Question

A$200\mathrm{mW}$vertically polarized laser beam passes through a polarizing filter whose axis is $35°$ from horizontal. What is the power of the laser beam as it emerges from the filter?

Short answer

The power of the laser beam is$65.8\mathrm{mw}$.

Step-by-step solution

Formula for power of laser beam

When unpolarized light strikes a polarizer, the power of the polarised light that emerges is half that of the unpolarized light.

Incident light that isn't polarised.

So,

$\mathrm{P}={\mathrm{P}}_0{\cos }^2\left(\mathrm{\theta }\right)$

Where,

role="math" localid="1648929202807" ${\mathrm{P}}_0$-Vertically polarized laser beam

$\mathrm{P}$-Power of laser beam

Figure for laser beam with axis of 35°

Figure is,

Calculation for power of laser beam

The beam angle is,

$\mathrm{\theta }={90}^{°}-{35}^{°}$

$={55}^{°}$

The beam's power is determined as follows:

$\mathrm{P}={\mathrm{P}}_0{\cos }^2\left(\mathrm{\theta }\right)$

$=200\mathrm{mW}\times {\cos }^2\left({55}^{°}\right)$

$\mathrm{P}\approx 65.8\mathrm{mW}$