Answer to Question #162575 in Optics for Darren

Question

Three polarizing plates whose planes are parallel are centered on a common axis. The directions of the transmission axes relative to the common vertical directions. A linearly polarized beam of light with plane of polarization parallel to the vertical reference direction is incident from the left onto the first disk with intensity Ii = 10.0 units. Calculate the transmitted intensity if when s1= 20.0degrees, s2 = 40.0degrees and s3 = 60.0degrees. Hint: Make repeated use of Malus's law

Answer 1

From Malus's law, the intensity of the light transmitted by the first polarizer is I₁ = I_i cos²θ₁⋅

The plane of polarization of this light is parallel to the axis of the first plate and is incident on the second plate. Malus's law gives the intensity transmitted by the second plate as

I₂=I₁​ cos²(θ₂−θ₁) = I_i cos²θ₁ cos²(θ₂−θ₁​)

₂

This light is polarized parallel to the axis of the second plate and is incident upon the third plate. A final application of Malus's law gives the transmitted intensity as

I_f=I₂cos²(θ₃−θ₂​)=

I_i cos²θ₁ cos²(θ₂−θ₁​) cos²(θ₃​−θ₂​)

With θ₁=20.0, θ​₂=40.0, and θ₃=60.0,

this result yields

I_f​=(10.0 units )(cos²20.0)(cos²20.0)(cos²20.0)= 6.89 units