MHT CET · Physics · Wave Optics
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
- A \(1.65\)
- B \(1.60\)
- C \(1.55\)
- D \(1.50\)
Answer & Solution
Correct Answer
(D) \(1.50\)
Step-by-step Solution
Detailed explanation
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:
\(
\begin{aligned}
& \mu=\frac{25 \times 5800 \times 10^{-10}}{2.9 \times 10^{-5}}+1 \\
& \mu=1.50
\end{aligned}
\)
\(
\begin{aligned}
& (\mu-1) \times \mathrm{t}=\mathrm{N} \lambda \\
& 25 \lambda=(\mu-1) \mathrm{t} \\
& \mu-1=\frac{25 \lambda}{\mathrm{t}}
\end{aligned}
\)
\(\therefore \quad\) The refractive index of the sheet is:
\(
\begin{aligned}
& \mu=\frac{25 \times 5800 \times 10^{-10}}{2.9 \times 10^{-5}}+1 \\
& \mu=1.50
\end{aligned}
\)
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