SATHEE: Optics 7 Question 9

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) $3 / 2$

(d) $1 / 3$

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Answer:

Correct Answer: 9. (d)

Solution:

By law of Malus i.e. $I = I_{0} \cos^{2} θ$

$Now, \begin{aligned} I_{A^{'}} & = I_{A} \cos^{2} 30^{\circ} \\ I_{B^{'}} & = I_{B} \cos^{2} 60^{\circ} \end{aligned}$

As,

$I_{A}^{'} = I_{B}^{'}$

$I_{A} \cos^{2} 30^{\circ} = I_{B} \cos^{2} 60^{\circ}$

$\Rightarrow I_{A} \frac{3}{4} = I_{B} \frac{1}{4} \Rightarrow \frac{I_{A}}{I_{B}} = \frac{1}{3}$

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Optics 7 Question 9

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