p39_046 - 46. We rewrite Eq. 39-9 as v h h cos = m m 1...

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46. We rewrite Eq. 39-9 as h h 0 cos φ = v p 1 ( v/c ) 2 cos θ, and Eq. 39-10 as h 0 sin φ = v p 1 ( v/c ) 2 sin θ. We square both equations and add up the two sides: µ h m 2 " µ 1 λ 1 λ 0 cos φ 2 + µ 1 λ 0 sin φ 2 # = v 2 1 ( v/c ) 2 , where we use sin 2 θ +cos 2 θ = 1 to eliminate θ . Now the right-hand side can be written as v 2 1 ( v/c ) 2 = c 2 · 1 1 1 ( v/c ) 2 ¸ , so 1 1 ( v/c ) 2 = µ h mc 2 " µ 1 λ 1 λ 0 cos φ 2 + µ 1 λ 0 sin φ 2 # +1 . Now we rewrite Eq. 39-8 as h mc µ 1 λ 1 λ 0 +1= 1 p 1 ( v/c ) 2 . If we square this, then it can be directly compared with the previous equation we obtained for [1
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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