Question

Explain how light bends during diffraction.

Answer 1

Short answer
Diffraction is the bending and spreading of light that happens because light is a wave. When a wavefront meets an obstacle or aperture whose size is comparable to its wavelength, every point on the wavefront acts like a little secondary source. The secondary wavelets interfere with each other and produce a redistributed pattern of intensity — light appears to “bend” into regions that geometric rays would leave dark. The characteristic diffraction angle is about θ ≈ λ/d (wavelength divided by aperture or obstacle size).

Physical picture (Huygens–Fresnel)
- Huygens’ principle: every point on a wavefront can be treated as a source of spherical secondary wavelets.
- The Fresnel idea adds that these wavelets interfere; the interference pattern of all those contributions gives the observed field.
- Near an aperture or edge, interference causes some directions to have constructive reinforcement and others destructive cancellation, so the transmitted light is spread out rather than confined to geometric rays.

Simple formulas and examples
- Single-slit (far-field/Fraunhofer) intensity pattern: I(θ) = I0 [sinβ/β]^2 with β = (π a sinθ)/λ, where a is slit width and λ the wavelength. The first minima occur where a sinθ = ±λ, so the main lobe width is about θ ≈ λ/a.
- Circular aperture → Airy pattern. The central bright spot (Airy disk) angular radius ≈ 1.22 λ/D (D = aperture diameter).
- Rule of thumb: if the aperture or obstacle is much larger than the wavelength (d >> λ), diffraction is negligible; if comparable, diffraction is significant. That’s why visible light (λ ≈ 0.5 μm) hardly diffracts around macroscopic objects, but radio waves (λ cm–m) do.

Quantum viewpoint
- Photons don’t “bend” as tiny particles pushed by a force. Quantum electrodynamics gives the same wave interference result: the probability amplitude for a photon passing an aperture is the superposition of amplitudes from all paths, producing the same diffraction pattern when many photons are detected.

Regimes and more formal theory
- Fresnel (near-field) vs. Fraunhofer (far-field) diffraction. Mathematically, far-field diffraction equals the Fourier transform of the aperture’s transmissivity.
- More complete derivations use the Kirchhoff or Rayleigh–Sommerfeld diffraction integrals and boundary conditions of Maxwell’s equations.

Practical consequences
- Limits resolution of optical instruments (diffraction limit).
- Produces patterns like fringes, Airy disks, and ringing around edges.
- Explains phenomena like light spreading through small openings, diffraction gratings producing spectra, and radio waves bending around buildings.

Summary
Diffraction is a wave-interference effect: secondary wavelets from an aperture or edge interfere and redistribute light, producing apparent bending and spreading. The amount of bending scales roughly with wavelength divided by the size of the feature causing the diffraction.