Third bright fringe separation, two wavelengths

In Young's double-slit experiment the position of the nth bright fringe is y_n = nλD / d. Two wavelengths give fringes at different positions, and the separation of the third-order fringes is the difference of their positions.

Given: λ₁ = 4300 Å = 4.3 × 10⁻⁷ m, λ₂ = 5100 Å = 5.1 × 10⁻⁷ m, D = 1.5 m, d = 0.025 mm = 2.5 × 10⁻⁵ m, n = 3.

y₁ = 3 × 4.3×10⁻⁷ × 1.5 / 2.5×10⁻⁵ = 7.74×10⁻² m = 77.4 mm
y₂ = 3 × 5.1×10⁻⁷ × 1.5 / 2.5×10⁻⁵ = 9.18×10⁻² m = 91.8 mm

Δy = y₂ − y₁ = 91.8 − 77.4 = 14.4 mm

Directly: Δy = nD(λ₂ − λ₁)/d = 3 × 1.5 × 8×10⁻⁸ / 2.5×10⁻⁵ = 1.44 × 10⁻² m.

Answer: the third-order bright fringes are separated by 1.44 cm (14.4 mm).