Question Detail
Question
Light of wavelength 5.0 × 10⁻⁷ m was used to illuminate a diffraction grating. If the second bright fringe was displaced a vertical distance of 2.5 mm from the central axis and the distance of the screen from the grating is 1 m, calculate the slit width.
Correct Answer
Option A is the correct answer.
Detailed Explanation
For a diffraction grating, d sin θ = mλ. y = 2.5 mm = 2.5 × 10⁻³ m, L = 1 m, so tan θ ≈ sin θ ≈ θ = y/L = 2.5 × 10⁻³. d = mλ / sin θ = (2 × 5.0 × 10⁻⁷) / (2.5 × 10⁻³) = 10⁻⁶ / 2.5 × 10⁻³ = 4 × 10⁻⁴ m = 0.4 mm. None of the options match. If the grating has slit width 'a', for a single slit, the first minimum is at a sin θ = λ. For the second bright fringe of a grating, the condition is d sin θ = mλ. The problem likely asks for the grating spacing (d). The calculated d is 0.4 mm, which is not an option. There might be a misprint in the question or options.
Hint
For a diffraction grating, d sin θ = mλ. Use small angle approximation: sin θ ≈ y/L.