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(A) According to Malus's law,the intensity of transmitted light is $I = I_0 \cos^2 	heta$,where $I_0$ is the incident intensity and $	heta$ is the a

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$10^{-4} \, J$

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(A) According to Malus's law,the intensity of transmitted light is $I = I_0 \cos^2 	heta$,where $I_0$ is the incident intensity and $	heta$ is the angle between the polarization direction and the polarizer axis.Since the polarizer is rotating,$	heta$ varies from $0$ to $2\pi$ in one revolution.The average intensity $I_{av}$ is given by $I_{av} = \frac{1}{2\pi} \int_0^{2\pi} I_0 \cos^2 	heta \, d	heta = \frac{I_0}{2}$.The incident power $P = 10^{-3} \, W$. The incident intensity $I_0 = \frac{P}{A} = \frac{10^{-3}}{3 	imes 10^{-4}} = \frac{10}{3} \, W/m^2$.The average power transmitted is $P_{av} = I_{av} 	imes A = \frac{I_0}{2} 	imes A = \frac{P}{2} = \frac{10^{-3}}{2} = 0.5 	imes 10^{-3} \, W$.The time period for one revolution is $T = \frac{2\pi}{\omega} = \frac{2 	imes 3.14}{31.4} = 0.2 \, s$.The energy passing through the polarizer per revolution is $E = P_{av} 	imes T = (0.5 	imes 10^{-3}) 	imes 0.2 = 10^{-4} \, J$.

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