Interference, Diffraction & Polarization
PHY232 Remco Zegers
[email protected] Room W109 – cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html
light as waves ¾ so far, light has been treated as if it travels in straight lines ¾ ray diagrams ¾ refraction ¾ To describe many optical phenomena, we have to treat light as waves. ¾ Just like waves in water, or sound waves, light waves can interact and form interference patterns. remember c=fλ
PHY232 - Remco Zegers
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interference, diffraction & polarization
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interference
constructive interference
destructive interference
at any point in time one can construct the total amplitude by adding the individual components PHY232 - Remco Zegers
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interference, diffraction & polarization
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demo: interference
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Interference III λ
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constructive interference waves in phase PHY232 - Remco Zegers
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destructive interference waves ½λ out of phase
interference, diffraction & polarization
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Interference in spherical waves
maximum of wave r =r 1 2
minimum of wave
r1
r2
positive constructive interference negative constructive interference destructive interference if r2-r1=nλ then constructive interference occurs if r2-r1=(n+½)λ the destructive interference occurs PHY232 - Remco Zegers
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interference, diffraction & polarization
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PHY232 - Remco Zegers
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interference, diffraction & polarization
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light as waves
it works the same as water and sound!
PHY232 - Remco Zegers
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interference, diffraction & polarization
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double slit experiment •the light from the two sources is incoherent (fixed phase with respect to each other •in this case, there is no phase shift between the two sources •the two sources of light must have identical wave lengths
PHY232 - Remco Zegers
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interference, diffraction & polarization
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Young’s interference experiment
there is a path difference: depending on its size the waves coming from S1 or S2 are in or out of phase PHY232 - Remco Zegers
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interference, diffraction & polarization
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Young’s interference experiment If the difference in distance between the screen and each of the two slits is such that the waves are in phase, constructive interference occurs: bright spot difference in distance must be a integer multiple of the wavelength: dsinθ=mλ, m=0,1,2,3… m=0: zeroth order m=1: first order etc
path difference PHY232 - Remco Zegers
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if the difference in distance is off by half a wavelength (or one and a half etc), destructive interference occurs (dsinθ=[m+1/2]λ, m=0,1,2,3…)
demo
interference, diffraction & polarization
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distance between bright spots
tanθ=y/L L if θ is small, then sinθ≈θ≈tanθ so: dsinθ=mλ, m=0,1,2,3… converts to dy/L=mλ difference between maximum m and maximum m+1: ym+1-ym= (m+1)λL/d-mλL/d= λL/d demo ym=mλL/d PHY232 - Remco Zegers
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interference, diffraction & polarization
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do loncapa 1,2,7 from set 9
PHY232 - Remco Zegers
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interference, diffraction & polarization
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question ¾ two light sources are put at a distance d from a screen. Each source produces light of the same wavelength, but the sources are out of phase by half a wavelength. On the screen exactly midway between the two sources … will occur distance is equal ¾ a) constructive interference so 1/2λ difference: ¾ b) destructive interference destructive int.
+1/2λ PHY232 - Remco Zegers
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interference, diffraction & polarization
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question ¾ two narrow slits are illuminated by a laser with a wavelength of 600 nm. the distance between the two slits is 1 cm. a) At what angle from the beam axis does the 3rd order maximum occur? b) If a screen is put 5 meter away from the slits, what is the distance between the 0th order and 3rd order maximum?
a) use dsinθ=mλ with m=3 θ=sin-1(mλ/d)=sin-1(3x600x10-9/0.01)=0.01030 b) ym=mλL/d m=0: y0=0 m=3: y3=3x600x10-9x5/0.01=9x10-4 m =0.9 mm
PHY232 - Remco Zegers
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interference, diffraction & polarization
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quiz (extra credit) Two beams of coherent light travel different paths arriving at point P. If constructive interference occurs at point P, the two beams must: a) travel paths that differ by a whole number of wavelengths b)travel paths that differ by an odd number of half wavelengths
PHY232 - Remco Zegers
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interference, diffraction & polarization
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other ways of causing interference ¾ remember
equivalent to:
n1>n2
n1n2 1
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n1 1 Not possible, so no patterns PHY232 - Remco Zegers
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