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

Answer:

10.028%

Explanation:

$\theta$ = Angle between polarizer

The polarized light after passing through first polarizer

$I=\frac{I_0}{2}$

The polarized light after passing through second polarizer

$I_2=\frac{I_0}{2}cos^2\theta\\\Rightarrow I_2=\frac{I_0}{2}cos^231.8\\\Rightarrow I_2=0.36115I_0$

The polarized light after passing through third polarizer

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

$\frac{I_3}{I_0}\times 100=\frac{0.10028I_0}{I_0}\times 100\\ =10.028\ \%$

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