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  4. Two beams, A and B, of plane polarised light with mutually perpendicular planes of polarisation 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° makes the two beams appear equally bright. If the initial intensities of the two beams are IA and IB respectively, then IA / IB equals

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Q. Two beams, A and B, of plane polarised light with mutually perpendicular planes of polarisation 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 $I_A \, and \, I_B$ respectively, then $I_A / I_B$ equals

JEE MainJEE Main 2014Wave Optics

Solution:

By law of Malus, $I=I_{0} \cos ^{2} \theta$
Now, $I_{A^{\prime}}=I_{A} \cos ^{2} \,30$
$I_{B'}=I_{B} \cos ^{2} \,60$
As $I_{A'}=I_{B'}$
$\Rightarrow I_{A} \times \frac{3}{4}=I_{B} \times \frac{1}{4}$
$\frac{I_{A}}{I_{B}}=\frac{1}{3}$