Chapter 24, Problem 61P

To determine

The intensity of transmitted beam.

Answer to Problem 61P

  $0.25I_0$ .

Explanation of Solution

Given:

Angle, $\theta =45°$

Formula used:

The intensity of plane polarized light beam incident on polaroid is reduced by the factor $I=I_0{\cos }^2\theta$

Where,

  $\theta$ is the angle between the axis of the polaroid and the initial plane of polarization.

  $I_0$ is the incoming intensity

Calculation:

According to the question, when plane-polarized light hits a sheet oriented at an angle $\theta$ .

Substitute the given value in formula: $I_2=I_1{\cos }^2\theta$ . Here, reduced intensity is $\frac{1}{2}$ .

The equation can be written as

  $I=\frac{1}{2}{\cos }^2\left(45\right)$

Conclusion:

The required value is $0.25I_0$ .