GATE 2025 IN – Question 55
The shown Michelson interferometer measures a gas refractive index. Its transparent chamber contains gas of index $n_g\ne1$ at atmospheric pressure. A 532 nm laser produces 30 interference fringes on the screen. A 632.8 nm laser produces ______ fringes (rounded to one decimal place). Neglect beamsplitter width. The surrounding air has refractive index 1.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 24.5 to 25.5
Explanation
The chamber produces optical-path difference $\Delta=2(n_g-1)L$.
Fringe count is $N=\Delta/\lambda$.
For the same optical-path difference, $N_2=N_1\lambda_1/\lambda_2=30(532/632.8)=25.2212\ldots$.
Thus the answer is **25.2**, assuming the same gas index at both wavelengths.