Q 12-10-141JEE MainJEE Main 2019 (9 Apr, Shift 1)Easy
In a Young's double slit experimental setup (slit separation $a$, screen at distance $D$), when a thin transparent sheet of thickness $t$ and refractive index $\mu$ is put in front of one of the slits, the central maximum gets shifted by a distance equal to $n$ fringe width. If the wavelength of light used is $\lambda$ then $t$ will be
Answer: (B) $\dfrac{n\lambda}{(\mu - 1)}$
The sheet adds an optical path $(\mu - 1)t$, which shifts the pattern by $(\mu - 1)t\dfrac Da$. Setting this equal to $n$ fringe widths $n\dfrac{\lambda D}{a}$:
$$(\mu - 1)t = n\lambda \Rightarrow t = \frac{n\lambda}{\mu - 1}$$
Solution by Sreeraj P, M.Sc Physics