JEE Main 2026 — Apr 4, Shift 2 — Physics solution

JEE Main2026Apr 4, Shift 2Physics

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at 30° and 90°, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at 60° with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is _____.

A
3/4
B
4/3
C
9/4
D
4/9

Solution

Without third polarizer (two polarizers at 30° and 90°): unpolarized $I_{0} \to \frac{I _{0}}{2}$ after first polarizer; angle between axes is $90° - 30° = 60°$ .

$I_{w i t h o u t} = \frac{I _{0}}{2} cos^{2} 60° = \frac{I _{0}}{2} \cdot \frac{1}{4} = \frac{I _{0}}{8}$ .

With third polarizer (axes at 30°, 60°, 90°): successive angles are 30° then 30°.

$I_{w i t h} = \frac{I _{0}}{2} cos^{2} 30° \cdot cos^{2} 30° = \frac{I _{0}}{2} \cdot \frac{3}{4} \cdot \frac{3}{4} = \frac{9 I _{0}}{32}$ .

$\frac{I _{w i t h}}{I _{w i t h o u t}} = \frac{9 I _{0} /32}{I _{0} /8} = \frac{9}{32} \cdot 8 = \frac{9}{4}$ .

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