Optics Question 574

Question: Two polaroids are placed in the path of unpolarized beam of intensity $ I _{0} $ such that no light is emitted from the second polaroid. If a third polaroid whose polarization axis makes an angle q with the polarization axis of first polaroid, is placed between these polaroids then the intensity of light emerging from the last polaroid will be

[UPSEAT 2005]

Options:

A) $ ( \frac{I _{0}}{8} ){{\sin }^{2}}2\theta $

B) $ ( \frac{I _{0}}{4} ){{\sin }^{2}}2\theta $

C) $ ( \frac{I _{0}}{2} ){{\cos }^{4}}\theta $

D) $ I _{0}{{\cos }^{4}}\theta $

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Answer:

Correct Answer: A

Solution:

No light is emitted from the second polaroid, so $ P _{1} $ and $ P _{2} $ are perpendicular to each other

Let the initial intensity of light is $ I _{0} $ .

So Intensity of light after transmission from first polaroid = $ \frac{I _{0}}{2} $ .

Intensity of light emitted from $ P _{3} $

$ I _{1}=\frac{I _{0}}{2}{{\cos }^{2}}\theta $ Intensity of light transmitted from last polaroid i.e. from $ P _{2}=I _{1}{{\cos }^{2}}(90^{o}-\theta ) $ = $ \frac{I _{0}}{2}{{\cos }^{2}}\theta .{{\sin }^{2}}\theta $

$ =\frac{I _{0}}{8} $

$ {{(2\sin \theta \cos \theta )}^{2}} $ = $ \frac{I _{0}}{8}{{\sin }^{2}}2\theta $ .



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