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Unformatted text preview: 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 is visibly different from the incoming angle . By definition of a wavefront the incident rays labeled 1 2 x cos x cos 1 2 G F x F G 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 = x cos , or = . (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 FG requires Eq. (1) to be satisfied for all values of x . So there is reflection if and only if = . 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 . 1 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 introducewavelength is 1 unit....
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- Spring '08