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 $
Show Answer
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 $ .
