In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by $5 × 10^{-2}m$ towards the slits, the change in fringe width is $3 × 10^{-5}m$. If the distance between the slits is $10^{-3}m$, The wave length of the light used is:

6000 Å

We know that fringe width is given by : $β = Dλ/2d$

In the given problem, wavelength λ and separation between the slits 2d is fixed. 

The fringe width changes due to a change of D (distance of screen from the
slits).

$∴Δβ=ΔD.\frac{λ}{2d}$ or $λ=\frac{Δβ.2d}{ΔD}$

Given that $ΔD = 5 × 10^{-2}m$ (decrease) and $Δβ = 3 × 10^{-5}m$ and $2d = 10^{-3} m$.

$∴λ=\frac{3 × 10^{-5}×10^{-3}}{5 × 10^{-2}}=6× 10^{-7}m=6000 Å$