Unpolarized light is incident on four polarizing sheets with their transmission

Question

Unpolarized light is incident on four polarizing sheets with their transmission axes oriented as shown in the figure, in which ?1 = 35.0? and ?2 = 69.0?. What percentage of the initial light intensity is transmitted through this set of polarizers?

_____ %

Unpolarized light is incident on four polarizing sheets with their transmission axes oriented as shown in the figure, in which ?1 = 35.0 and ?2 = 69.0. What percentage of the initial light intensity is transmitted through this set of polarizers? _____ %

Explanation / Answer

When unpolarized light hits a polarizer, the inensity on the output is about 1/2 of the intensity on the input. So if the first intensity is 'I', after the first polarizer, the intesity will be I_1 = 0.5*I.

When polarized light hist a polarizer at a different angle the new intensity is given by:
I_new = I_orig*(cos theta)^2 where theta is the angle difference between the between their axes.
Hence after the second and future polarizers, the intesity would be:
I_2 = I_1*(cos (35 - 0))^2 = 0.5I*0.671 = 0.335*I
I_3 = I_2*(cos (69-35))^2 = 0.335I*0.687 = 0.23*I
I_4 = I_3*(cos (90- 69))^2 = 0.23I*0.871 = 0.200*I

This means 20% of light is transmitted through the set of polarisers.

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