasers DO produce coherent light

How is light produced? Oscillating electrons!

For future reference: no interference patterns appear for incoherent light.

In a light bulb, billions of electrons are oscillating.

Is the phase difference between the light from each electron always the same?

In general, NO!In general, NO!

Phys 2: Chap. 24, Pg 12 [wavopt2b]

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ConcepTest 2ConcepTest 2(Post) PhasePhase

The two waves shown are

(1) out of phase by 180o



(4) in phase


The two waves are out of phase

by 1/4 wavelength1/4 wavelength (as seen in

the figure) , which corresponds

to a phase difference of 9090oo.

ConcepTest 2ConcepTest 2(dis) PhasePhase

The two waves shown are




(4) in phase

¼


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ConcepTest 3ConcepTest 3(post) PhasePhase


(2) out of phase, but not by 180o

(3) in phase

Two light sources emit waves of = 1 m which are in phase. The two waves from these sources meet at a distant point. Wave 1 traveled 2 m to reach the point, and wave 2 traveled 3 m. When the waves meet, they are


Since = 1 m, wave 1 has traveled twice this

wavelength while wave 2 has traveled three

times this wavelength. Thus, their phase

difference is one full wavelengthone full wavelength which

means they are still in phase.

ConcepTest 3ConcepTest 3(ans) PhasePhase


(2) out of phase, but not by 180o

(3) in phase

Two light sources emit waves of = 1 m which are in phase. The two waves from these sources meet at a distant point. Wave 1 traveled 2 m to reach the point, and wave 2 traveled 3 m. When the waves meet, they are


Interference of Sound WavesInterference of Sound Waves

Consider two sound waves that are in phase:shift source by 2 wavelengths (constructive interference)

22


Now what if the shifted wave is out of phase:shift source by 3/2 wavelengths (destructive interference)

3/2 3/2

Interference of Sound WavesInterference of Sound Waves


Question: Suppose light falls onto a screen with two slits.

What would you see on the wall behind the screen?

You might expect to see two bright lines on the wall:



Where are the dark and bright spots and how Where are the dark and bright spots and how

are they related to the light’s wavelength?are they related to the light’s wavelength?

If both waves travel the same distance:

constructive interference

Explanation of the double-slit observationsExplanation of the double-slit observations


Explanation of the double-slit ObservationsExplanation of the double-slit Observations

We can explain the pattern of bright and dark fringes by

1. bending (diffraction / Huygens’ Principle)

and 2. superposition (adding of amplitudes)

of 3. coherent light waves!

Bottom wave travels 1 whole extra wavelength. When waves

meet, they are in phase: constructive interference

Bottom wave travels ½ extra wavelength. When waves

meet, they are out of phase: destructive interference

1/2


constructive

destructive


Double-Slit Interference: The MathDouble-Slit Interference: The Math

Path difference betweenwaves determines phase

difference:

m is an integer: m = 0, ± 1, ± 2, ...

d

L

y

r1

r2

= r2 - r1 = d sin

For Destructive Interference

= 1/2, 3/2, 5/2, 7/2, …

= (m + 1/2)

d sin = (m + 1/2)

For Constructive Interference

= 1, 2, 3, 4, …

= m

d sin = m


Intensity of FringesIntensity of Fringes

m = 0 11 22 33ConstructiveInterference

m = DestructiveInterference

LightIntensity

0 01 12 23 3


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ConcepTest 4ConcepTest 4(Post) InterferenceInterference In a double-slit experiment, when the

wavelength of the light is increased, the

interference pattern (1) spreads out

(2) stays the same

(3) shrinks together

(4) disappears


If is increased is increased and dd does does

not changenot change, then must must

increaseincrease, so the pattern

spreads out.

ConcepTest 4ConcepTest 4(Ans) InterferenceInterference In a double-slit experiment, when the

wavelength of the light is increased, the

interference pattern (1) spreads out

(2) stays the same


(4) disappears

d sin d sin = m = m


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ConcepTest 5ConcepTest 5(Post) InterferenceInterference

(1) spreads out

(2) stays the same


(4) disappears

If instead the If instead the slitsslits are moved are moved farther apartfarther apart

(without changing the wavelength), the (without changing the wavelength), the

interference pattern interference pattern


If instead dd is increased is increased and

does not change does not change, then

must decrease must decrease, so the

pattern shrinks together.

ConcepTest 5ConcepTest 5(Ans) InterferenceInterference

(1) spreads out

(2) stays the same


(4) disappears

d sin d sin = m = m

If instead the If instead the slitsslits are moved are moved farther apartfarther apart

(without changing the wavelength), the (without changing the wavelength), the

interference pattern interference pattern


Light of wavelength Light of wavelength 680 nm680 nm falls on two slits and produces an falls on two slits and produces an

interference pattern in which the interference pattern in which the fourth-orderfourth-order maximummaximum is is 48 mm48 mm

from the central fringe on a screen from the central fringe on a screen 1.5 m1.5 m away. away.

