Three polarizing sheets are stacked on top of each other. Their polarization dir

Question

Three polarizing sheets are stacked on top of each other. Their polarization directions (relative to an arbitrary reference line) are 0, 45, and 90 degrees.

(a) Consider the fraction of initially unpolarized incident light that would be transmitted through the stack. Does the order in which they are stacked affect your answer? Explain briefly.

(b) Now suppose the first and third sheets are fixed in place, with polarization directions of 0 and 90 degrees respectively; the middle sheet can be rotated. How does the intensity of transmitted light vary qualitatively as you rotate the middle sheet from 0 to 90 degrees?

My Answers:

a)Yes, because if the two sheets with angles of 0 and 90 degrees are placed consecutively, the light passing through will be, hence no light is transmitted, but if the sheet with 45 degrees angle is placed in between the 90 and 0 degree sheets the polarization will change and there will be some light transmitted.

b) When the middle sheet is exactly at 0 and 90 degrees the transmitted intensity is zero(no light transmitted), when the middle sheet is at an angle between 0 and 90 there would be some transmitted intensity, and varies from minimum brightness to maximum brightness from 0 to 45, and maximum brightness to minimum brightness from 45 to 90.

I JUST WANT TO KNOW IF MY ANSWERS ARE COMPLETE AND CORRECT, THANK YOU!!

Explanation / Answer

a] Yes, your provided answer is correct; The order in which the polarizers are placed is crucial and one example is the first and third polarizer kept perpendicular to each other while the 2nd one bearing an angle of 45 degrees with respect to the first one. Following Malus' law, the intensity of light leaving the 3rd polarizer will not be zero now.

b] Yes, your provided answer is correct; The intensity is zero when the 2nd polarizer bears an angle 0 with the first polarizer since this one is now at 90 degrees to the 3rd polarizer hence giving zero intensity. Same applies when the angle of the 2nd polarizer is 90 degrees with the first polarizer.

The peak intensity will be when the angle is 45 degrees and intensity leaving the 3rd polarizer will be I = Io/8 where Io is the initial intensity of the unpolarizer light.

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