Optics Question 858
Question: A plane wave of monochromatic light falls normally on a uniform thin layer of oil which covers a glass plate. The wavelength of source can be varies continuously. Complete destructive interference is observed for $ \lambda =5000\overset{o}{\mathop{A}} $ and $ \lambda =1000\overset{o}{\mathop{A}} $ and for no other wavelength in between. If $ \mu $ of oil is 1.3 and that of glass is 1.5, the thickness of the film will be
Options:
A) $ 6.738\times {{10}^{-5}}cm $
B) $ 5.7\times {{10}^{-5}}cm $
C) $ 4\times {{10}^{-5}}cm $
D) $ 2.8\times {{10}^{-5}}cm $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] In this case, both the rays suffere a phase change of $ 180{}^\circ $
and the conditions for destructive interference is $ 2nd=( m+\frac{1}{2} ){\lambda _{1}} $
and $ 2nd=( m+\frac{3}{2} ){\lambda _{2}} $
$ \therefore \frac{m+\frac{1}{2}}{m+\frac{3}{2}}=\frac{{\lambda _{2}}}{{\lambda _{1}}}=\frac{5000}{700}=\frac{5}{7} $
and $ d=\frac{( m+\frac{1}{2} ){\lambda _{1}}}{2n}=\frac{2.5\times 7000}{2\times 1.3} $
$ =6.738\times {{10}^{-5}}cm $
