Question

In Young's experiment, one of the slit is covered with a transparent sheet of thickness \(3.6\times 10^{-3}\) cm due to which position of central image shifts to a position originally occupied by \(30^{th}\) bright fringe. The refractive index of the sheet is (\(\lambda =6000\ \text{Å}\))

• A. \(1.5\)
• B. \(1.2\)
• C. \(1.3\)
• D. \(1.7\)

Hint:

Shift of the central fringe equals the number of fringes shifted times the fringe width.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
A thin sheet of thickness \(t\) and refractive index \(\mu\) over one slit adds an extra optical path \((\mu-1)t\).
If the central image moves to the position of the \(30^{th}\) bright fringe, this path difference equals \(30\lambda\).

Step 2: Set up the Equation
\((\mu-1)t=30\lambda\)

Step 3: Calculation
\(30\lambda=30\times 6000\times 10^{-8}\ \text{cm}=1.8\times 10^{-3}\ \text{cm}\)
\(\mu-1=\dfrac{1.8\times 10^{-3}}{3.6\times 10^{-3}}=0.5\)

Step 4: Compare the options
\(\mu=1.5\), which is option (A).

Final Answer:
The refractive index of the sheet is 1.5. \[ \boxed{\text{(A) }1.5} \]