Optics Question 882

Question: 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 $ I _{A} $ and $ I _{B} $ respectively, then $ \frac{I _{A}}{I _{B}} $ equals

Options:

A) 3

B) $ \frac{3}{2} $

C) 1

D) $ \frac{1}{3} $

Show Answer

Answer:

Correct Answer: D

Solution:

[d] According to malus law, intensity of emerging beam is given by, $ I=I _{0}{{\cos }^{2}}\theta $

Now. $ {I _{A’}}=I _{A}{{\cos }^{2}}30^{o} $

$ {I _{B’}}=I _{B}{{\cos }^{2}}60^{o} $ 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} $



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