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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.
• 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))