Question

Two polaroid are kept crossed to each other. If one of them is rotated an angle\[{{45}^{0}}\], the percentage of incident light now transmitted through the system is
A- 15 %
B- 25 %
C- 50 %
D- 60 %

Answer 1

Hint: A polaroid is a polarizer which is used to restrict the vibrations or oscillations of electric field vectors to only one direction and such light is called plane polarized light. The phenomenon of polarization of light using polarizer is governed by Malus Law.

Complete step by step answer:The polarizers are placed crossed to each other, it means the angle between them is \[{{90}^{0}}\]. Now we rotate them such that the new angle between them is \[{{45}^{0}}\]. We know when an unpolarized light is incident on the polarizer then the intensity of the light coming out of it is just half of the incident.
Using the formula, \[I={{I}_{0}}{{\cos }^{2}}\vartheta \], here \[\vartheta \]is the angle between the polarizer and analyzer.
Let the intensity of unpolarized light be \[{{I}_{0}}\], then the intensity of light coming out of it is \[\dfrac{{{I}_{0}}}{2}\]
Now this is incident on the analyzer, thus intensity of light coming out of it will be,
\[I=\dfrac{{{I}_{0}}}{2}\times \dfrac{1}{2}=\dfrac{{{I}_{0}}}{4}\]
\[\Rightarrow 0.25{{I}_{0}}\]
So, the percentage of incident light now transmitted through the system is 25%
So, the correct option is (B)

Note:One important difference between the polarizer and the analyzer is that polarizer produces plane polarized light and analyzer is used to check whether the light has been polarized or not. The main thing is the angle between them.