Given, intensity of light falling on screen is I.
Intensity of light when
P1 and
P2 placed between screen and source is I/2.
As per Malus’s law, the intensity of transmitted light when passing through a pair of polariser and analyser having angle ϕ between their axis is given as
I=I0cos2ϕ
Initially let us consider the angle between analyser and polariser is 0°.
Then, the intensity of transmitted light is I / 2. Thus, intensity of light become I / 2 after transmitting through 1st polariser as shown in the figure.
If we rotate the polarise
P2 by angle ϕ, then the resulting intensity of light on screen will be
3/∕8.
Now, for second condition, apply Malus’s law,
=cos2ϕ cos2ϕ= ⇒
cosϕ= ϕ = 30°.
Thus,
P2 should be rotated by
30° to get intensity of light
31/∕8 on screen.