JEE Main · 2024 · 27 Jan 2024 · Shift 2 · Wave Optics

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When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of :

(A) $6 0^{\circ}$
(B) $3 0^{\circ}$
(C) $9 0^{\circ}$
(D) $4 5^{\circ}$ ✓ Correct

Answer: (D)

Solution

Unpolarized light of intensity

I_{0}

leaves the first polaroid with intensity

I_{1} = I_{0} /2

. Let the middle polaroid make angle

θ

with the first; since the outer two are crossed, it makes angle

(9 0^{\circ} - θ)

with the third. By Malus's law, the intensity emerging from the third polaroid is

I_{3} = I_{1} cos^{2} θ cos^{2} (9 0^{\circ} - θ) = \frac{I _{0}}{2} cos^{2} θ sin^{2} θ = \frac{I _{0}}{8} sin^{2} (2 θ) .

This is maximum when

sin (2 θ) = 1

, i.e.

θ = 4 5^{\circ}

JEE Main · 2024 · 27 Jan 2024 · Shift 2 · Single correct option

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