In a single-slit diffraction experiment, light of wavelength 600 nm passes through a slit of width 0.20 mm and forms a diffraction pattern on a screen 2.0 m away. What is the distance between the center of the central bright fringe and the first dark fringe?
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Correct answer
B. 6.0 mm
Principle or equation
For single-slit diffraction, the first dark fringe occurs when a sin θ = λ. For small angles, sin θ ≈ tan θ = y/L, so y = λL/a.
Why this answer is correct
Given λ = 600 nm = 600 × 10^-9 m, L = 2.0 m, a = 0.20 mm = 0.20 × 10^-3 m. y = (600 × 10^-9 × 2.0) / (0.20 × 10^-3) = (1.2 × 10^-6) / (2.0 × 10^-4) = 6.0 × 10^-3 m = 6.0 mm.
Example
If λ = 500 nm, L = 1.0 m, a = 0.10 mm, then y = (500e-9 * 1.0)/(0.10e-3) = 5.0 mm.
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