Q34E
Question
Three polarizing filters are stacked with the polarizing axes of the second and third at 45.0° and 90.0°, respectively, with that of the first. (a) If unpolarized light of intensity is incident on the stack, find the intensity and state of polarization of light emerging from each filter. (b) If the second filter is removed, what is the intensity of the light emerging from each remaining filter?
Step-by-Step Solution
Verified(a) The intensity and state of polarization of light emerging from each filter is
(b) There is no intensity of light.
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.
(a) The intensity of the incident light
The first polarizer;
The polarisation is the same as the first polarizer.
The second polarizer;
The polarisation is parallel to the second polarizer axis. establishing a angle with the first polarizer axis.
The third polarizer;
The polarisation is in the same direction as the third polarizer axis, forming a 45-degree angle with the second polarizer axis and a 90-degree angle with the first polarizer axis.
Hence, the intensity and state of polarization of light emerging from each filter is
(b) The second filter is removed;
The intensity of the incident light
The first polarizer;
The polarisation is the same as the first polarizer.
The second polarizer;
Hence, there is no intensity of light.