gen-define-diffraction-through-a-single-slit-and-give-one-short-f91c

Define diffraction through a single slit and give one short worked example.

# Diffraction Through a Single Slit ## Definition **Single slit diffraction** occurs when a wave (usually light) passes through a narrow aperture whose width is comparable to the wavelength. The wave spreads out and creates an interference pattern of bright and dark fringes on a screen, with a bright central maximum and progressively dimmer side maxima. ### Condition for Dark Fringes (Minima) The **dark fringes** occur at angles θ given by: $$a \sin \theta = n\lambda$$ where: - *a* = slit width - *θ* = angle from the central axis - *n* = order number (±1, ±2, ±3, ...) [n ≠ 0] - *λ* = wavelength of light --- ## Worked Example **Problem:** A laser beam of wavelength 632 nm passes through a single slit of width 0.15 mm. Find the angle to the first dark fringe. **Solution:** Given: - λ = 632 nm = 632 × 10⁻⁹ m - a = 0.15 mm = 1.5 × 10⁻⁴ m - n = 1 (first minimum) Using: $a \sin \theta = n\lambda$ $$\sin \theta = \frac{n\lambda}{a} = \frac{(1)(632 \times 10^{-9})}{1.5 \times 10^{-4}}$$ $$\sin \theta = 4.21 \times 10^{-3}$$ $$\theta = \sin^{-1}(4.21 \times 10^{-3}) = 0.24°$$ **Answer:** The first dark fringe occurs at **0.24°** from the central maximum.