JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Wave Optics

A source of light is placed in front of a screen. Intensity of light on the screen is I. Two Polaroids

P_{1}

and

P_{2}

are so placed in between the source of light and screen that the intensity of light on screen is

1/2

P_{2}

should be rotated by an angle of _____ (degrees) so that the intensity of light on the screen becomes

\frac{3 I}{8}

Answer: 30

Solution

Unpolarised light of intensity

I

emerges from the first polaroid with intensity

\frac{I}{2}

. Since the screen still receives

\frac{I}{2}

, Malus' law requires

\frac{I}{2} cos^{2} θ = \frac{I}{2} \Rightarrow cos^{2} θ = 1

so the two pass axes start out parallel. Turning

P_{2}

through an angle

α

from this position,

\frac{I}{2} cos^{2} α = \frac{3 I}{8} \Rightarrow cos^{2} α = \frac{3}{4}

cos α = \frac{3}{2}

and the polaroid must be rotated through

3 0^{\circ}

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Integer answer