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Unformatted text preview: energy emitted that passes through the surface is frac = A 4 πR 2 where R = h cos θ c is the distance from the pointsource to the edge of the “circle of light.” Now, the area A of the spherical cap of height H bounded by that circle is A = 2 πRH = 2 πR ( R − h ) may be looked up in a number of references, or can be derived from A = 2 πR 2 R θ c sin θ dθ . Consequently, frac = 2 πR ( R − h ) 4 πR 2 = 1 2 µ 1 − h R ¶ = 1 2 (1 − cos θ c ) . The critical angle is given by sin θ c = 1 /n , which implies cos θ c = p 1 − sin 2 θ c = p 1 − 1 /n 2 . When this expression is substituted into our result above, we obtain frac = 1 2 Ã 1 − r 1 − 1 n 2 ! . (b) For n = 1 . 33, frac = 1 2 Ã 1 − s 1 − 1 (1 . 33) 2 ! = 0 . 170 ....
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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.
 Fall '08
 SPRUNGER
 Physics, Light

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