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: Ratio:
$\frac{y'}{y} = \frac{\mu_2 - 1}{\mu_1 - 1} = \frac{0.66}{0.44}$.

Step 2: Simplify:
$\frac{0.66}{0.44} = \frac{66}{44} = \frac32$.

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