In a two-slit interference setup, constructive interference occurs when d sin θ = m λ. If d = 0.25 mm and λ = 600 nm, what is sin θ for the first bright fringe (m = 1)?

• A. 0.0024
• B. 0.0240
• C. 0.00024
• D. 0.240

Answer: (A)

In a two-slit setup, bright fringes occur when the path difference matches an integer multiple of the wavelength: d sin θ = m λ. For the first bright fringe, m = 1, so sin θ = λ / d.

Plugging in the values: d = 0.25 mm = 2.5 × 10^-4 m and λ = 600 nm = 6.0 × 10^-7 m gives sin θ = (6.0 × 10^-7 m) / (2.5 × 10^-4 m) = 2.4 × 10^-3, or 0.0024.

Since this is a very small angle, θ ≈ sin θ ≈ 0.0024 rad ≈ 0.14°.