{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ay45c3-page12

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online