Question

Unpolarized light of intensity Io is incident on a polarizer whose transmission axis makes an angle of zero degrees with the vertical. A second polarizing plate is placed after the first. The transmission axis of the second plate makes an angle phi with the vertical.

a) sketch a graph of the transmitted intensity vs the angle phi. your angle should vary from 0 to pi/2.

b) at what value of phi does the slope of your graph have its greatest magnitude? this value of phi is known as the opening point of maximum sensitivity.

c) Suppose the second polarizing plate is adjusted to be at this operating point. If the plane of polarization of light rotates by a small amount delta phi, by how much does the transmitted intensity change?

Answer 1

a)Let the intensity of the unpolarised light be . The inetensity of the light reduces by 1/2 after passing throigh the first polariser. And after passing through the second polariser is

To make the plot, let

Then the transmitted intensity is

Plot is shown below

b) The slope of the graph is maximum when

Hence

Hence the slope is maximum at

This is the opening point of maximum sensitivity. At this point the intensity is

where is the intensity of the unpolarised light incident on the first polariser which we had taken to be 2 W/m².

c) If the angle is changed by small amount around then the change can be found out using Taylor expansion

Therefore the change in intensity of the transmitted light is