Optics 7 Question 9
9. 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
(2014 Main)
(a) 3
(b) $3 / 2$
(c) 1
(d) $1 / 3$
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Solution:
- By law of Malus i.e. $I=I _0 \cos ^{2} \theta$
$$ \text { Now, } \quad \begin{aligned} I _{A^{\prime}} & =I _A \cos ^{2} 30^{\circ} \\ I _{B^{\prime}} & =I _B \cos ^{2} 60^{\circ} \end{aligned} $$
As,
$$ I _A^{\prime}=I _B^{\prime} $$
$$ I _A \cos ^{2} 30^{\circ}=I _B \cos ^{2} 60^{\circ} $$
$$ \Rightarrow \quad I _A \frac{3}{4}=I _B \frac{1}{4} \Rightarrow \frac{I _A}{I _B}=\frac{1}{3} $$
