Question

There are three polarizers: polarizer A has its transmission axis at 0 degrees relative to the vertical; polarizer B has its transmission axis at 30 degrees to the vertical; and polarizer C has its transmission axis at 90 degrees to the vertical. If you arrange them as A, B, C and light incident on A is unpolarized and has an intensity of 100 W/m^2, what will be the intensity of the light coming out of C? (Hint: When unpolarized light passes through a polarizer, the intensity is reduced by a factor of 1/2 irrespective of the angle).

Answer 1

Consider that the intensity of the unpolarized light is Io
i)
The intensity of light coming out of the first polarizer,
I1 = Io / 2
ii)
The intensity of light coming out of the second polarizer,
I2 = I1 * cos²(30) [According to Malu's law]
I2 = (Io / 2) * 0.75
= 0.375 Io
iii)
The intensity of light coming out of the third polarizer,
I3 = I2 * cos²(90 - 30) [According to Malu's law]
I3 = (0.375) * 0.25
= 0.09375 Io
Substituting the value of Io,
I3 = 0.09375 * 100
= 9.375 W/m²