Given wavelengths are λ1=650 nm and λ2=550 nm.
Slit separation d=2 mm =2×10−3 m.
Distance to screen D=1.2 m.
For the bright fringes of both wavelengths to coincide at a distance y from the central maximum, we have:
y=n1dλ1D=n2dλ2D
where n1 and n2 are integers representing the order of the fringes.
This simplifies to n1λ1=n2λ2.
n2n1=λ1λ2=650550=1311
The least values for coincidence are n1=11 and n2=13.
The least distance y is given by:
y=n1dλ1D=11×2×10−3650×10−9×1.2
y=11×650×0.6×10−6 m
y=11×390×10−6 m
y=4290×10−6 m
y=429×10−5 m.