Plane polarized light is incident on a single polarizing disc with the direction of vibrations parallel to the direction of the transmission axis. Through what angle should the disc be rotated so that the intensity in the transmitted beam is reduced by a factor of 4?

Explanation

To solve the problem, we need to determine the angle through which the polarizing disc should be rotated so that the intensity of the transmitted beam is reduced by a factor of 4. Here’s a step-by-step solution:

### Step 1: Understand the relationship between intensity and angle
When plane polarized light passes through a polarizer, the intensity of the transmitted light (I) is related to the initial intensity (I₀) and the angle (θ) between the light's polarization direction and the polarizer's transmission axis by Malus's Law:
\[ I = I_0 \cos^2(\theta) \]

### Step 2: Set up the equation for intensity reduction
According to the problem, the intensity is reduced by a factor of 4. Therefore, we can express this as:
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