# HW3 - δ p and δ s at three visible wave-lengths using...

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Assignment 3 Due Tuesday, May 23 Physics U603 Summer 1 2006 1. Hecht, Ch. 4: 14, 34, 44, 75 2. Rainbows: Rainbows result from light re f ected from the inner sur- faces of spherical raindrops and are visible when the Sun is behind you and the background intensity due to light scattered from the air is low enough to provide su cient contrast. 1

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(a) Work out the geometry to show that the primary and secondary re f ections deviate by angles δ s =4 θ 2 2 θ 1 and δ p = π +2 θ 1 6 θ 2 , respectively, from the antisolar direction. Here, θ 1 and θ 2 are the angles with respect to the normal before and after entering the raindrop. (b) Use appropriate derivatives of these expressions together with Snell’s Law to show that δ s and δ p have extrema for sin 2 θ 1 = (4 n 2 ) / 3 and sin 2 θ 1 =(9 n 2 ) / 8 , respectively. (The index of refraction is n for water and 1 for air.) Are these maxima or minima? (c) Calculate the extremal values of
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Unformatted text preview: δ p and δ s at three visible wave-lengths, using values for the index of refraction of water given in the table. Present these results in a table and explain the order of colors observed for the primary and secondary rainbow, from the inside to the outside of the bow. wavelength (nm) index of refraction 656.3 nm 1.331 589.3 nm 1.333 486.1 nm 1.337 (d) Use Fresnel’s equations to determine the fraction of incident in-tensity returned for the primary and secondary re f ections, in both S and P polarizations, at the extremal angles. Note that you will need to take into account three or four interfaces for each case. Based on the resulting four values, discuss the relative visibility of the primary and secondary bows, assuming that the sunlight is randomly polarized. 2...
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HW3 - δ p and δ s at three visible wave-lengths using...

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