Question

Plane polarised light is passed through an analyser and the intensity of emerging light is reduced by $75\%$. Optical vibrations make an angle $\theta$ with the axis of analyser. Then $\theta$ is.
A. ${60^0}$
B. ${45^0}$
C. ${50^0}$
D. ${58^0}$

Answer 1

In this solution, finding the direction of the light intensity by using Malus law $I = {I_0}{\cos ^2}\alpha$.

Complete step by step solution:
With the law of Malus, the light intensity is given by $I = {I_0}{\cos ^2}\alpha$ after a polarizer passes through. Where $\alpha$is the angle between polarization direction and axis is the polarizer.
Given,
$\dfrac{I}{{{I_0}}} = 0.75$
So,
$\begin{array}{c}{\cos ^2}\alpha = 0.75\\\\\alpha = 3{0^0}\end{array}$
However, the optical vibration is perpendicular to the axis of polarization.
Thus,
$\begin{array}{c}\theta + \alpha = 9{0^0}\\\\\theta = 9{0^0} - {30^0}\end{array}$
Therefore, $\theta = 6{0^0}$

Hence, the required answer is $6{0^0}$, option A.

Additional information:

Plane polarised light: Light which oscillates in only one plane. Light that is not polarised. In both directions, the electric field oscillates. Event that contributes to polarization. The term polarized plane refers to the direction in which linear polarized light or other electromagnetic radiation is polarized. As described initially in 1811 by Étienne-Louis Malus.

Malus law: The law states that after passing through a rotative polarizer the intensity of a plane-polarized light beam varies as a square of an angle cosine by which the polarizer is rotated from a position which gives maximum intensity. The light being emitted becomes polarized when it comes to a polarizer. Polarized light, called an analyzer, falls on another Polaroid, transmits light depending on the axes' location with the polarizer. Malus' law provides the strength of light that is transmitted through the analyser.
The intensity of emerging light: The intensity of the emerging light transmitted has 1/2 the intensity of the emerging light incident (perpendicular portion blocked). The material transmission axis is the direction of polarization of the light moving through the material.

Note: First, finding the direction of the light intensity by using Malus law $I = {I_0}{\cos ^2}\alpha$, then subtract it from ${90^0}$because , the optical vibration is perpendicular to the axis of polarization.