A linearly polarized electromagnetic wave is sent through two sheets of polarizing material. The first sheet, A, is oriented so that its transmission axis makes an angle of 30° with respect to the incident electric field of the wave. The second sheet, B, is oriented so that its transmission axis makes an angle of 90° with the incident electric field of the wave. The incident beam has an electric field of peak magnitude E₀ and average intensity S₀.
-What is the average intensity of the wave after it passes through B?

Question

A linearly polarized electromagnetic wave is sent through two sheets of polarizing material. The first sheet, A, is oriented so that its transmission axis makes an angle of 30° with respect to the incident electric field of the wave. The second sheet, B, is oriented so that its transmission axis makes an angle of 90° with the incident electric field of the wave. The incident beam has an electric field of peak magnitude E₀ and average intensity S₀.

-What is the average intensity of the wave after it passes through B?

Quizplus · Accepted Answer

When a linearly polarized electromagnetic wave passes through a polarizing material, the transmitted intensity is given by Malus's law:

I = I0 cos²θ

where I0 is the incident intensity and θ is the angle between the transmission axis and the direction of the electric field.

For the first sheet A, the angle between its transmission axis and the incident electric field is 30°, so the transmitted intensity is:

I1 = I0 cos²30° = 0.75I0

For the second sheet B, the angle between its transmission axis and the incident electric field is 90°, so it blocks all of the incident electric field. Therefore, the intensity of the wave after it passes through B is zero.

The average intensity of the wave after it passes through B is just the averaged intensity of the transmitted wave through A, which is:

I_avg = 0.5 I1 = 0.5(0.75I0) = 0.375I0

Substituting the given expressions for I0 and SS1U1B0, we get:

I_avg = 0.375(ES1U1B10S1U1B0)(c/μ0) = 0.19SS1U1B10S1U1B0

Therefore, the correct answer is (A).

A Linearly Polarized Electromagnetic Wave Is Sent Through Two Sheets