5) Natural light is randomly polarized, which means that, on average, half the l

Question

5) Natural light is randomly polarized, which means that, on average, half the light energy is polarized along any given direction (in the plane orthogonal to the direction of propagation) and the other half of the energy is polarized along the direction orthogonal to the first polarization direction. Hence, when treating natural light incident upon a planar boundary, we can consider half of its energy to be in the form of parallel-polarized waves and the other half as perpendicularly polarized waves. Determine the fraction of the incident power reflected by the planar surface of a piece of glass with n = 1.5 when illuminated by natural light at 70 degree.

Explanation / Answer

n1 sin(theta 1 ) = n2 sin(theta 2 )

1 sin (70) = 1.5 sin(theta 2 )

sin(theta 2 )= sin(70) /1.5 = 0.626

theta 2 = arcsin(0.626) = 38.8

k1 = ( n1 cos(theta 1) - n2 cos(theta 2) ) / ( n1 cos(theta 1) + n2 cos(theta 2) )

= ( cos(70) - 1.5 cos(38.8) ) / ( cos(70) - 1.5 cos(38.8) ) = - 0.55

k2 = ( n1 cos(theta 2) - n2 cos(theta 1) ) / ( n1 cos(theta 2) + n2 cos(theta 2) )

=  ( cos(38.8) - 1.5 cos(70))/( cos(38.8)+1.5cos(70)) = 0.21

R = 0.5 ( k1^2 + k2^2 ) = 0.5 (0.55^2 + 0.21^2) = 0.173

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fraction of incident power reflected = 0.173

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