Answer to Question #112662 in Optics for Shane

Question

An unpolarized light wave passes through two (2) polarizers whose planes of polarization are 90 degrees apart. We therefore observe that there is no light passing through the 2nd polarizer.

Now we insert a 3rd polarizer between the two polarizers above. You vary the polarization plane of the 3rd polarizer by making it make a full 360-degree turn while observing the light passing through the 3 polarizers. You observe then, that there are 4 angles for which the outgoing light is maximum.

Determine these angles based on the angle of the 1st polarizer, and explain why we observe such maximums.

Answer 1

As per the condition given in the question,

When wave is passing through the two polarize, the intensity of the wave will vary as per given below, $I=I_o\cos^2\theta$ , The intensity of wave become half after passing through the first polarizer.

Now, the intensity of the wave will vary as per the angle between the two polarizer.

Intensity of wave will be maximum if $\theta =0^\circ or\theta=180^\circ$ and intensity of the wave will be minimum if $\theta =90^\circ and 270^\circ$

Now when we will insert another polarizer between the two polarizer sheet, then intensity of the wave will vary as $I=\dfrac{I_o}{2}\cos^2\theta$

Now, when wave will passes through the 3rd polarizer, then the intensity of the wave will vary as per the below, $I_2=\dfrac{I_o \cos^2\theta}{2}\cos^2\theta=\dfrac{I_o}{2}\cos^4\theta$

From the above we can conclude that , if $\theta =0 and \theta = 180$ then intensity of the wave will be maximum and if $\theta =90 and \theta =270$ then the intensity of the wave will be minimum.