Optics Question 845
Question: From a medium of index of refraction $ n _{1} $ , monochromatic light of wavelength $ \lambda $ is incident normally on a thin film of uniform thickness L $ (whereL>0.1\lambda ) $ and index of refraction $ n _{2} $ . The light transmitted by the film travels into a medium with refractive index $ n _{3} $ .The value of minimum film thickness when maximum light is transmitted If $ (n _{1}<n _{2}<n _{3})$ is
Options:
A) $ \frac{n _{1}\lambda }{2n _{2}} $
B) $ \frac{n _{1}\lambda }{4n _{2}} $
C) $ \frac{\lambda }{4n _{2}} $
D) $ \frac{\lambda }{2n _{2}} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Equation of path difference form maxima in transmission (or weak reflection)
$ \Delta P _{opt}=2n _{2}L=\frac{{\lambda _{vacuum}}}{2},\frac{3{\lambda _{vacuum}}}{2}…. $
$ \Rightarrow 2( \frac{n _{2}}{n _{1}} ) $
$ L=\frac{\lambda }{2} $ , $ \frac{3\lambda }{2}……\Rightarrow L=\frac{\lambda }{4n _{2}} $
(notice that $ \lambda $ = wavelength in medium is related to $ {\lambda _{vacuum}} $ as, $ {\lambda _{vacuum}}=n _{1}\lambda $ )
