In a single-slit diffraction pattern produced using light of wavelength 628 nm, the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right is 30°. Find the slit width in μm.
Physics · Wave Optics · young's dubble slit experiments
JEE Mains 2025 2 April Morning Shift

Question

In a single-slit diffraction pattern produced using light of wavelength 628 nm, the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right is 30°. Find the slit width in μm.

Physics · Wave Optics · young's dubble slit experiments

JEE Mains 2025 2 April Morning Shift

G1 Physics · Accepted Answer

For a single slit, minima occur approximately at θₘ = mλ/d for small diffraction angles. The second minimum on one side is at magnitude θ₂ = 2λ/d, and the third minimum on the opposite side is at θ₃ = 3λ/d. Therefore their total angular separation is θ = θ₂ + θ₃ = 5λ/d. Given θ=30°=π/6: π/6 = 5λ/d ⇒ d = 30λ/π. With λ=628 nm: d = 30×628×10⁻⁹/π m ≈ 6.0×10⁻⁶ m = 6 μm. Answer: 6.