Question

When an unpolarized light of intensity ${I_0}$ is incident on a polarizing sheet, the intensity of the light which does not get transmitted, is:
(A) Zero
(B) ${I_0}$
(C) $\dfrac{{{I_0}}}{2}$
(D) $\dfrac{{{I_0}}}{4}$

Answer 1

Hint: To solve this question, we need to see the working of a polarizer. We have to observe the effect of a polarizer on the vibration of an electromagnetic wave and then find the intensity of the wave that gets transmitted. The intensity difference between the incident wave and the resultant wave will give us the answer.

Complete step by step solution:
Consider the polarizing sheet through which the un-polarized light is passed. We know that a light is the visible part of the electromagnetic spectrum. So it is an electromagnetic wave. Let it move along the x axis, so that its electric field and magnetic field vibrate in the y-z plane, as shown below.

As we can see above, the axis of the polarizing sheet is parallel to the y-axis. So, it will allow the vibrations in the y-direction only. So, all the vibrations, which are along the z-axis will not get transmitted. Since all the oscillations of the light are uniformly distributed in the y-z plane, therefore half of the original intensity of the light gets transmitted after passing through the polarizing sheet as shown below.

Therefore, the intensity of the light which does not get transmitted is
$\Rightarrow I = {I_0} - \dfrac{{{I_0}}}{2}$
$\Rightarrow I = \dfrac{{{I_0}}}{2}$
Hence, the correct answer is option C.

Note:
The polarization of light, which is discussed in the above question, is used in many daily life applications. For example, the sunglasses, which are generally used by the drivers for protecting their eyes from the sunlight, are made of the polarizing material. Also, it is used for improving the microscopy of the transparent tissues. This is done by using a double refracting material and a polarizer in succession. This technique is used in the field of medicines and in the study of the rock materials.