A beam of light consisting of two wavelengths $7000\ \text{Å}$ and $5500\ \text{Å}$ is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is $2.5\ \text{mm}$ and the distance between the plane of slits and the screen is $150\ \text{cm}$. The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is $n\times10^{-5}$ m. The value of $n$ is ______.
Numerical value type. Enter your answer.
Answer: 462
$7000n_1=5500n_2\Rightarrow14n_1=11n_2$; first at $n_1=11$: path $=77000\ \text{Å}=7.7\times10^{-6}\ \text{m}$.
$$y=\frac{7.7\times10^{-6}\times1.5}{2.5\times10^{-3}}=4.62\times10^{-3}\ \text{m}=462\times10^{-5}\ \text{m}$$
Solution by Sreeraj P, M.Sc Physics