Question

2. Initially unpolarized light of intensity I, is passed through three polarizing filters. The second and third filters have axes of transmission at the given angles with the axes of transmission for the first filter. a) What is the intensity of light passing through the first filter? b) What is the intensity of light after passing through the second filter? c) What is the intensity of light after passing through the third filter?

Answer 1

a)
When an unpolarized light passes through a polarizer, its intensity reduces to half of its original value irrespective of the orientation of the filter.
The intensity of light passing through the first filter, I1 = Io / 2
= (1.30 * 10^-12) / 2
= 0.650 * 10^-12 W/m²

b)
According to Malu's law,
I2 = I1 * cos²$\theta$1
Where I1 is the intensity of the already polarized light.
I2 is the intensity of the light coming through the second polarizer.
$\theta$ 1 is the angle of the second polarizer with respect to the first polarizer.

Here, I1 = 0.650 * 10^-12 W/m² and $\theta$ 1 = 15 degrees
Substituting values,
I2 = (0.650 * 10^-12) * cos²(15)
= 0.606 * 10^-12 W/m²

c)
Again using Malu's law,
I3 = I2 * cos²$\theta$2
Where I2 is the intensity of the polarized light coming from the second polarizer.
I3 is the intensity of the light coming through the third polarizer.
$\theta$ 2 is the angle of the third polarizer with respect to the second polarizer.

Here, I2 = 0.606 * 10^-12 W/m²
$\theta$ 2 = 37 - 15 = 22 degrees
Substituting values,
I2 = (0.606 * 10^-12) * cos²(22)
= 0.521 * 10^-12 W/m²