Using the monochromatic light of same wavelength in the experimental set-up of the diffraction pattern as well as in the interference pattern where the slit separation is 1mm. 10 interference fringes are found to be within the central maximum of the diffraction pattern. Determine the width of the single slit, if the screen is kept at the same distance from the slit in the two cases.

For Diffraction pattern
For interference pattern
Wavelength λ is same
D is same for both.
Linear width of the central max. of single slit is given by,
y = (2Dλ/a)
a = Width of slit
y = x (given)
For both (given)
d = Slit separation
d = 1mm = 10⁻³m
β = Fringe width
β = (λD/d)
N = 10 fringes
So, x = 10β = (10λD/d)
10 fringes are found within central maxima
2Dλ/a = 10λD/d
a = d/5 = 1mm/5 = 0.2mm
Thus, width of the single slit = a = 0.2mm