^Malus law

Let I₀ be the intensity and ‘A’ the amplitude of the unpolarized light falling on the polarizer & θ be the angle between the pass axis of the polaroid & amplitude vector, then the component Acosθ, parallel to the pass axis (y) of polarizer passes through it & the component Asinθ, perpendicular to pass axis is blocked by the polarizer, thus the intensity of light transmitted by the polarizer is

I = k (A cosθ)² = k A² cos² θ

or         I = I₀ cos² θ        [called Malus law

Actually the phase angle for a beam of unpolarised light can have any value from 0⁰ to 360⁰. Now as the average value of cos² θ for the range 0⁰ to 360⁰ is 0.5, thus the average intensity of light transmitted by a polarizer is only 0.5 I₀.  Following observations can be explained on the basis of Malus law.

1. Two polarizes with parallel pass axis (y & y)

2. Two polarizes with crossed pass axis (y & z)