Optics - Diffraction Grating

Consider a single-slit diffraction pattern for a slit of width d. It is observed that for a light of wavelength 400 nanometers, the angle between the first minimum and the central maximum is 4 × 10⁻³ radians. The value of d is

A. 1 × 10⁻⁵ m
B. 5 × 10⁻⁵  m
C. 1 × 10⁻⁴  m
D. 2 × 10⁻⁴ m
E. 1 × 10⁻³ m

(GR9677 #57)

Solution:

Single slit diffraction: d sin θ = mλ

λ = 400 nm = 4 × 10⁻⁷ m
θ = 4 × 10⁻³ radians
sin θ ≈ θ for small θ

dθ = mλ
d = mλ / θ = 1 × (4 × 10⁻⁷) / (4 × 10⁻³) = 10⁻⁴ m

Answer: C