Chapter 24, Problem 58P

To determine

The initial polarization direction of incident light.

Answer to Problem 58P

  $60°$ .

Explanation of Solution

Given:

Polarizer are oriented at ${\text{θ}}_2=40°$ .

  $15\%$ of light intensity is passing through both of them.

Formula used:

It is known that: ${\text{I}}_1={\text{I}}_0{\text{cos}}^{\text{2}}{\text{θ}}_1$

Where,

  $I_0$ is initial intensity.

  ${\text{I}}_1$ is intensity after passing the first Polarizer.

  $\theta$ is an angle.

Calculation:

  $I_0$ is initial intensity and ${\text{I}}_1$ will be first intensity after passing the Polarizers,

  ${\text{I}}_1={\text{I}}_0{\text{cos}}^{\text{2}}{\text{θ}}_1$

  $\therefore {\text{I}}_2={\text{I}}_1{\text{cos}}^{\text{2}}{\text{θ}}_2={\text{I}}_0{\text{cos}}^{\text{2}}{\text{θ}}_1{\cos }^2{\text{θ}}_{\text{2}}$

It is given that , only $15\%$ of light intensity is passing through both of them. Hence,

  $0.15{\text{I}}_0={\text{I}}_0{\text{cos}}^{\text{2}}{\text{θ}}_1{\cos }^{2}40°$

  $\therefore {\text{θ}}_1=60°$

Conclusion:

The initial polarization direction of incident light is $60°$ .