Question

Unpolarized light is incident upon two polarization filters that do not have their transmission axes aligned. If 21% of the light passes through, what is the measure of the angle between the transmission axes of the filters?

Answer 1

Answer:

49.6°

Explanation:

$I_0$ = Unpolarized light

$I_2$ = Light after passing though second filter = $0.21I_0$

Polarized light passing through first filter

$I_1=\frac{I_0}{2}$

Polarized light passing through second filter

$I_2=\frac{I_0}{2}cos^2\theta\\\Rightarrow 0.21I_0=\frac{I_0}{2}cos^2\theta\\\Rightarrow cos^2\theta=\frac{0.21I_0}{\frac{I_0}{2}}\\\Rightarrow cos\theta=\sqrt{\frac{0.21I_0}{\frac{I_0}{2}}}\\\Rightarrow \theta=cos^{-1}\sqrt{\frac{0.21I_0}{\frac{I_0}{2}}}\\\Rightarrow \theta=cos^{-1}\sqrt{0.21\times 2}\\\Rightarrow \theta=cos^{-1}\sqrt{0.42}\\\Rightarrow \theta=49.6^{\circ}$

The angle between the two filters is 49.6°