Consider three polarizing filters oriented as shown in the figure below. A beam

Question

Consider three polarizing filters oriented as shown in the figure below. A beam of unpolarized light is directed through the three filters. The first filter has a polarization axis along the vertical, the second has its polarization axis rotated at an angle of 24° from the vertical, and the third has its axis along the horizontal.

(a) What fraction of the light intensity comes out of the third filter?

If/Io=

(b) What fraction makes it through the system if the middle filter is removed?

If/Io=

Explanation / Answer

(a)
Let the Intesitty of Light be I.
Using Malus Law,
Intensity of light coming out of 1st Polarizer, = I/2
Intensity of light coming out of 2nd Polarizer, = (I/2) * cos^2(24)
Intensity of light coming out of 3rd Polarizer, = (I/2) * cos^2(24) * cos^2(90-24)

If = 0.069 * I
If/I = 0.069

(b)
If we remove middle Filter,
Intensity of light coming out of 1st Polarizer, = I/2
Intensity of light coming out of 3rd Polarizer, = (I/2) *cos^2(90)
As Cos(90) = 0
Therefore If = 0

If/Io = 0 (i.e No light will come out of the filter.)

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