ch38-p071

# ch38-p071 - 71. We rewrite Eq. 38-9 as h h v cos = cos , m...

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where we use sin 2 θ + cos 2 = 1 to eliminate . Now the right-hand side can be written as v vc c 2 2 2 2 1 1 1 1 =− L N M O Q P (/) , so 1 1 11 1 1 2 22 2 = F H G I K J F H G I K J + F H G I K J L N M M O Q P P + ' cos ' sin . h mc λλ λ φφ Now we rewrite Eq. 38-8 as h mc 1 1 1 2 F H G I K J += ' . If we square this, then it can be directly compared with the previous equation we obtained for [1 – ( v / c ) 2 ] –1 . This yields 2 2 1 1c o s s i n 1 . hh mc mc ⎡⎤ ⎛⎞ −+= + + ⎢⎥ ⎜⎟ ′′ λ ⎝⎠ ⎣⎦ We have so far eliminated and v . Working out the squares on both sides and noting that sin 2 φ + cos 2 φ = 1, we get = = '( c o s ) . −−
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## This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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