gen-define-diffraction-at-small-apertures-and-give-one-short-wor-f378

Define diffraction at small apertures and give one short worked example.

# Diffraction at Small Apertures ## Definition **Diffraction** is the bending and spreading of waves when they pass through an aperture (opening) or around obstacles. When the aperture size is comparable to or smaller than the wavelength of the wave, significant diffraction occurs, causing the wave to spread out rather than travel in straight lines. At small apertures, waves don't simply pass straight through—they fan out on the other side, creating characteristic interference patterns. --- ## Worked Example **Problem:** A laser beam (wavelength λ = 632 nm) passes through a single slit of width *a* = 0.1 mm. Find the angular width of the central bright maximum on a screen far from the slit. **Solution:** For single-slit diffraction, the first minimum occurs at angle θ given by: $$a \sin\theta = m\lambda$$ where *m* = 1 for the first minimum. $$\sin\theta = \frac{\lambda}{a} = \frac{632 \times 10^{-9} \text{ m}}{0.1 \times 10^{-3} \text{ m}} = 6.32 \times 10^{-3}$$ For small angles: θ ≈ sin θ = 6.32 × 10⁻³ rad = **0.36°** The **angular width of the central maximum** = 2θ = **0.72°** (or 12.6 × 10⁻³ rad) This shows the wave spreads significantly despite the aperture being much larger than the wavelength.