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ay45c3-page12

ay45c3-page12 - θ θ L the momentum transfer is now only...

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Unformatted text preview: θ θ L the momentum transfer is now only 2p cos , and also it takes longer between bounces, L=C t = 2cos  : Therefore P = cos2 u : Adding up all the photons is the same as averaging an isotropic distribution over cos2 : hcos2 i cos2  d sin d' = d sin  d'  cos2  sin  d = 2 20  sin  d = 0 RR RR R R R 1 R 2 1  d 1 d 1 =1 3 (where we set  = cos ). Another way to get this result is by symmetry: Consider a randomly oriented unit vector, (x; y; z), with x2 + y2 + z2 = 1. Since there is nothing special about the x; y, or z directions with respect to the unit sphere, we must have hx2i = hy2i = hz2i : But hx2i + hy2i + hz2i = hx2 + y2 + z2i = h1i = 1 ; so each one must be 1/3. Note that in spherical coordinates z = cos , and we are done. 36 ...
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