In a single-slit diffraction experiment, light of wavelength 480 nm passes through a slit of width 0.10 mm and forms a diffraction pattern on a screen 2.5 m away. What is the width of the central bright fringe on the screen? (Assume small angles and use sin θ ≈ tan θ ≈ θ.)

Correct answer

B. 24 mm

Principle or equation

For single-slit diffraction, the first dark fringe occurs at a sin θ = λ. For small angles, y1 = (λ L) / a. The central bright fringe extends from y = -y1 to y = +y1, so its width is 2y1 = 2λL / a.

Why this answer is correct

Given λ = 480 nm = 480 × 10^-9 m, L = 2.5 m, a = 0.10 mm = 1.0 × 10^-4 m. y1 = (480 × 10^-9 × 2.5) / (1.0 × 10^-4) = (1.2 × 10^-6) / (1.0 × 10^-4) = 0.012 m = 12 mm. The width of the central bright fringe is 2y1 = 24 mm.

Example

If λ = 600 nm, L = 2.0 m, a = 0.20 mm, then y1 = (600e-9 × 2.0)/(0.20e-3) = 0.006 m = 6 mm, so width = 12 mm.