The axes of the polarizer and analyser are inclined to each other at 450. 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?

Question

The axes of the polarizer and analyser are inclined to each other at 450. 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) (a/2) (B) (a/√2) (C) (√3/2) (D) (3/4)a

Tardigrade Admin · Accepted Answer

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} co s^{2} φ

Intensity after passing through the analyser,

I_{2} = I_{1} (\frac{1}{2})^{2} = \frac{I _{1}}{2} = \frac{I _{0}}{4}

Amplitude,

a \propto I

\frac{a _{2}}{a _{0}} = \frac{I _{2}}{I _{0}} = \frac{I _{0}}{4 I _{0}} = \frac{1}{2}

\Rightarrow a_{2} = \frac{a}{2}

Q. The axes of the polarizer and analyser are inclined to each other at $4 5^{0} .$ 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?

$\frac{a}{2}$

$\frac{a}{2}$

$\frac{3}{2}$

$\frac{3}{4} a$

Q. The axes of the polarizer and analyser are inclined to each other at 450. 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?

2a​

2​a​

23​​

43​a

Q. The axes of the polarizer and analyser are inclined to each other at $4 5^{0} .$ 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?

$\frac{a}{2}$

$\frac{a}{2}$

$\frac{3}{2}$

$\frac{3}{4} a$