Question

Unpolarized light passes through three polarizing filters. The first one is oriented with a horizontal transmission axis, the second filter has its transmission axis 31.8° from the horizontal, and the third one has a vertical transmission axis. What percent of the light gets through this combination of filters?

Answer 1

10.028%

Step-by-step explanation:

`\theta` = Angle between polarizer

The polarized light after passing through first polarizer

`I=(I_0)/(2)`

The polarized light after passing through second polarizer

`I_2=(I_0)/(2)cos^2\theta\\\Rightarrow I_2=(I_0)/(2)cos^231.8\\\Rightarrow I_2=0.36115I_0`

The polarized light after passing through third polarizer

`I_3=I_2cos^2(90-31.8)\\\Rightarrow I_3=0.36115I_0cos^2(90-31.8)\\\Rightarrow I_3=0.10028I_0`

`(I_3)/(I_0)* 100=(0.10028I_0)/(I_0)* 100\\ =10.028\ \%`

The percent of the light gets through this combination of filters is 10.028%