Question

Through what angle the analyzer must be rotated so that the intensity gets reduced to 0.625 of the maximum value

Answer 1

To find:

Angle by which the analyser must be rotated so that the intensity of the electromagnetic wave gets reduced to 0.625 of the max value.

Calculation:

Let the angle of analyser to the plane of vibration of polarised- electromagnetic wave be $\theta$.

Let max intensity be I.

$\boxed{\therefore \: I_{new} = I \times { \cos}^{2} ( \theta)}$

$= > \: (0.625 \times I)= I \times { \cos}^{2} ( \theta)$

$= > \: (0.625 \times \cancel I)= \cancel I \times { \cos}^{2} ( \theta)$

$= > \: { \cos}^{2} ( \theta) = 0.625$

$= > \: \cos( \theta) = 0.79$

$= > \: \theta = 37.41 \degree$

So, final answer is :

$\boxed{ \bold{ \red{ \large{ \: \theta = 37.41 \degree}}}}$