Three polarizing filters are stacked with the polarizing...

Three polarizing filters are stacked with the polarizing axes of the second and third at 45.0$^\circ$ and 90.0$^\circ$, respectively, with that of the first. (a) If unpolarized light of intensity $I_0$ 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?

Key Concepts

Unpolarized Light

Unpolarized light consists of waves vibrating in multiple planes perpendicular to the direction of propagation. When unpolarized light passes through a polarizing filter, only the component of the electric field aligned with the filter's axis is transmitted, effectively converting the light into linearly polarized light with reduced intensity.

Linear Polarizers

Linear polarizers are optical devices designed to transmit light waves vibrating in only one particular plane. Their function is to selectively absorb or transmit light based on the alignment of the light's electric field with the polarizer’s axis, which can be used to control the polarization state of light in optical systems.

Malus's Law

Malus's Law quantitatively describes how the intensity of polarized light changes when it passes through a polarizer. According to the law, the transmitted intensity is proportional to the square of the cosine of the angle between the light’s polarization direction and the polarizer’s axis. This principle is fundamental when analyzing the transmission of light through multiple polarizers with varying orientations.

Successive Polarization and Polarizer Orientation

When light passes through multiple polarizers arranged at different angles, each polarizer alters the polarization direction of the transmitted light and reduces its intensity according to the cosine-squared relationship. The use of intermediary polarizers between two orthogonal orientations can result in some transmitted light, illustrating the gradual rotation of the polarization direction through a sequence of filters.

Transcript

00:01 We have three polarizers.

00:03 This is one, two, and three.

00:07 And a light of intensity i nod is incident.

00:12 And then we are asked to find after each polarizer what will be the intensity and how the light is polarized.

00:20 So after a first polarizer, the light intensity will be i nod over two.

00:28 And after second polarize, so after first polarizer, the first, light will be i node over 2 and the light is linearly polarized along the axis of the first polarizer.

00:41 So this will be linearly polarized along the first axis.

00:48 First axis.

00:50 So the light after a second polarizer will be the light that came from the first polarizer, which is i node over 2 times the cost.

01:04 The angle it is making is 45 degrees, so we will light a 45 degrees here and square.

01:11 So this will be our i2 intensity of light after the second polarizer.

01:19 This gives us answer which is a 0 .250 times the intensity which is incident.

01:32 I nod.

01:33 So this is the intensity of a light after second polarizer and the light is polarized along the x -axis of a second polarizer so this is polarized along the x -axis of a second polarizer so after third let me make this circle so this is first polarizer this is second polarizer and this is third polarizer so after the third polarizer the light the intensity of light will be the that we got from 2, which is 0 .250 .250 i nod times cost 45...

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