Two beams, A and B, of plane polarized light with mutually… | JEE Main 2014

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Polarisation

Two beams, $A$ and $B$ , of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity), a rotation of polaroid through $30^\circ$ makes the two beams appear equally bright. If the initial intensities of the two beams are $\mathrm{I}_A$ and $\mathrm{I}_B$ respectively, then $\frac{\mathrm{I}_A}{\mathrm{I}_B}$ equals:

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Answer: (d)

Initially the polaroid axis is along A's plane, so B's plane is at $90^\circ$ to it.
After rotating by $30^\circ$ : A transmits $I_A\cos^2 30^\circ$ , B transmits $I_B\cos^2 60^\circ = I_B\sin^2 30^\circ$ .
Equal brightness: $I_A \cdot \frac{3}{4} = I_B \cdot \frac{1}{4} \Rightarrow \frac{I_A}{I_B} = \frac{1}{3}$
So the answer is (d) $\frac{1}{3}$ .

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Polarisation question from JEE Main 2014

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