Question

A particular beam of light, with an intensity of 440 W/m², is linearly polarized at an angle of +5.00° to the vertical. You have three polarizers, which have their transmission axes aligned as follows:

Polarizer A - the transmission axis is at +19.0° to the vertical;
Polarizer B - the transmission axis is at +72.0° to the vertical;
Polarizer C - the transmission axis is at +25.0° to the vertical.

You will select two of these polarizers, and have the light pass through one and then the other.

(a) If you want to maximize the intensity of the light emerging from the second polarizer, which two polarizers should you select, and in what order should the light pass through them?

(b) For the situation in (a), when you maximize the intensity of the light emerging from the second polarizer, what is that intensity?
___________ W/m²

(c) If, instead, you want to minimize the intensity of the light emerging from the second polarizer, which two polarizers should you select, and in what order should the light pass through them?

(d) For the situation in (c), when you minimize the intensity of the light emerging from the second polarizer, what is that intensity?
____________ W/m²

For the remaining parts of the problem, we now replace the original polarized light by unpolarized light of the same intensity. For reference, the intensity is 440 W/m², and the three polarizers have their transmission axes aligned as follows:

Polarizer A - the transmission axis is at +19.0° to the vertical;
Polarizer B - the transmission axis is at +72.0° to the vertical;
Polarizer C - the transmission axis is at +25.0° to the vertical.

(e) If you want to maximize the intensity of the light emerging from the second polarizer, which two polarizers should you select, and in what order should the light pass through them?

(f) For the situation in (e), when you maximize the intensity of the light emerging from the second polarizer, what is that intensity?
___________ W/m²

(g) If, instead, you want to minimize the intensity of the light emerging from the second polarizer, which two polarizers should you select, and in what order should the light pass through them?

(h) For the situation in (g), when you minimize the intensity of the light emerging from the second polarizer, what is that intensity?
____________ W/m²

Answer 1

a)The light should first pass through A, and then through B . The light should first pass through B, and then through A . Use polarizers A and B, but it does not matter which order they are in . The light should first pass through A, and then through C .The light should first pass through C, and then through A Use polarizers A and C, but it does not matter which order they are in. The light should first pass through B, and then through C The light should first pass through C, and then through B Use polarizers B and C, but it does not matter which order they are in. Use any two polarizers, and it does not matter which order they are in .

Since the light intensity from the polarizer is proportional to the square of the cosine of the difference in angle between the polarization axis of light and the polarizer's transmission axis, we need to minimize this angle in order to achieve maximum intensity. Since we need maximum intensity from the 2 filters, we would like to minimize the angles for the two filters.Since polarizer A has transmission axis at 19°which is closest to 5°. Then, the light coming out of polarizer A would have its polarization axis at 19° and polarizer C has the transmission axis that is closest to 19°.

b)Consider the case when the first polarizer is A. The transmitted beam after passing through filter A has an intensity of W/m².This beam is linearly polarized at an angle of 19°. When this beam is incident on polarizer C then the intensity of the beam coming out of polarizer C is W/m².

c)The light should first pass through A, and then through B .The light should first pass through B, and then through A .Use polarizers A and B, but it does not matter which order they are in. The light should first pass through A, and then through C. The light should first pass through C, and then through A Use polarizers A and C, but it does not matter which order they are in .The light should first pass through B, and then through C The light should first pass through C, and then through B Use polarizers B and C, but it does not matter which order they are in. Use any two polarizers, and it does not matter which order they are in  

Since the frequency of light from the polarizer is proportional to the square of the cosine of the difference in angle between the polarization axis of light and the polarizer's transmission axis, we need to optimize this angle in order to achieve minimal strength.Since polarizer B has transmission axis at 72° which differs most from 5°. Then, the light coming out of polarizer B would have its polarization axis at 72° and polarizer A has the transmission axis that differs most from 72°

d)Consider the case when the first polarizer is B. The transmitted beam after passing through filter B has an intensity of . This beam is linearly polarized at an angle of 72°. When this beam is incident on polarizer A then the intensity of the beam coming out of polarizer A is