Question

A 200 mW horizontally polarized laser beam passes through apolarizing filter whose axis is 25 degrees fromvertical.

What is the power of the laser beam as it emerges from thefilter?

Answer 1

Concepts and reason

The concept required to solve this problem is Malus law.

Initially solve for the angle between the light's initial polarization direction and the axis of the polarizer. Then, use the Malus law to calculate the emerging power.

Fundamentals

The law of Malus gives the intensity of emerging light pulse.

$I = {I_0}{\cos ^2}\theta$

Here, ${I_0}$ is the initial intensity, and $\theta$ is the angle between the light's initial polarization direction and the axis of the polarizer.

The incident light is horizontally polarized. The polarizer makes an angle of $25^\circ$ to the vertical. The angle between the horizontal and vertical is $90^\circ .$ Thus, angle between the light's initial polarization direction and the axis of the polarizer is,

$\begin{array}{c}\\\theta = 90^\circ - 25^\circ \\\\ = 65^\circ \\\end{array}$

The Power is directly proportional to Intensity of light.

$P \propto I$

Here, P is the power, and I is the intensity.

Substitute $P$ for $I$ in the law of malus equation $I = {I_0}{\cos ^2}\theta$.

$P = {P_0}{\cos ^2}\theta$

Substitute $200{\rm{ mW}}$ for ${P_0}$, and $65^\circ$ for $\theta$ in the above equation $P = {P_0}{\cos ^2}\theta$ and calculate $P$ the power of the laser beam as it emerges from the filter.

$\begin{array}{c}\\P = \left( {200{\rm{ mW}}} \right){\cos ^2}65^\circ \\\\ = 35.72{\rm{ mW}}\\\end{array}$

Ans:

The power of the laser beam as it emerges from the filter is $35.72{\rm{ mW}}$.