(a) What fraction of initially unpolarized light makes it through a polarizer (c

Question

(a) What fraction of initially unpolarized light makes it through a polarizer (call in #1) whose polarization axis is vertical? (b) What is the polarization of light after it passes through polarizer #1? (c) Imagine this now-polarized light incident on polarizer #2 whose polarization axis is horizontal. What fraction of the initial intensity makes it through the two polarizers? (d) Now imagine that polarizer #3 is inserted between #1 and #2 such that its polarization axis is at a 40 degree angle with respect to that of polarizer # 1. What fraction of the initial intensity makes it through all three polarizers? (e) Now imagine the same setup as in (d) but now the 40 degree angle is between polarization axes of polarizers #3 and #2. Does your answer to (d) change? If so, calculate the new value. If not, explain why not. Unpolarized light is incident on a setup of two polarizers, as shown in the figure on the right The first polarizer's polarization axis is vertical, and the second polarizer's polarization is oriented at an angle of theta = 35.0 degree with respect to the first one, as shown in the figure to the right. What fraction of the original intensity of light makes it through both polarizers?

Explanation / Answer

A

Intensity of unpolarized light after passes through a given axis remain half of orginal intensity. This is because initially vibrations are in all the directions. When this light passes through the polarizer intensity is given by

I = I0 cos2()

And average value of cos2() is ½.

So fraction of light which makes it through the polarizer#1 is 50%.

B.

After passing through the polarizer #1 , light have only vibration in vertical plane.   

So, polarization of light through the polarizer #1 is in horizontal direction.

C.

After passing through polarizer #1

According to law of Malus , intensity of polarized light after passing through the polarizer

I =   I0 cos2()

As, = 900

So, fraction of polarized light making it pass through the polarizer#2 is 0%

D.

As, intensity of polarized light after passing through the polarizer = I0 cos2 ()

Angle between polarizer#1 and inserted polarizer is 400

Intensity of light after passing through inserted polarizer = I0 cos2400

Intensity of light after passing through polarizer#2 = I0 cos2400 cos2500

E.

Intensity of light after passes through inserted polarizer when angle is 500= I0 cos2500

Intensity of light after passes through polarizer#2= I0 cos2500cos2400

So, answer does not change and this is because it is the relative angles which matter not the sequence.

                                                                                                                                                

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