Optics Question 471
Question: In a standard Young’s double-slit experiment with coherent light of wavelength 600 nm, the fringe width of the fringes in the central region (near the central fringe, $ P _{0} $ ) is observed to be 3 mm. An extremely thin glass plate ’ is introduced in front of the first slit, and the fringes are observed to be displaced by 11 mm. Another thin plate is placed before the second slit and it is observed that the fringes are now displaced by an additional 12 mm. If the additional optical path lengths introduced are $ {\Delta _{1}} $ and $ {\Delta _{2}} $ then
Options:
A) $ 11{\Delta _{1}}=12{\Delta _{2}} $
B) $ 12{\Delta _{1}}=11{\Delta _{2}} $
C) $ 11{\Delta _{1}}>12{\Delta _{2}} $
D) None of the above
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ S _{1}=\frac{{\Delta _{1}}D}{d}=11\times {{10}^{-3}} $
$ S _{2}=\frac{{\Delta _{2}}D}{d}=12\times {{10}^{-3}} $
$ \Rightarrow {\Delta _{1}}/{\Delta _{2}}=11/12\Rightarrow 12{\Delta _{1}}=11{\Delta _{2}} $
