Question

If light of intensity ${I_o}$ is incident at an angle $45^\circ$ with optical axis of polaroid, so intensity of emerging light is
(A) ${I_o}$
(B) $0.5{I_o}$
(C) $0.25{I_o}$
(D) zero

Answer 1

In the question intensity of the light is given, and its incident angle is also given, so we can take help from Malus’s law because it gives information about the polarization of light as well as tells about the intensity of the polarized light that passes through a polarizer.

Complete step by step answer:
The polarizer is the optical device used to convert the white light into plane-polarized light. The polarizer can make a light beam a polarized plane beam of light. It can be rotated up to 360 degrees. Due to this device, we can polarize the light that is coming from the light source. In photography, a polarizer is also used in cameras so that we can take better pictures.
The polaroid is the special type of material sheet which can act as a polarizer. We can obtain the intensity of the polarized light that passes through the polarizer with the help of Malus’s law. It gives the relation of the intensity of the incident light that incident on the polarizer with the intensity of the light that emerges through the polarizer. The expression used for intensity calculation is,
$I = {i_o}{\cos ^2}\theta$
Here, ${I_o}$ is the intensity of the incident light and $I$ is the intensity of the emergent light.
In the question, the intensity of the incident light and its incident angle is given, so by substituting values in the above equation, we can obtain the intensity of emerging light.

Therefore, we get
$I = {I_o}{\left( {\cos 45^\circ } \right)^2}$

We know that$\cos 45^\circ = \dfrac{1}{2}$, therefore
$I = {I_o}{\left( {\dfrac{1}{2}} \right)^2}\\\ \implies I = \dfrac{{{I_o}}}{4}\\\ \implies I = 0.25{I_o}$
Therefore, if light of intensity ${I_o}$ is incident at an angle $45^\circ$ with optical axis of polaroid, so intensity of emerging light is $0.25{I_o}$.

So, the correct answer is “Option C”.

Note:
Try to remember the expression obtained from Malus's law and put the correct value of $\cos \theta$ , so that we can obtain the correct answer easily. You can revise the concept of trigonometry for the various values of $\cos \theta$ because wrong values may give incorrect answers.