Question

The angle between polariser and analyser is ${30}^{\circ }$. The ratio of intensity of incident light and transmitted by the analyser is
A. $3:4$
B. $4:3$
C. $\sqrt{3}:2$
D. $2:\sqrt{3}$

Answer 1

Hint: In this question, the angle between polariser and analyser is given to us. So, we use the law of Malus to solve this question. To solve this question we make the ratio of the intensity of incident light and transmitted light as the subject in the law of Malus formula and solve the equation.

Formula used:
Law of Malus , $I=I_{0}co{s}^2\theta$
The angle between the analyser and the polariser is represented by $\theta$.
The intensity of incident light is represented by $I_0$.
The intensity of transmitted light is represented by $I$.

Complete step by step answer:
From the law of Malus,
$I=I_{0}co{s}^2\theta$
The angle between polariser and analyser is given as ${30}^{\circ }$
Substituting this in the equation
$I=I_{0}co{s}^2({30}^{\circ })$
We are asked to find the ratio of intensities
${\displaystyle \frac{I}{I_0}}=co{s}^2({30}^{\circ })$
$\therefore {\displaystyle \frac{I}{I_0}}=({\displaystyle \frac{\sqrt{3}}{2}}{)}^2={\displaystyle \frac{3}{4}}$
Hence the ratio of ${\displaystyle \frac{I}{I_0}}$ is equal to ${\displaystyle \frac{3}{4}}$

Hence,option A is the correct answer.

Additional information:
The process of transforming unpolarized light into polarized light is known as polarization. Unpolarized light has the direction of propagation of the wave in multiple directions, whereas a polarized light has the direction of propagation of its light only in one direction. This angle at which the light is getting polarized can also be found from the law of Malus.

Note: The angle between polariser and analyser is the angle which the slit of the polariser and analyser make. The law of Malus states that the intensity of a beam of plane-polarized light after passing through a rotatable polarizer varies as the square of the cosine of the angle through which the polarizer is rotated from the position that gives maximum intensity.