PHY2049ch35A%284-12-10%29%20

PHY2049ch35A%284-12-10%29%20 - Interference In chapter 33...

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Interference In chapter 33 you were introduced to the idea of light as an electromagnetic wave. We now explore some implications of this aspect of light. m E(x,t) E sin(kx t) =− ω m B(x, t) B sin(kx ω Since there is a definite relationship between & , (i.e. ) if we know either the electric or magnetic part we can get the other, so we need only consider one of them. B(x, t) Ec B = Usually only the electric part is considered. 2 k π = λ 2f ω
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A beam of polarized laser light can thus be represented by the propagation of its electric vector through space. The beam has a width to it and the different parts of the beam have a definite phase relation to each other. Any cross-section through the beam ( to its direction of travel) has the same phase. E.g. at the instant shown, E is a maximum everywhere for the cross-section on the red dotted line.
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If we call the peaks of the electric field magnitudes (coincident with the peak magnetic fields) wavefronts, then the propagating light beam can be represented by the motion of these wavefronts: λ (wavelength) The measured speed of light in vacuum is, 88 mm c 2.998 10 3 10 ss × Recall that for waves the wavelength and speed are related by the frequency, fv λ= wavefronts moving with speed v .
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Hence for light of given frequency, f, moving through vacuum the wavelength must satisfy, c f λ = It is experimentally found, however, that the speed of light in a material (water, glass, …) depends on the material and is always less than c . The frequency of light is independent of the material (i.e. light of frequency f in vacuum has the same frequency f in any material) If the speed of light in the material is v n then the wavelength in the material is: n n v f λ= Where, since we always have v n < c , means that the wavelength in the material, λ n is shorter than the wavelength in vacuum, λ . n vc < ,
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This means that on crossing from vacuum into a material the wavefronts bunch up in the material, and then stretch out again on exiting back to vacuum. v (speed) λ n λ Since the frequency is the same in both regions & we can write, λ v f = λ n n cv f == λ λ Or on rearranging, nn c v λ = λ
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These ratios of the speed (or wavelength) in vacuum to those in the material is the index of refraction specific to the material that you learned about in chapter 33, nn c n v λ == λ In fact it is this slowing down of the light on entering the material that is responsible for refraction.
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This note was uploaded on 04/23/2010 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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PHY2049ch35A%284-12-10%29%20 - Interference In chapter 33...

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