A laser produces linearly polarized light that is polarized in the vertical direction.The light travels in the +y-direction and passes through two polarizers.The polarization axis of the first polarizer is tipped towards the negative x-axis at 24 $\circ$ from vertical (z-axis).The polarization axis of the second polarizer is tipped towards the positive x-axis at 15 $\circ$ from vertical (z-axis).The laser beam is collimated (neither converging nor expanding),has a circular cross section with a diameter of 1.00 mm,and has an average power of 15 mW.What is the average power of the laser beam after passing through both polarizers?

Question

Quizplus · Accepted Answer

The intensity of light after passing through a polarizer is given by 
I = I0 cos^2(θ), 
where I0 is the initial intensity and θ is the angle between the polarization axis of the polarizer and the polarization direction of the incident light.

Applying this formula to the first polarizer, the intensity of light after passing through it is 
I1 = I0 cos^2(24°).

Similarly, the intensity of light after passing through the second polarizer is 
I2 = I1 cos^2(15°) = I0 cos^2(24°) cos^2(15°).

The power of the laser beam is given by P = I0 A c, 
where A is the area of the beam and c is the speed of light.

Since the beam is collimated and has a circular cross-section, its area is A = π (0.5 mm)^2 = 7.85×10^-7 m^2.

After substituting the given values and evaluating, we get 
P = 15 mW × I0/I0 × A c = 7.56 W.

Therefore, the average power of the laser beam after passing through both polarizers is 7.56 W, which corresponds to choice (B).

A Laser Produces Linearly Polarized Light That Is Polarized in the Vertical