Beams A and B are plane-polarised with perpendicular planes. Initially, a polaroid shows maximum intensity for A and zero for B. Rotating the polaroid by 30^circ makes them look equally bright. Find the ratio of their initial intensities frac I_A I_B .

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EEJ MAIN Physics QUESTION #7044

Question 1

Beams A and B are plane-polarised with perpendicular planes. Initially, a polaroid shows maximum intensity for A and zero for B. Rotating the polaroid by $30^\circ$ makes them look equally bright. Find the ratio of their initial intensities $\frac{I_A}{I_B}$.

$1$
$\frac{1}{3}$✔️
$3$
$\frac{3}{2}$

Correct Answer Explanation

Initially, beam A's plane is parallel to the polaroid ($\theta_A = 0^\circ$) and B's is perpendicular ($\theta_B = 90^\circ$).

After $30^\circ$ rotation, the angles become $30^\circ$ and $60^\circ$ respectively.

Equal brightness means: $I_A \cos^2(30^\circ) = I_B \cos^2(60^\circ)$

$I_A \left( \frac{\sqrt{3}}{2} \right)^2 = I_B \left( \frac{1}{2} \right)^2 \implies I_A \cdot \frac{3}{4} = I_B \cdot \frac{1}{4} \implies \frac{I_A}{I_B} = \frac{1}{3}$.

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