Optics Question 457
Question: Two Polaroids are placed in the path of unpolarised 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 $ \theta $ with the polarization axis of first polaroid, is placed between these polaroids then the intensity of light emerging from the last polaroid will be
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}}2\theta $
D) $ I _{0}{{\cos }^{4}}\theta $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] 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{}^\circ -\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 $
