Question

A horizontal beam of vertically polarized light of intensity 43 $W/m^2$ is sent through two polarizing sheets. The polarizing direction of the first is 60$^\circ$ to the vertical, and that of the second is horizontal. The intensity of the light transmitted by the pair of sheets is (nearly).

• A. $8.1\,W/m^2$
• B. $7.3\,W/m^2$
• C. $6.4\,W/m^2$
• D. $3.8\,W/m^2$

Answer 1

Answer: (A)

$\frac{\text { Intensity after passing through first sheet }}{\text { Incident intensity }}=1-\cos ^{2} \theta$
$
\begin{array}{l}
=1-\cos ^{2} 60^{\circ} \\
=1-\left(\frac{1}{2}\right)^{2}\left(\because \cos 60^{0}=1 / 2\right) \\
=3 / 4
\end{array}
$
So, now intensity is $=\frac{3}{4} \times 43$
$
=32.25 w / m ^{2}
$
again, $\frac{\text { intensity after passing throught second sheet }}{\text { new intersity }}=1-\cos ^{2} \theta$
$
\begin{array}{l}
=1-\cos ^{2} 30^{\circ} \\
=1-\left(\frac{\sqrt{3}}{2}\right)^{2}\left(\because \cos 30^{0}=\frac{\sqrt{3}}{2}\right) \\
=1-\frac{3}{4} \\
=1 / 4
\end{array}
$
So, intensity after passing through second sheet $=\frac{1}{4} \times 32.25$
$
=8.1 w / m ^{2}
$