(III) Describe how to rotate the plane of polarization of a...

Key Concepts

Successive Polarizer Method

To rotate the plane of polarization while minimizing intensity loss, multiple polarizers can be used in succession. Each polarizer is set at a small angle relative to the previous one, so that the overall rotation accumulates gradually. By carefully choosing the number of polarizers and the small angular differences between them, it is possible to achieve a 90° rotation while maintaining most of the initial intensity, as the losses at each step combine to give an overall small reduction in light intensity.

Malus' Law

Malus' Law quantifies the intensity of polarized light after it passes through a polarizer. It states that the transmitted intensity is proportional to the square of the cosine of the angle between the light’s initial polarization direction and the polarizer's axis. This concept is essential in calculating intensity losses when light is rotated through angles using polarizers.

Polarization

This refers to the orientation of the oscillations of the electromagnetic field in a light wave. In linearly polarized light, the electric field oscillates in a single plane. Understanding polarization is crucial because the behavior of light when passing through devices like polarizers is determined by its polarization state.

Polarizers

Polarizers are optical devices that transmit light oscillating in a specific direction while absorbing or reflecting light polarized in other directions. They are used to control the polarization state of light, and their effectiveness depends on the alignment of their transmission axes relative to the incoming light's polarization.

Transcript

00:01 For this question, it says to describe how to rotate the plane of polarization of a plane polarized beam of light 90 degrees and produce only 10 % lost intensity using polarizers, wherein is the number of polarizers and theta, which are going to be the same for every polarizer is the angle between the successive polarizers.

00:20 So normally if you just had two polarizer or one polarizer and it was at 90 degrees, there would be no light emitted through, right? but for this problem, that's not what we're going to consider.

00:30 We want it to be rotated 90 degrees using lots of polarizers, so 10 % is let through.

00:35 And the intensity of a plane polarized beam transmitted by a polarizer is given by the equation that says that the amount of polarized light, that's transmitted i, is equal to the incoming polarized light.

00:46 For initial polarized light, this is i0, times the cosine squared of the angle of the polarizer, theta.

00:58 So again, i not is the incoming intensity, and theta is the angle between the polarizer.

01:02 Transmission access and the plane of polarization.

01:05 So the number of polarizers for us is n, and we're going to suppose that the angle between successive polarizers is some angle theta prime.

01:15 The percentage of loss intensity is 10%.

01:17 So if n polarizers provide a rotation of 90 degrees, then the angle at which each polarizer of light will have been rotated, which we're going to call theta prime, is going to be equal to 90 degrees divided by n, right? because if n was equal to 1, then it would just be 90 degrees, but we have n polarizers, and we need to figure out how many we need in order for this to be true to 10 % of the light gets through.

01:46 So the intensity of a plane polarized beam transmitted by the first polarizer would be i1 is equal to i0 cosine squared theta prime, right? following that equation, then i2 would be equal to i1 times the cosine squared of theta prime, but i1 was i0 times the cosine squared of theta prime.

02:08 So if you continue this out, you find that in general, for n polarizers, i subn is equal to i0, the initial unpolarized light times the cosine of theta, uh, the co -sign of theta, uh, the cosine squared of theta prime, again, because each individual one has an angle of theta prime, and then this is all raised to the n because this is going to happen n times, right? because i1 is equal to i0 cosine squared theta prime.

02:50 I2 is equal to i1, cosine squared theta prime.

02:53 And so then you plug in i1, which is i not cosine squared theta prime, and it gives you i subn is equal to i not cosine squared theta prime to the end.

03:02 So you can rewrite this just to simplify it a little bit further as i0 times the cosine of theta prime.

03:15 It's right this way to the 2n.

03:27 So on equating this, you can then say that since there is 10 % of loss of intensity in the plane polarized beam, i subn also has to be equal to 0 .9 times i sub not.

03:41 Because 90%, since there's only a 10 % loss, that means 90 % of the original intensity gets through.

03:50 So we have 0 .9 times i sub not is also equal to i sub -n...

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