Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# Two polaroid are kept crossed to each other. If one of them is rotated at an angle $60{}^\circ ,$ the percentage of incident light now transmitted through the system is.

Last updated date: 17th Jun 2024
Total views: 372.9k
Views today: 4.72k
Verified
372.9k+ views
Hint: When the two polaroid is kept across to each other one of them have rotated angle of $60{}^\circ$, So, we have the intensity of polarized light as ${{I}_{0}}$ so the intensity of the first polaroid is $\dfrac{{{I}_{0}}}{2}$. Using the given information the equation. $I={{I}_{0}}{{\cos }^{2}}\theta$. Which can be written as ${{I}_{0}}=\dfrac{{{I}_{0}}}{2}{{\cos }^{2}}\theta$ and it used for finding the answer.

Complete step by step solution:When the two polaroid are kept crossed to each other. If one of them is rotated at an angle of $60{}^\circ$
Let,
The intensity of un polarized light be ${{I}_{0}},$ So, the intensity of the first polaroid is $\dfrac{{{I}_{0}}}{2}$
On rotating through $60{}^\circ .$ The intensity of light from sound polaroid.
As we have, $I={{I}_{0}}{{\cos }^{2}}\theta$
$\therefore I=\left( \dfrac{{{I}_{0}}}{2} \right){{\left( \cos 60{}^\circ \right)}^{2}}$
$=\dfrac{{{I}_{0}}}{2}\times \dfrac{1}{4}$
$=\dfrac{{{I}_{0}}}{8}$
$\therefore I=0.125{{I}_{0}}$
Therefore,
Percentage of incident light transmitted through the system $=0.125\times 100=12.5%$
Hence,
The required percentage is $12.5%$