Two polaroids are set in crossed positions.A third polaroid is placed between the two making an angle `angle` with the pass axis of the first polaroid. Write the expression for the intensity of light transmitted from the second polaroid. In what orientations will the ransmitted intensity be (i) minimum and (ii) maximum.

Explanation

Let polaroids `P_1` and `P_2` be in crossed position. Let the polaroid `P_2` make an angle with the pass axis of polaroid `P_1`
Let `I_1` be the intensity of polarised light emerging our of `P_1` . Then intensity of light after passing through `P_2` will `I_2 = I_1 cos^2 theta`
Since `P_3 and P_1` are in crossed position therefore the angle made by` P_2 ` with `P_3` is ` (pi/2 - theta)`
`therefore ` Intensity of light coming out of `P_3` is
` I_3 = I_2 cos^2 (pi/2 - theta)`
` I_3 = I_2 cos^2 sin^2 theta = I_1 (1/2 sin 20)^2`
If ` I_0` is the intensity of the unpolarised light falling on `P_1` then `I_1 = (I_0)/(2)`
` therefore I_3 = (I_0)/(2) (1/2 sin 20)^2`
(i) Minimum outcoming intensity is zero.
(ii) Maximum outcoming intensity is received when `theta = pi/4`
`therefore (I_3)_(max) = (I_0)/(2) (1/2)^2 = (I_0)/(8) `