Question

A 225 mW horizontally polarized laser beam passes through a polarizing filter whose axis is 23° from vertical. What is the power of the laser beam as it emerges from the filter?

answer units must be in mW

Answer 1

if you consider that a vertical polariser, in an ideal world, stop 100% of a horizontally polarised beam and if it were at 90° to vertical (i.e. horizontal) then it would pass 100% of the beam. So if you turn it just 23° from vertical it will be passing a possible 100% divided by 90° and multiplied by 23°, which gives 25.55%

If the input beam was 225mW then 25.55% of that is 57.5mW

This assumes perfect world scenario, that the polariser is 100% transmissive when aligned, and 100% opaque when misaligned (not the case in the real world)

Or

Method2)

The plane of polarization of the laser beam is vertical, so it makes an angle of 90⁰- 23⁰ = 67⁰ with the polarizing filter plane.

I = I₀cos²(67⁰)
= 225mW x 0.39²
= 34.35mW