Fringe Width in Double-Slit Interference

Steps:

• Fringe width β = λL/d, where λ is wavelength, L is screen distance, d is slit separation.
• From original setup, λ = βd/L = (0.012 m)(0.0001 m)/(2.4 m) = 5 × 10^{-7} m.
• New parameters: L' = 1.8 m, d' = 2 × 0.0001 m = 0.0002 m.
• New β' = λL'/d' = (5 × 10^{-7})(1.8)/(0.0002) = 0.0045 m = 4.5 mm.

Why B is correct:

• β ∝ L/d; new ratio (1.8/2.4)/2 = 0.375, so 0.375 × 12 mm = 4.5 mm, per interference formula.

Why the others are wrong:

• A: 1.5 mm ignores correct scaling of L and d factors.
• C: 0 mm impossible; interference persists with finite β.
• D: 0 mm impossible; interference persists with finite β.

Final answer: B