The width of each slit should be 0.2 mm, option A.
How to find width?
This essentially means that the width of the central maximum in the single-slit pattern should be ten times the width of each double-slit fringe. Therefore:
Width of central maxima in a single slit diffraction = 2λD / a
Fringe width in double slit pattern:
β = λD / d
Applying the Values:
d = 1mm (slit separation which is 10⁻³ m)
λ = 500nm (500 × 10⁻⁹ m)
d = 10⁻³ m
D = 1 mm
Substituting the formulas for each width:
10 × β = 2λD / a
Simplifying:
10 × λD/d = 2λD / a
Solving for a:
a = d / 5 mm
a = 0.2 mm
Therefore: a = 0.2 mm
Conclusion:
For ten double-slit maxima to fit within the central maximum of the single-slit pattern, the width of each slit should be 0.2 mm. So, the correct answer is (a) 0.2 mm