Question

The axes of the polarizer and analyser are inclined to each other at $45^{0}.$ If the amplitude of the unpolarised light incident on the polarizer is $'a',$ then what is the amplitude of the light transmitted through the analyser?

• A. $\frac{a}{2}$
• B. $\frac{a}{\sqrt{2}}$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{3}{4}a$

Answer 1

Answer: (A)

Let the intensity of unpolarised light be $I_{0}$
Intensity after passing through the polariser, $I_{1}=\frac{I_{0}}{2}$
By law of Malus,
$I=I_{0}cos^{2}\varphi$
Intensity after passing through the analyser,
$I_{2}=I_{1}\left(\frac{1}{\sqrt{2}}\right)^{2}=\frac{I_{1}}{2}=\frac{I_{0}}{4}$
Amplitude, $a \propto \sqrt{I}$
$\frac{a_{2}}{a_{0}}=\sqrt{\frac{I_{2}}{I_{0}}}=\sqrt{\frac{I_{0}}{4 I_{0}}}=\frac{1}{2}$
$\Rightarrow a_{2}=\frac{a}{2}$