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A beam of plane-polarised light with a large cross-section and uniform intensity 3.3 W m⁻² falls normally on a polariser of cross-sectional area 3 x 10⁻⁴ m². The polariser rotates about the beam axis at an angular speed of 31.4 rad s⁻¹. The energy of light transmitted through the polariser in one complete revolution is closest to:

1. 1.0 x 10⁻⁵ J
2. 5.0 x 10⁻⁴ J
3. 1.0 x 10⁻⁴ J
4. 1.5 x 10⁻⁴ J

Correct answer: 1.0 x 10⁻⁴ J

Solution

By Malus's law I = I0 cos²(theta); averaged over one rotation, <cos²> = 1/2, so average transmitted intensity = I0/2 = 1.65 W/m². Average transmitted power = (I0/2)*A = 1.65 * 3e-4 = 4.95e-4 W. Period T = 2 pi/omega = 2 pi/31.4 = 0.2 s. Energy per revolution = power * T = 4.95e-4 * 0.2 = 9.9e-5 ~ 1.0e-4 J.

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