Optics Question 863
Question: A monochromatic light is used in Young’s double slit experiment when one of the slits is covered by a transparent sheet of thickness 1.8 mm, made of material of refractive index $ {\mu _{1}} $ number of fringes which shift is 18, when another sheet of thickness 3.6 mm, made of material of refractive index $ {\mu _{2}} $ is used, number of fringes which shift is 9. Relation between $ {\mu _{1}} $ and $ {\mu _{2}} $ is given by
Options:
A) $ 4{\mu _{2}}-{\mu _{1}}=3 $
B) $ 4{\mu _{1}}-{\mu _{2}}=3 $
C) $ 3{\mu _{2}}-{\mu _{1}}=4 $
D) $ 2{\mu _{1}}-{\mu _{2}}=4 $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ (\mu -1)t=n\beta $
$ \frac{({\mu _{1}}-1)\times 1.8\times {{10}^{-5}}}{({\mu _{2}}-1)\times 3.6\times 10^{5})}=\frac{18\beta }{9\beta } $
$ ({\mu _{1}}-1)=4({\mu _{2}}-1) $
$ 4{\mu _{2}}-{\mu _{1}}=3 $
