Answer to Question #186290 in Optics for Carla

Question

 A beam of vertically polarized linear light is perpendicularly incident on an ideal linear polarizer. Show that if its transmission axis makes an angle of 60° with the vertical only 25% of the irradiance will be transmitted by the polarizer. 

Answer 1

Let the irradiance of beam of polarized light be $I(0)$ then,

According to Malus Law,

$$I(\theta)=I(0)cos^2\theta\ \ \ \ .....(i)$$

where $\theta$ = angle between direction of polarized light and transmission axis

Here $\theta$ = ${60}\degree$

$I(\theta)=$ Irradiance of polarized light after emerging from ideal linear polarizer

On substituting the value of $\theta$ = ${60}\degree$ in equation (i) we get,

$$I(60\degree)=I(0)cos^260\degree\\I(60\degree)=I(0)\times(0.5)^2\\I(60\degree)=0.25I(0)\\\Rightarrow I(60\degree)=25\% \ of \ \ I(0)$$

Hence, 25% of the irradiance will be transmitted by the polarizer if transmission axis makes an angle of 60° with the vertical .