In a Young's double slit experiment with slit separation $0.1\ \text{mm}$, one observes a bright fringe at angle $\dfrac1{40}\ \text{rad}$ by using light of wavelength $\lambda_1$. When the light of wavelength $\lambda_2$ is used a bright fringe is seen at the same angle in the same set up. Given that $\lambda_1$ and $\lambda_2$ are in visible range ($380\ \text{nm}$ to $740\ \text{nm}$), their values are:
Answer: (C) $625\ \text{nm},\ 500\ \text{nm}$
For a bright fringe $d\sin\theta \approx d\theta = n\lambda$:
$$d\theta = \frac{0.1\times10^{-3}}{40} = 2500\ \text{nm}$$
So $\lambda = \dfrac{2500}{n}\ \text{nm}$: $n = 4$ gives $625\ \text{nm}$, $n = 5$ gives $500\ \text{nm}$ (and $n = 6$ gives $417\ \text{nm}$). Among the options only $625\ \text{nm}$ and $500\ \text{nm}$ both fit.
Solution by Sreeraj P, M.Sc Physics