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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

Asked in JEE Main 27th Jan 2nd Shift 2024 · Malus's law and polaroids

(1) 60°
(2) 30°
(3) 45°
(4) 90°

Answer: (3) 45°

Step-by-step solution

Middle sheet at θ to the first polaroid, 90°-θ to the last.

I=(I₀)/2 cos²θ sin²θ=(I₀)/8 sin² 2θ.

Maximum at 2θ=90°, i.e. θ=45°.

Why the other options are wrong

(1) Picks an angle where sin² 2θ=3/4, not the maximum.
(2) Same as 60° by symmetry; sin² 2θ is only 3/4 there.
(4) At 90° the sheet is parallel to one crossed polaroid, so the output is zero.

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