In a Young's double slit experiment, the slits are 2 mm apart and are illuminated with a mixture of two wavelength λ₀ = 750 nm and λ = 900 nm. The minimum distance from the common central bright fringe on a screen 2m from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other is

4.5 mm

From the given data, note that the fringe width (β₁) for λ₁ = 900 nm is greater than fringe width (β₂) for λ₂ = 750 nm. This means that at though the central maxima of the two coincide, but first maximum for λ₁ = 900 nm will be further away from the first maxima for λ₂ = 750nm, and so on. A stage may come when this mismatch equals β₂, then again maxima of λ₁ = 900 nm, will coincide with a maxima of λ₂ = 750 nm, let this correspond to n^th order fringe for λ₁. Then it will correspond to (n+1)^th order fringe for λ₂.

Therefore $\frac{n \lambda_1 D}{d}=\frac{(n+1) \lambda_2 D}{d} \Rightarrow n \times 900 \times 10^{-9}=(n+1) 750 \times 10^{-9} \Rightarrow n=5$

Minimum distance from

Central maxima $=\frac{n \lambda_1 D}{d}=\frac{5 \times 900 \times 10^{-9} \times 2}{2 \times 10^{-3}}=45 \times 10^{-4}$ m = 4.5 mm