Question

A clear sheet of polaroid is placed on the top of similar sheet so that their axes make an angle $si{n}^{-1}\left(\frac{3}{5}\right)$ with each other. The ratio of intensity of the emergent light to that of unpolarised incident light is

• A. $16:25$
• B. $9:25$
• C. $4:5$
• D. $8:25$

Answer 1

Answer: (D)

If $l$ is the intensity of the incident unpolarized light, the intensity transmitted by the first is $\frac{l}{2}.$ This is the intensity of incident light on the second polaroid. Intensity transmitted by the second polaroid is $\left(\frac{l}{2}\right){\left(cos\right)}^2\theta ,$ where $\theta$ is the angle between the axes. Here $sin\theta =\frac{3}{5}$ , $cos\theta$ is therefore $\frac{4}{5}.$
$\frac{1}{2}{\cos }^2\theta =\frac{1}{2}\times {\left(\frac{4}{5}\right)}^2=\frac{8}{25}1$
$\frac{8}{25}$ is the required ratio