homework2_answers

homework2_answers - ATOC/ASEN 5235 Homework #2 Due...

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ATOC/ASEN 5235 Homework #2 Due Thursday, 9 September Please staple all pages together !!! All problems are worth 10 points each. 1. Starting with the full Jones vector for elliptically polarized light, derive its standard, normalized form as shown on slide 36 of the chapter 2 lecture. The full Jones vector for elliptically polarized light is: ) exp( ) exp( y y x x i A i A φ Step 1. Divide by one component (e.g., the x-component) to get: ) exp( ) exp( 1 x x y y i A i A = ) exp( 1 Δ i A A x y , since Δ = φ x φ y Note, however, that we defined β = inv tan (Ay/Ax), so Ay/Ax = tan( β ). Thus this becomes: ) exp( tan 1 Δ i β Step 2. Normalize the above vector by multiplying by a constant “C”. Thus: () 2 2 2 tan 1 1 ) exp(i tan 1 ) exp( tan 1 + = = Δ Δ C i C Note that 1+tan 2 β = (cos 2 β + sin 2 β )/cos 2 β = 1/cos 2 β , so C 2 = cos 2 β , or C = cos β . Thus our normalized vector is ) exp( tan 1 cos Δ i = ) exp( sin cos Δ i 2. Petty Problem 2.7. For red light ( λ = 0.64 μ m), n i in pure water is approximately 1.3 × 10 -8 ; for blue light ( λ = 0.48 μ m), n i ~ 1.0 × 10 -9 . The deep end of a typical home swimming pool is approximately 2.5 m deep. Compute the fraction of each wavelength that survives the two-way trip to the bottom of the pool and back, when illuminated (and viewed) from directly above. In light of your findings (and in view of the appearance of most swimming pools as seen from the air), comment on the common assumption that water is “colorless”.
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Use Petty Equations 2.43 & 2.44: F/F o = exp(-4 π n i x/ λ ) λ r = 0.64 μ m, n i = 1.3 × 10 -8 λ b = 0.48 μ m, n i = 1.0 × 10 -9 x = 2 × 2.5m = 5.0 m F/F o (red) = exp(-4 π 1.3 × 10 -8 × 5.0 / 0.64 × 10 -6 ) = 0.28 F/F o (blue) = exp(-4 π 1.0 × 10 -9 × 5.0 / 0.48 × 10 -6 ) = 0.88 Water will appear blue because more blue reaches our eyes (transmission of 88% as
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This note was uploaded on 01/19/2011 for the course ATOC 5235 taught by Professor Randell during the Fall '10 term at Colorado.

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homework2_answers - ATOC/ASEN 5235 Homework #2 Due...

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