Question

Unpolarized light passes through three polarizers. The axis of transmission of the first polarizer is vertical, the second has a transmission axis rotated 30.0^o with respect to the first, and the third has a transmission axis rotated 75.0^o relative to the first. If the initial light intensity of the beam is I_o, calculate the light intensity after the beam passes through...

a)The second polarizer

b)The third polarizer

Answer 1

Initial intensity of the beam = I_o  

When an unpolarized light passes through a polariser intensity reduced to half, then intensity I = I_o / 2

so, after first polarizer Intensity of beam, I₁ = I_o / 2

When a polarized light passes through a polariser that is vertical, then intensity, I = I_initial * cos²

here is the angle between two polarizer,

a) so, Intensity of beam after second polariser, I₂ = I₁*cos²₁ =  I₀/2 * cos² (30) =  3/4 * I₀/2

= 3/8 I₀

b)In this case angle ₂ will be angle between second and third polariser,  so ,  ₂ = 75-30 = 45 degree

so, Intensity of beam after second polariser, I₃ = I₂*cos²₂ = 3/8 I₀ * cos²(45) =3/8 * 1/2 * I_o

=  3/16 I_o