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 ${60}^0$ 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)

8.1 W/m${}^2$

$\frac{Intensityafterpassingthroughfirstsheet}{Incidentintensity}=1-co{s}^2\theta$
$=1-co{s}^2{60}^0$
$=1-\left(\frac{1}{2}{)}^2\right(\because cos{60}^0=1/2)$
$=3/4$
So, now intensity is $=\frac{3}{4}\times 43$
$=32.25w/m^2$
again, $\frac{intensityafterpassingthroughtsecondsheet}{newintersity}=1-co{s}^2\theta$
$=1-co{s}^2{30}^0$
$=1-\left(\frac{\sqrt{3}}{2}{)}^2\right(\because cos{30}^0=\frac{\sqrt{3}}{2})$
$=1-\frac{3}{4}$
$=1/4$
So, intensity after passing through second sheet $=\frac{1}{4}\times 32.25$
$=8.1w/m^2$