Q 12-10-054JEE MainJEE Main 2024 (4 Apr, Shift 1)Medium
Two wavelengths $\lambda_1$ and $\lambda_2$ are used in Young's double slit experiment: $\lambda_1 = 450\ \text{nm}$ and $\lambda_2 = 650\ \text{nm}$. The minimum order of the fringe produced by $\lambda_2$ which overlaps with a fringe produced by $\lambda_1$ is $n$. The value of $n$ is ______.
Numerical value type. Enter your answer.
Answer: 9
Bright fringes overlap when $n_1\lambda_1 = n_2\lambda_2$:
$$450\,n_1 = 650\,n_2 \Rightarrow 9n_1 = 13n_2$$
The smallest whole numbers are $n_1 = 13$, $n_2 = 9$. So $n = 9$.
Solution by Sreeraj P, M.Sc Physics