In a YDSE bi-chromatic light of wavelengths 400 nm and 560 nm are used. The distance between the slits is 0.1 mm and the distance between the plane of the slits and the screen is 1 m. The minimum distance between two successive regions of complete darkness is

28 mm

Let n^th minima of 400 nm coincides with m^th minima of 560 nm then

(2n - 1)400 = (2m - 1)560

⇒ $\frac{2 n-1}{2 m-1}=\frac{7}{5}=\frac{14}{10}=\frac{21}{15}$

i.e. 4th minima of 400 nm coincides with 3rd minima of 560 nm.

The location of this minima is $=\frac{7(1000)\left(400 \times 10^{-6}\right)}{2 \times 0.1}$ = 14 mm

Next, 11th minima of 400 nm will coincide with 8th minima of 560 nm

Location of this minima is $=\frac{21(1000)\left(400 \times 10^{-6}\right)}{2 \times 0.1}$ = 42 mm

∴  Required distance = 28 mm

∴  (d)