Question

Two Polaroid A and B are kept with their transmission axis at an angle $\theta $ with respect to one another. If the transmitted intensity of light is $I_t$ = $0.75{I_0}$, where $I_0$ is the intensity of light incident on the system, then $\theta $ is:

A) $30^\circ$
B) $45^\circ$
C) $60^\circ$
D) $90^\circ$

Answer 1

Hint: Transmission and incident intensity of the polarized light relation is given by Malus's Law:
$I_t$ = $I_0$ ${\cos ^2}\theta $ ($I_t$ and $I_0$ are the intensities of the transmitted and incident light, $\theta $)
is the angle formed between the two Polaroid)
Using the above relation we will calculate the value of $\theta $.

Complete step by step solution:
Let us discuss some facts about Polaroid and then we will proceed for the calculation part.
Polaroid is a large sheet of synthetic material packed with tiny crystals of a dichroic substance oriented parallel to one another so that it transmits light only in one direction of the electric vector.
Now we will calculate the value of $\theta $.
We have,
${I_t} = {I_0}0.75$ (Given in the question)...............(1)
According to the Malus's Law
${I_t} = {I_0}{\cos ^2}\theta $ ....................(2)
On substituting the value of equation 1 in equation 2
$ \Rightarrow 0.75{I_0} = {I_0}{\cos ^2}\theta $
$ \Rightarrow 0.75 = {\cos ^2}\theta $(Cancelled the common terms)
$ \Rightarrow {\cos ^2}\theta = \dfrac{3}{4}$ (we will remove the square from both sides)
$ \Rightarrow \theta = {\cos ^{ - 1}}\dfrac{{\sqrt 3 }}{2}$ ($\cos30^\circ$ is equal to the ratio of square root three to two)
$ \Rightarrow \theta = {30^\circ}$

Therefore, option (A) is correct.

Note: Polaroid has many applications which are: light usually scatters in all directions but when it's reflected from flat surfaces, it tends to become polarized, used in glass windows of an airplane to control the intensity of light, used to view three dimensional pictures and movies, used as filter in photographic camera, used in the production of plane polarized light, They are used to improve color contrast in oil paintings, used calculators, monitors of laptops having LCD screen, watches, sun glasses etc.