Question

Two polaroid are oriented with their transmission axes making angle of \[30^{\circ}\] with each other. The fraction of incident unpolarised light is transmitted.
A. 37%
B. 37.5%
C. 3.36%
D. 33.6%

Answer 1

Hint:Light turns into linearly polarised light when it passes through a polaroid. According to the Law of Malus, the transmitted intensity is inversely proportional to the square of the amplitude (square of the cosine of the angle between the two polaroid). Malus's Law describes the relationship between polarised light transmission and incident intensity.

Formula used:
${I_t} = {I_0}{\cos ^2}\theta $
($\theta $is the angle created between the two Polaroid, ${I_t},{I_0}$are the intensities of the incident and transmitted light, respectively.)

Complete answer:

Also, the value of ${I_0} = \dfrac{{{I_i}}}{2}$

Before moving on to the calculating portion, let's talk about a few Polaroid facts.
In order to transmit light exclusively in one direction of the electric vector, Polaroid is made of a huge sheet of synthetic material densely packed with small crystals of a dichroic substance that are positioned parallel to one another.

When the angle is 30 degrees, we will now determine the value of the fraction.

According to the Malus's Law,
$ \Rightarrow {I_t} = {I_0}{\cos ^2}30$
$ \Rightarrow \dfrac{{{I_t}}}{{{I_i}}} = \dfrac{1}{2} \times {(\dfrac{{\sqrt 3 }}{2})^2}$
$ \Rightarrow \dfrac{{{I_t}}}{{{I_i}}} = \dfrac{3}{8}$

So converting into percentage we get,
$ \Rightarrow \dfrac{{{I_t}}}{{{I_i}}} = 37.5\% $

So the correct option is B.


Note: Light typically scatters in all directions, but when it reflects from flat surfaces, it tends to become polarised. Polaroid is used in aeroplane glass windows to control light intensity, to view three-dimensional images and movies, as a filter in photographic cameras, to create plane polarised light, to enhance colour contrast in oil paintings, in calculators, and on LCD monitors in laptops