A system of three polarizers $\mathrm{P}_{1}, \mathrm{P}_{2}, \mathrm{P}_{3}$ is set up such that the pass axis of $\mathrm{P}_{3}$ is crossed with respect to that of $\mathrm{P}_{1}$. The pass axis of $\mathrm{P}_{2}$ is inclined at $60^{\circ}$ to the pass axis of $\mathrm{P}_{3}$. When a beam of unpolarized light of intensity IO is incident on $\mathrm{P}_{1}$, the intensity of light transmitted by the three polarizers is I. The ratio (Io/I) equals (nearly) :

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Wave Optics

A system of three polarizers

P_{1}, P_{2}, P_{3}

is set up such that the pass axis of

P_{3}

is crossed with respect to that of

P_{1}

. The pass axis of

P_{2}

is inclined at

6 0^{\circ}

to the pass axis of

P_{3}

. When a beam of unpolarized light of intensity IO is incident on

P_{1}

, the intensity of light transmitted by the three polarizers is I. The ratio (Io/I) equals (nearly) :

Answer: (A)

Unpolarised light loses half its intensity through the first polariser, leaving

\frac{I _{0}}{2}

. Since

P_{3}

is crossed with

P_{1}

and

P_{2}

lies

6 0^{\circ}

from

P_{3}

P_{2}

sits

3 0^{\circ}

from

P_{1}

. By Malus's law through

P_{2}

\frac{I _{0}}{2} cos^{2} 3 0^{\circ} = \frac{3 I _{0}}{8}

, and then through

P_{3}

a further

6 0^{\circ}

on,

\frac{3 I _{0}}{8} cos^{2} 6 0^{\circ} = \frac{3 I _{0}}{32}

. So

\frac{I _{0}}{I} = \frac{32}{3} \approx 10.67

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option