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Chapter 29: Problem 26

Polarized light is incident on a sheet of polarizing material, and only \(20 \%\) of the light gets through. Find the angle between the electric field and the material's transmission axis.

Short Answer

Expert verified
The angle between the electric field and the material's transmission axis is 胃 = arccos(sqrt(0.20)).

Step by step solution

01

Identify Given Values

Given that the light intensity after passing through the polarizer is 20% or 0.20 of the original light intensity, so I = 0.20*I0.
02

Apply Malus's Law

According to Malus's Law, the intensity of the polarized light after passing through the polarizer follows the equation I=I0cos^2(胃). Substitute I with 0.20*I0.
03

Solve for 胃

The equation becomes 0.20*I0 = I0cos^2(胃). Divide both sides by I0, and we get 0.20 = cos^2(胃). Take the square root of both sides to isolate cos(胃), which gives cos(胃) = 卤 sqrt(0.20). We only consider the positive value since the angle between the electric field and the polarizing filter cannot be negative. So, cos(胃) = sqrt(0.20).
04

Find the angle

To find the angle 胃, we use the inverse cosine or arccos, and so 胃=arccos(sqrt(0.20)), which can be calculated using a scientific calculator.

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