Question

Unpolarized light of intensity 20.0 W/${\mathbf{cm}}^{\mathbf{2}}$is incident on two polarizing filters. The axis of the first filter is at an angle of 25.0° counterclockwise from the vertical (viewed in the direction the light is traveling), and the axis of the second filter is at 62.0° counterclockwise from the vertical. What is the intensity of the light after it has passed through the second polarizer?

Short answer

The intensity of the light after it has passed through the second polarizer 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.

The intensity of the light after it has passed through the second polarizer

The intensity of incident light is

The first polarizer;

The second polarizer;

Hence, the intensity of the light after it has passed through the second polarizer is