Chapter 24, Problem 30Q

To determine

To explain: The effect on unpolarized light if a person align four polarized sheets with respect to the one in front of it.

Explanation of Solution

Introduction:

A plane polarized light can be obtained from an un-polarized light using Polaroid sheet. A Polaroid sheet can be defined as an orientation of long molecules which are arranged in parallel to one another.

The intensity of a plane polarized beam of light is given by: $I=I_0{\cos }^2\theta$

When the half of the light is eliminated, then the intensity can be given as: $I=\frac{1}{2}{I}_0$

Here, $I_0$ is the incoming intensity.

According to the given statement, the intensity of the first sheet can be given as: $I_1=\frac{1}{2}{I}_0$

The intensity of the next sheet can be written as:

  $\begin{array}{l}{I}_2=I_1{\cos }^2{30}^0\\ I_2=\left(\frac{1}{2}{I}_0\right){\cos }^2{30}^0\\ I_2=0.375I_0\end{array}$

Similarly, next polarized sheets have the intensities as follows:

  $\begin{array}{l}{I}_3=I_2{\cos }^2{30}^0\\ I_3=\left(0.375I_0\right){\cos }^2{30}^0\\ I_3=0.28125I_0\end{array}$

  $\begin{array}{l}{I}_4=I_3{\cos }^2{30}^0\\ I_4=\left(0.28125I_0\right){\cos }^2{30}^0\\ I_4=0.2109I_0\end{array}$

Hence, when each polarized sheet is rotated at an angle of ${30}^0$ then 21% of the light will travel through them.

Conclusion:

21% of the light will pass through each of the polarized sheet.