One of the slits in Young's double slit experiment is covered with a transparent sheet of thickness $2.9…
One of the slits in Young's double slit experiment is covered with a transparent sheet of thickness $2.9 \times 10^{-3} \mathrm{~cm}$. The central fringe shifts to a position originally occupied by the $25^{\text {th }}$ bright fringe. If $\lambda=5800 Å$, the refractive index of the sheet is
$1.65$
$1.60$
$1.55$
$1.50$
Solution
As it is given that a transparent sheet of certain thickness is inserted, we use
$\begin{aligned}
& (\mu-1) \times \mathrm{t}=\mathrm{N} \lambda \\
& 25 \lambda=(\mu-1) \mathrm{t} \\
& \mu-1=\frac{25 \lambda}{\mathrm{t}}
\end{aligned}$
$\therefore \quad$ The refractive index of the sheet is:
$\begin{aligned}
& \mu=\frac{25 \times 5800 \times 10^{-10}}{2.9 \times 10^{-5}}+1 \\
& \mu=1.50
\end{aligned}$