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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 where beam A has maximum intensity. A rotation of polaroid through 60° makes two beams appears equally intense. If initial intensities of two beams is IA and IB 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 where beam $A$ has maximum intensity. A rotation of polaroid through $60^{\circ}$ makes two beams appears equally intense. If initial intensities of two beams is $I_{A}$ and $I_{B}$ then $\frac{I_{A}}{I_{B}}$ equals

Solution:

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By Malus law
$I'_{A}=I_{A} \cos ^{2} 60^{\circ}$
$I_{B}'=I_{B} \cos ^{2} 30^{\circ}$
$I_{A}'=I' B \therefore I_{A} \times \cos ^{2} 60^{\circ}$
$=I_{B} \cos ^{2} 30^{\circ}$
$I_{A} \times \frac{1}{4}=I_{B} \times \frac{3}{4}$
$\frac{I_{A}}{I_{B}}=3$