Question

Unpolarized light of intensity $I_0$ is incident on a polarizer and the emerging light strikes a second polarizing filter with its axis at 45${}^{\circ }$ to that of the first. The intensity of the emerging beam :

• A. $\frac{I^{}o}{2}$
• B. $\frac{I^{}o}{4}$
• C. $I_o$
• D. $\frac{I^{}o}{3}$

Answer 1

The correct option is B $\frac{I^{}o}{4}$

The unpolarized light of Intensity $I_0$ is incident on a polarizer then a polarized light at intensity $I_0/2$ comes out.
Intensity of transmitted beam
$I_t=I_0/2co{s}^{2}45$ from the formula $I=I_{0}co{s}^2\theta$
$I_t=\frac{I_0}{2}\times \frac{1}{2}=\frac{I_0}{4}$