What is the separation between the two slits?What is the separation between the two slits?

Double-slit interferenceDouble-slit interference

See Problem 24-7

1


Double-Slit InterferenceCalculate the distance of the

bright fringes from the axis:

Note that tan = y/L.

By hypothesis, L >> y, so then

tan and thus are both << 1.

Then tan sin to a good

approximation.

So the bright fringes will be at:

therefore: d

Lmy bright

So the bright fringes are evenly spaced a distance L/d apart.

Ly

dm tansin


Light of wavelength 680 nm falls on two slits and produces an interference pattern in which the fourth-order maximum is 48 mm from the central fringe on a screen 1.5 m away. What is the separation between the two slits?

Problem Problem

Constructive orDestructive Interference? “maximum” Constructive

Equation for fringes? Constructive d sin = m

Algebra d = m / sin= mL / y

Plug in numbers

m = 4 = 680 nm = 680 10–9 mL = 1.5 my = 0.048 m

d = 0.085 mm

What is sin?

L

ysin tan = y/L

Phys 2: Chap. 24, Pg 31 [wavop10b]

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ConcepTest 10ConcepTest 10(Post) InterferenceInterference An interference pattern is seen from two An interference pattern is seen from two

slits.slits.(1) pattern vanishes

(2) pattern expands

(3) bright and dark spots are interchanged

(4) pattern shrinks

(5) no change at all

Double slit Interference patternDouble slit Interference pattern

wavewave

Now cover one slit with Now cover one slit with glassglass, ,

introducing a introducing a phase difference phase difference

of 180of 180° (½ wavelength)° (½ wavelength) at the at the

slits. How is the pattern altered?slits. How is the pattern altered?


If the waves originating from the two

slits have a phase difference of phase difference of

180°180° when they start off, the

central spot will now be darkdark.

To the left and the right, there will

be bright spots. Thus, bright and bright and

dark spots are interchangeddark spots are interchanged.


Double slit Interference patternDouble slit Interference pattern

wavewave

(1) pattern vanishes

(2) pattern expands

(3) bright and dark spots are interchanged

(4) pattern shrinks

(5) no change at all

An interference pattern is seen from two An interference pattern is seen from two

slits.slits.

Now cover one slit with Now cover one slit with glassglass, ,

introducing a introducing a phase difference phase difference

of 180of 180° (½ wavelength)° (½ wavelength) at the at the

slits. How is the pattern altered?slits. How is the pattern altered?


What is Diffraction?What is Diffraction?

Waves can bend around corners!

This is a characteristic of all waves:EM waves

sound waves

water waves


DiffractionWhat is actually seen, close to the edge of the shadow, is

inci

den

t lig

ht

screen


Diffraction

What if we shined coherent light through a single slit?


Diffractionpattern


Single-slit diffractionSingle-slit diffraction Light falls straight through the slitLight falls straight through the slit

forms a forms a central bright linecentral bright line on the screen on the screen

Now look at light falling through atNow look at light falling through at angle angle such that the top and bottom waves are such that the top and bottom waves are one wavelength one wavelength apart. apart.

this gives destructive interference

This center wave is exactly This center wave is exactly half a half a wavelength wavelength 22 out of phase with out of phase with this bottom wavethis bottom wave


Single-slit diffractionSingle-slit diffraction

DD

Eventually we get following pattern:Eventually we get following pattern:

sin = D

The angle corresponding The angle corresponding to the to the first minimum first minimum ::

D sin = m

Equation for all minima:



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ConcepTest 7ConcepTest 7(Post) DiffractionDiffraction

screenSlide with slit

The diffraction pattern below

arises from a single slit. If we

would like to sharpen the pattern,

i.e. make the central bright spot

narrower, what should we do to

the slit width?

(1) narrow the slit

(2) widen the slit

(3) enlarge the screen

(4) close off the slit


The angle at which the first minimum occurs is:

The central bright spot can be made

narrower by having a smaller anglesmaller angle,

which can be accomplished by

widening the slitwidening the slit (increasing D).

ConcepTest 7ConcepTest 7(ans) DiffractionDiffraction

DD

sin = D

The diffraction pattern below

arises from a single slit. If we

would like to sharpen the pattern,

i.e. make the central bright spot

narrower, what should we do to

the slit width?

(1) narrow the slit

(2) widen the slit

(3) enlarge the screen

(4) close off the slit


RESPONDEX

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ConcepTest 8ConcepTest 8(Post) DiffractionDiffraction Blue light of wavelength passes

through a single slit of width d and

forms a diffraction pattern on a screen.

