9702/May Jun/11/2016/Q27

Fringes of separation x are observed on a screen 1.00 m from a double slit that is illuminated by
yellow light of wavelength 600 nm.

At which distance from the slits would fringes of the same separation x be observed when using
blue light of wavelength 400 nm?

A 0.33 m
B 0.67 m
C 0.75 m
D 1.50 m

Solution:
Answer: D

For double slits: Separation of slits, a = Dλ / w

where D is the distance of the slits from the screen, λ is the wavelength and w is the fringe spacing

Fringe separation = y = Dλ / a = 1.00 × 600 / a

The same Young’s slit arrangement is being used. So, the slit separation a is the same.

For the blue light,

Wavelength λ = 400nm, Fringe separation = y, Slit separation = a and D = ???

Distance D = ay / λ = a (1.00 × 600 / a) / 400 = 3/2 = 1.50m

Reference: PYQ - May/Jun 2016 Paper 11 Q27