Question

What will be the intensity (irradiance) of the transmitted light when an unpolarized beam of irradiance I0 is incident on four ideal linear polarizers, where the first transmission axis is vertical, the second is inclined at 45o to the vertical, the third is horizontal, and the fourth is 30o to the horizontal. Repeat when the second polarizer is removed without disturbing the first, third, and the fourth.

Answer 1

for the first polarizer :

I_o = intensity of unpolarized light

I₁ = intensity of light from the first polarizer = I_o /2

for the second polarizer :

= 45 deg

I₂ = intensity of light from the second polarizer = I₁ Cos² = (I_o /2 ) Cos²45 = I_o /4

for the third polarizer :

= 45 deg

I₃ = intensity of light from the third polarizer = I₂ Cos² = (I_o /4 ) Cos²45 = I_o /8

for the fourth polarizer :

= 30 deg

I₄ = intensity of light from the fourth polarizer = I₃ Cos² = (I_o /8 ) Cos²30 = 3I_o /32

when second polarizer is removed :

for the first polarizer :

I_o = intensity of unpolarized light

I₁ = intensity of light from the first polarizer = I_o /2

for the third polarizer :

= 90 deg

I₃ = intensity of light from the third polarizer = I₁ Cos² = (I_o /2 ) Cos²90 = 0

for the fourth polarizer :

= 30 deg

I₄ = intensity of light from the fourth polarizer = I₃ Cos² = (0 ) Cos²30 = 0