If the blue light is replaced by red light

of wavelength 2, the original diffraction

pattern can be reproduced if the slit

width is changed to:

(1) d/4

(2) d/2

(3) no change needed

(4) 2 d

(5) 4 d


ConcepTest 8ConcepTest 8(ans) DiffractionDiffraction

dd

d sin = m (minima)

If 2 then we must have

d 2d for sin to remain

unchanged (and thus give the

same diffraction pattern).

Blue light of wavelength passes

through a single slit of width d and

forms a diffraction pattern on a screen.

If the blue light is replaced by red light

of wavelength 2, the original diffraction

pattern can be reproduced if the slit

width is changed to:

(1) d/4

(2) d/2

(3) no change needed

(4) 2 d

(5) 4 d


How wide is the central diffraction peak on a screen How wide is the central diffraction peak on a screen

2.50 m2.50 m behind a behind a 0.0348 mm0.0348 mm wide slit illuminated by wide slit illuminated by

589 nm589 nm light? light?

DiffractionDiffraction

See Problem 24-22

1

DD


Diffraction + InterferenceDiffraction + InterferenceWait a minute! If we have two slits, don’t we also get a diffraction pattern from each slit, in addition to the interference pattern?

If another slit is opened adjacent to the first, the pattern now has an interference pattern:

If laser light illuminates one slit:

diffractionminimum

interferenceminimum


Intensity of FringesIntensity of Fringes

m = 0 11 22 33ConstructiveInterference

m = DestructiveInterference

LightIntensity

0 01 12 23 3


Diffraction GratingDiffraction Grating

A large number of equally spaced A large number of equally spaced slits (up to 10,000 !) is called a slits (up to 10,000 !) is called a diffraction grating diffraction grating

useful for measuring useful for measuring

wavelengthswavelengths

what does the interference what does the interference

pattern look like?pattern look like?

Similar to the 2-slit situation, Similar to the 2-slit situation,

but peaks are but peaks are much narrowermuch narrower..


Assume that the light striking a diffraction grating has

several wavelengths (it is not monochromatic).

Remember that white light contains all the colors of the

s p e c t r u m

The Visible SpectrumThe Visible Spectrum

each color in the spectrum has a different wavelength


Diffraction grating with different colorsDiffraction grating with different colors

If the light has If the light has twotwo wavelengths, we get wavelengths, we get twotwo sets of maxima: sets of maxima:

If it is white light (If it is white light (all colors, all colors, thereforetherefore all wavelengths all wavelengths):):


Interference by Thin FilmsInterference by Thin Films

Example -- thin oil film on water: Example -- thin oil film on water:

Part of the incoming light is reflected Part of the incoming light is reflected off the top surface (off the top surface (point Apoint A), part at ), part at the lower surface (the lower surface (point Bpoint B).).

Light traveling through oil travels Light traveling through oil travels extra distanceextra distance (from (from A A toto B B toto C C).).

If this distance is If this distance is 223344……

» constructive interferenceconstructive interference!!

If this distance is If this distance is 2233225522……

» destructive interferencedestructive interference!!


Newton’s RingsNewton’s Rings More interference: air gap between two pieces of glass.More interference: air gap between two pieces of glass.

Path difference increases for the wave reflected at Path difference increases for the wave reflected at bottom surface (bottom surface (point Cpoint C).).

If the extra path length is If the extra path length is 223344……

» constructive interference! constructive interference!

If the extra path length is If the extra path length is 2233225522… …

» destructive interference! destructive interference!


ConcepTest 11ConcepTest 11(Pre) InterferenceInterference

[wavop11a]

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A laser shines on a pair of identical A laser shines on a pair of identical

glass microscope slides that form glass microscope slides that form

a very narrow edge. The waves a very narrow edge. The waves

reflected from the top and the reflected from the top and the

bottom slide interfere. What is the bottom slide interfere. What is the

interference pattern from top view?interference pattern from top view?edgeedge

(1)(1)

(2)(2)


Right at the edge, the two reflected rays have no phase differenceno phase difference and therefore should interfere constructivelyconstructively. However, the light ray reflected at the lower surface (point E) changes changes phase by phase by 22 because the index of refraction of glass is larger than that of air.


edgeedge

(1)(1)

(2)(2)

A laser shines on a pair of identical A laser shines on a pair of identical

glass microscope slides that form glass microscope slides that form

a very narrow edge. The waves a very narrow edge. The waves

reflected from the top and the reflected from the top and the

bottom slide interfere. What is the bottom slide interfere. What is the

interference pattern from top view?interference pattern from top view?


