4. 1 = 30° 5. 2 = 87° Let\'s put it all together in an example. Two Polaroids ar

Question

4. 1 = 30°

5.2 = 87°

Let's put it all together in an example. Two Polaroids are along the z axis as shown in the figure. The planes of the Polaroids are parallel to the xy plane. The polarizing direction is shown as a thick line, at angle theta_1 and theta_2 relative to the x axis, respectively. Unpolarized light of intensity I_a shines on polarizer 1 from the left. After going through the first Polaroid, the intensity is I_1. After through the second Polaroid, the intensity is I_2. If theta_1 = degree, what is the ratio I_1/I_0? If theta_2 = degree, what is the ratio I_2/I_1?

Explanation / Answer

See firstly, when the unpolarized/randomly polarized light(call that intensity I0) hits the first polarizer and emerges polarized along the direction of the polarizing axis, i.e., along the axis inclined at an angle of 30° parallel to the x-axis. Call this polarized light's intensity I1. Now I1 = I0/2, irrespective of what angle the first polarizer makes with the incident unpolarized light.

Now again this polarized light from the first polarizer hits the second polarizer and emerges out(call that intensity I2). This intensity is now given my Malus Law, where I2 = I1 cos²(theta). Now theta is the angle between the polarizing axis of the polarizer and the polarizing direction of the polarized light. This angle theta is thus (theta2 - theta1) = 57°. Thus I2 = I1 Cos²(57°).

I2/I0 = .1483

I2/I1 = .2966

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