Wave Optics: JEE Mains 2022 June 29 Shift 2

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by $5\times10^{-2}\ \text{m}$ towards the slits, the change in fringe width is $3\times10^{-3}\ \text{cm}$. If the distance between the slits is $1\ \text{mm}$, then the wavelength of the light will be ______ nm.