Question

Unpolarized light is incident upon two ideal polarizing filters that do not have their transmission axes aligned. If 19% of the light passes through this combination, what is the angle between the transmission axes of the two filters?

Answer 1

51.94°

Step-by-step explanation:

`I_0` = Unpolarized light

`I_2` = Light after passing though second filter =
`0.19I_0`

Polarized light passing through first filter

`I_1=(I_0)/(2)`

Polarized light passing through second filter

`I_2=(I_0)/(2)cos^2\theta\\\Rightarrow 0.19I_0=(I_0)/(2)cos^2\theta\\\Rightarrow cos^2\theta=(0.19I_0)/((I_0)/(2))\\\Rightarrow cos\theta=\sqrt{(0.19I_0)/((I_0)/(2))}\\\Rightarrow \theta=cos^(-1)\sqrt{(0.19I_0)/((I_0)/(2))}\\\Rightarrow \theta=cos^(-1)√(0.19* 2)\\\Rightarrow \theta=cos^(-1)√(0.38)\\\Rightarrow \theta=51.94^(\circ)`

The angle between the two filters is 51.94°