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Solutions9

# Solutions9 - Physics 208 Assignment 9 Solutions RT Problem...

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Physics 208, Assignment 9, Solutions, 3/30/09, RT Problem 1. The figure shows a conjectured “reflection” for which, in order to set up equations, the outgoing angle β is visibly different from the incoming angle α . By definition of a “wavefront” the incident rays labeled 1 2 x cos α x cos β α α β 1’ 2’ G F’ x F G’ β 1 and 2 are “in phase” at the points F and G, points on the same wavefront. According to Huyghens, when the outgoing rays 1’ and 2’ are viewed in the distance (or, as one says, at infinity) they will add constructively if they are in phase at the points F’ and G’. This will be true if the distances GG’ and FF’ are equal, or x cos β = x cos α, or β = α. (1) Strictly speaking we also have to prove an only if statement as well. Eq. (1) is also satisfied when distances GG’ and FF’ differ by an inte- gral number of wavelengths. This can happen for various discrete values of x . But, for constructive interference of all rays on the wavefront F’G’ requires Eq. (1) to be satisfied for all values of x . So there is reflection if and only if α = β . This reflection is referred to as “specular” which, I think, means, “the same for all colors”. The argument above showing independence from x can be rephrased to prove independence of wavelength λ . 1

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Problem 2. The problem states that two slits are separated by 25 wave- lengths. It would not be wrong to work in units of length such that the wavelength is 1 unit. But that might be confusing. Hence we introduce
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Solutions9 - Physics 208 Assignment 9 Solutions RT Problem...

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