In a young's double slit experiment, two slits are illuminated by a mixture of two wavelengths 12000 Å and 10000 Å. At 6.0 mm from the common central bright fringe on a screen 2 m away from the slits, a bright fringe of one interference pattern coincides with the bright fringe of other. Distance between the slits should be

2.0 mm

$x=nλ\frac{D}{d}=(n+1)λ'\frac{D}{d}$

$∴ n × 12000 = (n+1) × 10000$

or n = 5 and $x = nλ\frac{D}{d}$

$∴d=\frac{n\,λ\,D}{x}=\frac{5×12000×10^{-10}×2}{6×10^{-3}}m$

$= 2 × 10^{–3} m = 2 mm$