•• InterferenceInterference

•• Young’s interference experimentYoung’s interference experiment

•• Thin filmsThin films

•• Coherence and incoherenceCoherence and incoherence

•• Michelson interferometerMichelson interferometer

•• WaveWave--like characteristics of lightlike characteristics of light

•• HuygensHuygens--FresnelFresnel principleprinciple

Physical Optics. Physical Optics. Diffraction.Diffraction.

Interference.Interference.

InterferenceInterference = = superposition of two (or more) superposition of two (or more) coherentcoherent waves waves that results in a new wave pattern.that results in a new wave pattern.

CoherentCoherent = = same frequencysame frequency

Examples. Examples. (from Phys 213)(from Phys 213)

1. Standing waves = incident wave + reflected wave1. Standing waves = incident wave + reflected wave

2. Two identical sound sources2. Two identical sound sources

3

To see if the light interferes, we pass it subsequently through two separated slits and see if an interference pattern is produced

This is aninterference

pattern!

screen

Where crests from S1 and crests from S2 meet at the screen, a bright fringe appears. Where crests and troughs meet, a dark fringe appears.

Young’s Double Slit Experiment.Young’s Double Slit Experiment. Qualitative.Qualitative.

4

Example of an

interference pattern

Young’s Double Slit Experiment.Young’s Double Slit Experiment. Experimental.Experimental.

5

Basic idea: waves from each slit will, in general, travel different distances to a given

point on the screen

� if they arrive perfectly in phase, they constructively interfere, i.e., they add to one another:

bright fringe

� if they arrive perfectly out of phase, they destructively interfere (as shown below): dark

fringe

� if they arrive in between, they do a little of both: part of fringe pattern in between bright and

dark fringes

Young’s Double Slit Experiment.Young’s Double Slit Experiment. Quantitative.Quantitative.

6

Constructive interference

∆L = dsinθθθθ = mλλλλ, m=0,1,2,..(bright fringes)

Young’s Double Slit Experiment.Young’s Double Slit Experiment. Quantitative.Quantitative.

Location on the screen

Question: what happens to the interference pattern

if we use green laser light instead of red?

Monochromatic green light, wavelength

550 nm, illuminates two parallel narrow

slits 7.7µµµµm apart. Calculate the angular

deviation θθθθ of the third-order (m=3) bright fringe in radians and degrees.

Young’s double slit experiment. Young’s double slit experiment. Sample Problem.Sample Problem.

8

The colors seen

in a soap bubble,

or from some oil

spilled on the

ground, are due

to interference

effects

physics.utoledo.edu

www-viz.tamu.edu

Thin Film InterferenceThin Film Interference

9air soapfilm air

Constructive interference (bright)

2Ln2/cosθ = m+½ , m=0,1,2,…

Thin Film InterferenceThin Film Interference

Destructive interference (dark)

2Ln2/cosθ = m, m=0,1,2,…

• On reflection, waves mayexperience a phase shift of π or λλλλ/2

• Example: pulses on stringsa) denser����lighter (slower����faster):

no shift

b) lighter����denser (faster����slower):

λλλλ/2 shift

10

Monochromatic light of λλλλ=624nm is incident perpendicularly on a soap film

with n=1.33, suspended in air.

What are the least two thicknesses of the film

for which the reflections from the film

undergo fully constructive interference?

Thin Film Interference. Thin Film Interference. Sample problemSample problem

11

Monochromatic light of λλλλ=400 nm is incident perpendicularly on a soap film

with n=1.33, covering glass (n=1.8).

What is the least thickness of the film for

which the glass is invisible?

Can we apply that to “stealth” technology?

Thin Film Interference. Thin Film Interference. Sample problemSample problem

12

A broad beam of light of wavelength 623 nm is sent directly

downward through the top plate of a pair of glass plates. The

plates are 120 mm long, touch at the left end, and are separated

by a wire of diameter 0.048 mm at the right end. The air

between the plates acts as a thin film. How many bright fringes

will be seen by an observer looking down through the top plate?

Thin Wedge InterferenceThin Wedge Interference

• You may have noticed that in the Young’s double slit experiment, there was a single slit in front

• But when I used the laser—or the microwave—apparatus, this single slit was not needed, and yet the interference patterns were essentially the same in all cases

Coherence and IncoherenceCoherence and Incoherence

• The reason is that Young had to use sunlight

� sunlight is incoherent light, meaning that the phase difference between the light waves at any two points in space is not constant over time

• it is nearly constant at small distances, but not constant over distances comparable to “d” the distance between the double-slits

� if incoherent light is sent through the double slits, the interference pattern would not be seen

• the first slit in the Young’s experiment insures that the light that hits the double slits hits each slit with the same relative phase

• We got around this problem by using a coherent emitter of radiation, namely the laser (or the klystron that emitted the microwaves)

Coherence and IncoherenceCoherence and Incoherence

For incoherent sources For incoherent sources intensitiesintensities add up not field amplitudes!add up not field amplitudes!

(recall unpolarized light and (recall unpolarized light and polarizerspolarizers))

Michelson InterferometerMichelson Interferometer

Applications:Applications: LIGO! LIGO! (recitation)(recitation)

� Permits measurements of distances as small as a fraction of the wavelength of light used

� Principle of operation:• light from source S goes to partially silvered mirror, M

� transmits some of light, reflects rest

• light goes to mirror M1 or M2, and back to M, traveling distances 2d1 and 2d2, respectively

• these two light waves interfere and this interference pattern is seen by the observer

• if one mirror (say M2) is moved by l/4, the observer will see (say) a dark fringe change into a bright fringe

1852-1931

First to measure speed of lightFirst to measure speed of light

(with high precision, 1879)(with high precision, 1879)

First American Noble Prize First American Noble Prize

winner (1907)winner (1907)

HuygensHuygens--FresnelFresnel principle.principle.

“Each point reached by a wave

acts as a (point) source of secondary waves”

“New wavefront is the result of

interference of the secondary waves”

1629-1695 1788-1827

Later supplemented by Kirchhoff (1824-1887)

(Phys 212 fellow)

18

HuygensHuygens--FresnelFresnel principle.principle.

Propagation of lightPropagation of light Refraction of lightRefraction of light

•• Thin filmsThin films--brightbright

•• Thin wedge Thin wedge -- # fringes# fringes

•• Double SlitDouble Slit--brightbright

•• Michelson InterferometerMichelson Interferometer

∆L = dsinθθθθ = mλλλλ

2L = (m+½)(λλλλ/n)

Shift one mirror arm, see change in fringes

RecapRecap

m=[2Ln/ l -½]

• Diffraction

� Quantifying single slit diffraction

� Intensity in single slit diffraction

� circular aperture diffraction

� double slit diffraction

• Diffraction gratings

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