NEET 2025 — Physics solution

NEET2025Physics

The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at $22. 5^{\circ}$ from the polarization axis of one of the polaroids, is ( $I_{0}$ is the intensity of polarised light after passing through the first polaroid):

A
$\frac{I _{0}}{2}$
B
$\frac{I _{0}}{4}$
C
$\frac{I _{0}}{8}$
D
$\frac{I _{0}}{16}$

Solution

Two crossed polaroids are at $9 0^{\circ}$ . The middle polaroid is at angle $θ = 22. 5^{\circ}$ from the first, so it's at $9 0^{\circ} - 22. 5^{\circ} = 67. 5^{\circ}$ from the second.

After first polaroid: $I_{0}$ . After middle: $I_{0} cos^{2} (22. 5^{\circ})$ . After last: $I_{0} cos^{2} (22. 5^{\circ}) cos^{2} (67. 5^{\circ}) = I_{0} cos^{2} (22. 5^{\circ}) sin^{2} (22. 5^{\circ})$ .

Using $2 sin θ cos θ = sin 2 θ$ : $I_{0} \cdot \frac{sin ^{2} ( 2 \times 22. 5 ^{\circ} )}{4} = \frac{I _{0}}{4} sin^{2} (4 5^{\circ}) = \frac{I _{0}}{4} \cdot \frac{1}{2} = \frac{I _{0}}{8}$ .

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