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?

Explanation / Answer

a] Yes, if the third polarizer will come after first one then intensity will become zero as the angle between the consecutive polarizers will be 90 degree.

b] Let unpolarised light have intensity i0. Intensity after first polariser will be i1=io/2, intensity after second polariser will be: i2 = i1*[cos theta]^2

intensity after third polariser i3 = i2*[cos (90 degree -theta)]^2

i3 =  i0/2 *[cos theta]^2 *[cos (90 degree -theta)]^2

= 0.5 i0*[cos theta]^2 * [sin theta]^2

= 0.5* [cos theta* sin theta]^2

= 0.5* [0.5 sin 2theta]^2

So, the transmitted intensity increases with as we rotate from 0 to 45 degree, achieving maximum at 45 degree and then will decrease as we rotate from 45 degree to 90 degree.

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