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

Answer 1

Answer: (A)

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