Optical Phenomena

Problem : A polaroid sheet and an analyzer are placed such that their transmission axes are co-linear. The analyzer is then rotated by 22.5 ^o . What is the irradiance of the transmitted light as a fraction of its previous value?

Problem : You have three ideal linear polarizers. Light of irradiance 1000 W/m ² is shone through two of the polarizers, with their transmission axes placed at a relative angle of 40 ^o . What is the intensity of the transmitted light? Now place the third polarizer at an angle of 20 ^o between the other two. What is the irradiance?

Problem : What is Brewster's angle for reflection from air off a glass ( n = 1.52 ) surface?

Solution for Problem 3 >>

We have tanθ _p = , thus θ = tan^-1(n _t/n _i) = tan^-1(1.52) = 56.7 ^o .

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Problem : Consider the following waves:

E x		= E xcos(kz - σt)
E y		= E ysin(kz - σt + 2Π)

Problem : Write the equation for the linearly polarized light wave of angular frequency σ and amplitude E ₀ propagating along the x-axis with its plane of vibration at 30 ^o to the xy -plane (assume that E = 0 when x = 0 and t = 0 ).

Solution for Problem 5 >>

The wave will consist of two waves, one oscillating in the y -direction and one in the z -direction, both propagating in x . The amplitude of the y -wave is given by E _0y = E ₀cos(30 ^o ) = E ₀ /2 and the z -wave by E _0z = E ₀sin(30 ^o ) = E ₀/2 . Thus we can write the wave as:

E(x, t) = (/2 +1/2)E 0sin(kx - σt)

This satisfies the condition at x = t = 0 .

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