You have three polarizers that can be placed on an optical rail between an unpol

Question

You have three polarizers that can be placed on an optical rail between an unpolarized light source and a detector. Polarizer 1 is oriented horizontally (theta1=0 degrees), polarizer 2 is oriented at an angle of theta2=40 degrees from the horizontal, and the orientation of polarizer 3 is vertical (theta3=90 degrees from the horizontal). You conduct serveral trials by passing the unpolarized light through one or more of these polarizers. In each case, determine the fraction of the initial intensity Io that reaches the detector. Show all work and express your answers as fractions or decimals in terms of Io (i.e. I = 1/2 Io)

a) Polarizer 1

b) Polarizers 1 and 2

c) Polarizers 2 and 3

d) Polarizers 1,2,and 3

e) Polarizers 1 and 3

Explanation / Answer

a) Polarizer 1

?=0o

Let I0 be the intensity of the unpolarized light. Then the intensity of light after passing through polarizer 1 [?=0o] is

I1= 1/2Io

b) Polarizers 1 and 2

Let I0 be the intensity of the unpolarized light. Then the intensity of light after passing through polarizer 1 [?=0o] is

I1= 1/2Io

The intensity of light after passing through polarizer 2[?=40o] is

I2=I1cos2[45o-0o]=1/2Io *cos2[45o-0o]= 1/4Io

c) Polarizers 2 and 3

Let I0 be the intensity of the unpolarized light. The intensity of light after passing through polarizer 2 [?=40o ] is

I2=I0cos2[45o-0o]= 1/2Io

The intensity of light after passing through polarizer 3 [?=90o ] is

I3=I2cos2[90o-45o]= 1/2Io *cos2[90o-45o]=1/4Io

d) Polarizers 1, 2, and 3

Let I0 be the intensity of the unpolarized light. Then the intensity of light after passing through polarizer 1 [?=0o] is

I1= 1/2Io

The intensity of light after passing through polarizer 2[?=40o ] is

I2=I1cos2[45o-0o]=1/2Io *cos2[45o-0o]= 1/4Io

The intensity of light after passing through polarizer 3 [?=90o] is

I3=I2cos2[90o-45o]= 1/4Io *cos2[90o-45o]=1/8Io

e) Polarizers 1 and 3

Let I0 be the intensity of the unpolarized light. Then the intensity of light after passing through polarizer 1 [?=0o] is

I1= 1/2Io

The intensity of light after passing through polarizer 3 [?=90o ] is

I3=I1cos2[90o-45o]= 1/2Io *cos2[90o-45o]=1/4Io

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