Question

When a glass plate of refractive index \(1.44\) is introduced in the path of one of the interfering beams, the fringes are displaced by a distance '\(y\)'. If this plate is replaced by another plate of same thickness but of refractive index \(1.66\), the fringes will be displaced by a distance

• A. \(\frac{2y}{3}\)
• B. \(\frac{4y}{5}\)
• C. \(\frac{5y}{4}\)
• D. \(\frac{3y}{2}\)

Hint:

Fringe displacement is proportional to (mu - 1) t.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
When a thin transparent plate of thickness \(t\) and index \(\mu\) covers one slit, the fringes shift by \(\Delta y = \frac{D}{d}(\mu - 1)t\).

Step 2: Key Formula or Approach:
For the same thickness, geometry and wavelength, the shift is proportional to \((\mu - 1)\).

Step 3: Detailed Explanation:
First plate: \(\mu - 1 = 0.44\), shift \(= y\).
Second plate: \(\mu - 1 = 0.66\).
\[ y' = y \times \frac{0.66}{0.44} = \frac{3y}{2} \]
The options \(\frac{2y}{3}\) and \(\frac{4y}{5}\) are smaller than \(y\), but a higher index must shift the fringes more.

Final Answer:
The new shift is \(\frac{3y}{2}\), option (D). \[ \boxed{\frac{3y}{2}} \]