Question

Three polarizing filters are stacked, with the polarizing axis of the second and third filters at 23.0° and 62.0°, respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity 55.0 W/${\mathbf{cm}}^{\mathbf{2}}$after it passes through the stack. If the incident intensity is kept constant but the second polarizer is removed, what is the intensity of the light after it has passed through the stack?

Short answer

The intensity of the light after passing through the stack is

Step-by-step solution

Malus’s law

According to Malus' law, the intensity of plane-polarized light that travels through an analyzer varies as the square of the cosine of the angle between the plane of the polarizer and the analyzer’s transmission axes.

the intensity of polarised light that passes through an analyzer

maximum transmitted light

angle between the polarization axis of light and the analyzer

No matter how the polarising axis is oriented, when unpolarized light is incident on an ideal polarizer, the intensity of the transmitted light is exactly half that of the incident unpolarized light.

The incident wave's E field is divided into two components: one parallel to the polarizing axis and one perpendicular to it. Because the incident light is a random mixture of all polarisation states, these two components are equal on average. Because the perfect polarizer only transmits the component parallel to the polarising axis, only half of the incoming intensity is transferred.

Calculation

The intensity of incident light

The first stack;

The second stack;

The third stack;

Given;

On putting the values;

Intensity of the light after passing through the stack

After removing the second stack;

The first stack;

The second stack;

Hence, the intensity of the light after passing through the stack is