Chapter 24, Problem 80GP

(a)

To determine

The angle at which the two axes should be placed for the given factor.

Answer to Problem 80GP

  $60°$

Explanation of Solution

Given:

Additional factor of $4$

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:

If the original intensity is $I_0$ , first Polaroid sheet will reduce the intensity of the original beam to $I_1=\frac{1}{2}{I}_0$ . If the axis of the second Polaroid sheet is oriented at an angle $\theta$ , the intensity is $I_2=I_1{\cos }^2\theta$

Substitute the given value in formula: $I_2=I_1{\cos }^2\theta$

  $I_2=I_1{\cos }^2\theta =0.25I_1$

  $\theta =60°$

(b)

To determine

The angle at which the two axes should be placed for the given factor.

Answer to Problem 80GP

  $72°$ .

Explanation of Solution

Given:

Additional factor of $10$

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:

If the original intensity is $I_0$ , first Polaroid sheet will reduce the intensity of the original beam to $I_1=\frac{1}{2}{I}_0$ . If the axis of the second Polaroid sheet is oriented at an angle $\theta$ , the intensity is $I_2=I_1{\cos }^2\theta$

Substitute the given value in formula: $I_2=I_1{\cos }^2\theta$

  $I_2=I_1{\cos }^2\theta =0.10I_1$

  $\theta =72°$

(c)

To determine

The angle at which the two axes should be placed for the given factor.

Answer to Problem 80GP

  $84°$ .

Explanation of Solution

Given:

Additional factor of $100$

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:

If the original intensity is $I_0$ , first Polaroid sheet will reduce the intensity of the original beam to $I_1=\frac{1}{2}{I}_0$ . If the axis of the second Polaroid sheet is oriented at an angle $\theta$ , the intensity is $I_2=I_1{\cos }^2\theta$

Substitute the given value in formula: $I_2=I_1{\cos }^2\theta$

  $I_2=I_1{\cos }^2\theta =0.010I_1$

  $\theta =84°$