Reflection of waves on surfacesReflection of waves on surfaces If a light wave is reflected by a material If a light wave is reflected by a material

whose whose index of refractionindex of refraction is is greatergreater than than that of the material it is going through, that of the material it is going through, the wave the wave changes phase by changes phase by 22example: example: air and oil, oil and water, etc.air and oil, oil and water, etc.

This is similar to a wave pulse This is similar to a wave pulse traveling on a rope and being traveling on a rope and being reflected with the end reflected with the end tied downtied down..

The pulse flips over The pulse flips over the the wave wave changes phasechanges phase..


And the other way around...And the other way around...

If a light wave is reflected by a material If a light wave is reflected by a material whose whose index of refractionindex of refraction is is lessless than than that of the material it is going through, that of the material it is going through, there is no phase changethere is no phase change..

This is similar to a wave pulse This is similar to a wave pulse traveling on a rope and being traveling on a rope and being reflected with the end reflected with the end looseloose..

The pulse travels back the same The pulse travels back the same way it came way it came no phase changeno phase change..

Phys 2: Chap. 24, Pg 55 [wavop12b]

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ConcepTest 12ConcepTest 12(post) InterferenceInterference Consider two identical microscopic Consider two identical microscopic

slides in air illuminated with light from slides in air illuminated with light from

a laser. The bottom slide is rotated a laser. The bottom slide is rotated

upwards so that the wedge angle gets upwards so that the wedge angle gets

a bit smaller. What happens to the a bit smaller. What happens to the

interference fringes?interference fringes?

(1) Spaced farther apart

(2) Spaced closer together

(3) No change


The path difference between Ray #2 and Ray #3 is 2t. Ray #3 also experiences a phase change of 180°. Thus, the dark fringes will occur for:

2t = m2t = m m = 0,1,2, m = 0,1,2,……

If t gets smaller, Ray #2 and Ray #3 have to be further apart before they can interfere. Thus, the fringes move apart.

ConcepTest 12ConcepTest 12(ans) InterferenceInterference Consider two identical microscopic Consider two identical microscopic

slides in air illuminated with light from slides in air illuminated with light from

a laser. The bottom slide is rotated a laser. The bottom slide is rotated

upwards so that the wedge angle gets upwards so that the wedge angle gets

a bit smaller. What happens to the a bit smaller. What happens to the

interference fringes?interference fringes?

ray 1

ray 2

ray 3

t

(1) Spaced farther apart

(2) Spaced closer together

(3) No change



1 electronE field oscillatesin one direction

polarized light

3-D view:

The E field in an EM wave is perpendicular to the direction of travel

But there are many possible orientations for the E field!

millions ofelectrons

E field oscillatesin all directions

unpolarized light

3-D view:

In polarized light, all of the electric fields in the wave oscillate in the same direction


Polarization by AbsorptionPolarization by Absorption

1) scatteringThree ways to polarize light 2) reflection

3) absorption

unpolarizedpolarized

E fieldof wave

Wave passes throughE field

of waveWave

absorbed

Polarization by absorption:

Vertical components of wave are absorbed by antenna

Horizontal components pass through

polaroid

long thinmolecules (light)wires (radio waves)


How much light gets through?How much light gets through?

E field: Eo

Intensity: Io

E field: ?Intensity: ?

Intensity of the outgoing polarized light:Intensity of the outgoing polarized light: I = II = I00 cos cos22



No light

First polaroid allows only First polaroid allows only

one orientation of the electric one orientation of the electric

field to pass, thus polarizing field to pass, thus polarizing

the light.the light.

Second polaroid is oriented Second polaroid is oriented

perpendicular to the first perpendicular to the first

one, so no light can pass one, so no light can pass

through it.through it.


[wavop14b]

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ConcepTest 14ConcepTest 14(post) PolarizationPolarization

If unpolarized light is incident

from the left, in which case

will some light get through?

(1) only case 1

(2) only case 2

(3) only case 3

(4) cases 1 and 3

(5) all three cases


ConcepTest 14ConcepTest 14(ans) PolarizationPolarization

If unpolarized light is incident

from the left, in which case

will some light get through?

(1) only case 1

(2) only case 2

(3) only case 3

(4) cases 1 and 3

(5) all three cases

In cases 1 and 3, light is

blocked by the adjacent

horizontal and vertical

polarizers. In case 2, the

intermediate 45° polarizerintermediate 45° polarizer

allows some light to get

through the last vertical

polarizer.


Two polarizers are oriented at Two polarizers are oriented at 58°58° to one another. to one another.

Light polarized at a Light polarized at a 29°29° angle to each polarizer angle to each polarizer

passes through both. passes through both.

What reduction in intensity takes place What reduction in intensity takes place ??


See Problem 24-61

1

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Phys 2: Chap. 24, Pg 1 l Waves vs. particles l Some properties of waves: çHuygens’ principle...

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