Question

Unpolarized light passes through two Polaroid sheets. The transmission axis of the analyzer makes an angle of 21.0 with the axis of the polarizer. 

(a) What fraction of the original unpolarized light is transmitted through the analyzer? (Enter your answer to at least three decimal places.) 

(b) What fraction of the original light is absorbed by the analyzer?

Answer 1

When Unpolarized light is incident on an ideal polarizer the intensity of the transmitted light is exactly half that of the incident unpolarized light no matter how the polarizing axis is oriented,i.e. I_P=I₀/2

After passing through the polariser, the light gets polarised along the direction of axis of polariser. When it passes through an analyser whose axis is at θ=21⁰

Then, the intensity out of it is given by Malus' law, I=I_pcos²(θ) =(I₀/2) cos²(21⁰) = 0.436 I₀

So, Intensity out of analyzer is 0.436 times Intensity of unpolarised light.

b) Now, intensity absorbed by analyser = Intensity falling on it - intensity coming out

= (0.5 I₀) - 0.436 I₀ = 0.064 I₀

So, Intensity absorbed by analyzer is 0.033 times Intensity of unpolarised light.