MHT CET · Physics · Wave Optics
On replacing a thin film of mica of thickness \(12 \times 10^{-5} \mathrm{~cm}\) in the path of one of the interfering beams in Young's double slit experiment using monochromatic light, the fringe pattern shifts through a distance equal to the width of bright fringe. If \(\lambda=6 \times 10^{-5} \mathrm{~cm}\), the refractive index of mica is
- A 1.1
- B 1.3
- C 1.5
- D 1.4
Answer & Solution
Correct Answer
(C) 1.5
Step-by-step Solution
Detailed explanation
The equation for the shift in the fringe pattern is given as,
\(\mathrm{n} \lambda=(\mu-1) \mathrm{t}\)
\(\therefore \quad\) Refractive index of mica is:
\(\begin{array}{ll}
& \mu=\frac{\mathrm{n} \lambda}{\mathrm{t}}+1 \\
\therefore \quad & \mu=\frac{1 \times 6 \times 10^{-5}}{12 \times 10^{-5}}+1=0.5+1 \\
\therefore \quad & \mu=1.5
\end{array}\)
\(\mathrm{n} \lambda=(\mu-1) \mathrm{t}\)
\(\therefore \quad\) Refractive index of mica is:
\(\begin{array}{ll}
& \mu=\frac{\mathrm{n} \lambda}{\mathrm{t}}+1 \\
\therefore \quad & \mu=\frac{1 \times 6 \times 10^{-5}}{12 \times 10^{-5}}+1=0.5+1 \\
\therefore \quad & \mu=1.5
\end{array}\)
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