Two polarizing sheets have their transmission axes crossed so that no light gets

Question

Two polarizing sheets have their transmission axes crossed so that no light gets through. A third sheet is inserted between the first two such that its transmission axis makes an angle with that of the first sheet. Unpolarized light of intensity I0 is incident on the first sheet. Find the intensity of the light transmitted through all three sheets for the following values of .
(a) = 45°
through first sheet

x Io

through first two sheets

x Io

through all three sheets

x I0

(b) = 22°
through first sheet

x Io

through first two sheets

x Io

through all three sheets

x I0

Explanation / Answer

Unpolarized light of intensityI0 is incident on the first sheet.
so through first sheet, intensity I1 =0.5I0
through first two sheets, intensity I2= 0.5I0 *cos2
through all three sheets, intensityI3 = 0.5I0 *cos2 * cos2(90 - )
a) = 45o
I1 = 0.5I0
I2 = 0.5I0 *cos2(45) = 0.25I0
I3 = 0.5I0 *cos2(45) * cos2(45) = 0.125I0
b) =32o
I1 = 0.5I0
I2 = 0.5I0 *cos2(22) = 0.42I0
I3 = 0.5I0 *cos2(22) * cos2(58) = 0.120I0

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