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•• 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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