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

`(I_(3) )/(I_(0) )` = 0.1104 ( 11 percent of the initial intensity will come out )

Step-by-step 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
`(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)` ∅ =
`(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 =
`(I_(3) )/(I_(0) )` = 0.1104