A linearly polarized beam of light of intensity I 0 is propagating in the + z di

Question

A linearly polarized beam of light of intensityI0 is propagating in the +z direction and its direction of polarization makes an angle of 70° with the x-axis (the angle between the initial direction of polarization and the transmission axis of the first polarizer is 20° as described below). Two linear polarizing sheets are lined up perpendicular to the beam. The first sheet has its transmission axis at an angle q 1 = 90° with respect to thex-axis. The transmission axis of the second is variable. (See lower panels of the figure.)

(a) Calculate the intensity I1 of the light after it has passed through the first polarizer. Express your answer as a fraction of I0.

I1 / I0 =        

(b) Calculate the electric field amplitudeE1 of the light after it has passed through the first polarizer. Express your answer as a fraction of the electric field amplitude E0 of the initial beam.

E1 / E0 =       

(c) The second polarizer is set at various angles within the rangeq 2 = 0 to 90°.Calculate the intensity of the light after it has passed through thesecond polarizer for the following values of q 2. Express each answer as a fractionof I1.

At q 2 = 0°:   I2 / I1 =     

At q 2 = 27°:   I2 / I1 =     

At q 2 = 90°:   I2 / I1 =

Explanation / Answer

Given: Initially the polarization of light with intensity Io has polarization at an angle of 70° w.r.t. x-axis.

1st polarizer has transmission axis perpendicular to x-axis.

Part a) When light having polarization at 70° w.r.t. x-axis passes through 1st polarizer with transmission axis perpendicular to x-axis will allow light to pass through according to law of Malus given by I1 = Io cos2q. Where q is the angle between transmission axis and polarization of light. In this case it is 90° - 70° = 20°.

So I1/Io = cos220°

b) Intensity is proportional to square of amplitude. So E1/Eo = sqrt(I1/Io) = cos 20°.

c) Now in case q2 = 0° w.r.t. x axis

In this case angle between transmission axis of Polarizer 1 and 2 is 90°. So according to Law of Malus

I2/I1 = cos2 90° = 0

for q2 = 27° angle between Polarizer 1 and 2 is 90° - 27° = 63°.

I2/I1 = cos2 63° = .20

for q2 = 90° angle between Polarizer 1 and 2 is 90° - 90° = 0°

I2/I1 = cos2 0° = 1

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