Question

A beam of plane polarised light of large cross sectional area and uniform intensity of $3.3 Wm ^{-2}$ falls normally on a polariser (cross sectional area $3 \times 10^{-4} m ^{2}$ ) which rotates about its axis with an angular speed of $31.4 rad / s$. The energy of light passing through the polariser per revolution, is close to :

• A. $1.0 \times 10^{-5} J$
• B. $5.0 \times 10^{-4} J$
• C. $1.0 \times 10^{-4} J$
• D. $1.5 \times 10^{-4} J$

Answer 1

Answer: (B)

Intensity, $I_{0}=3.3 Wm ^{-2}$
Area, $A=3 \times 10^{-4} m ^{2}$
Angular speed, $\omega=31.4 rad / s$
Average energy $\left.=I_{0} A<\cos ^{2} \theta\right\rangle$
$\because\left\langle\cos ^{2} \theta\right\rangle=\frac{1}{2}$ per revolution
$\therefore$ Average energy $=\frac{(3.3)\left(3 \times 10^{-4}\right)}{2} \simeq 5 \times 10^{-4} J$