Question

Two polarizing sheets are placed together with their transmission axes crossed so that no light is transmitted. A third sheet is inserted between them with its transmission axis at an angle of 35.0° with respect to the axis of the first sheet. Find the fraction of incident unpolarized light intensity transmitted by the three-sheet combination. (Assume each polarizing sheet is ideal.)

Answer 1

Answer:

$\frac{I_{3} }{I_{0} }$ = 0.1104  ( 11 percent of the initial intensity will come out )

Explanation:

The fraction of incident unpolarized light intensity transmitted by the three-sheet combination

assuming the intensity of unpolarized light is $I_{0}$ then the intensity of polarized light coming out of the first polarizing sheet would be $\frac{I_{0} }{2}$ ( $I_{1}$ )

note the angle between the first and second sheet = 35⁰ c

hence the intensity of polarized light coming out of second plane ( $I_{2}$ ) polarized sheet will be = $I_{1}$ $cos^{2}$ ∅ = $\frac{I_{0} }{2}$ 0.67101 = 0.3355 $I_{0}$

Angle between the second and third sheet = 90 - 35 = 55⁰c

hence the intensity of polarized light coming out of the third plane ( $I_{3}$ ) polarized sheet will be = $I_{2}$ $cos^{2}$ 55⁰c  = 0.3355 $I_{0}$ 0.32898 = 0.1104$I_{0}$

The fraction of incident unpolarized light intensity transmitted by the three-sheet combination = $\frac{I_{3} }{I_{0} }$ = 0.1104