Question

Compare and contrast reflection, refraction, and diffraction.

Answer 1

Brief definitions
- Reflection: when a wave bounces off a boundary and returns into the medium it came from.
- Refraction: when a wave crosses into a different medium and changes direction because its speed changes.
- Diffraction: when a wave spreads out or bends around obstacles or through apertures, especially when those features are comparable in size to the wavelength.

How they arise (mechanism)
- Reflection: boundary conditions at an interface cause part of the incident energy to be sent back. Can be analyzed with ray optics or with wave-boundary conditions (Fresnel equations).
- Refraction: arises because the wave speed (and thus wavelength) changes in a new medium; Huygens’ principle explains the bending of wavefronts at the interface.
- Diffraction: Huygens–Fresnel principle: every point on a wavefront acts as a source of secondary wavelets whose superposition produces bending and interference when unobstructed symmetry is broken (aperture, edge, grating).

Key laws / formulas
- Reflection: law of reflection — angle of incidence = angle of reflection (measured from the normal).
- Refraction: Snell’s law — n1 sinθ1 = n2 sinθ2; wavelength changes so v = c/n and frequency remains constant.
- Diffraction:
- Single-slit minima: a sinθ = mλ (m = ±1, ±2, …).
- Double-slit maxima: d sinθ = mλ.
- Grating: d sinθ = mλ (sharp maxima).
- Regimes: Fraunhofer (far-field) and Fresnel (near-field).

Dependence on wavelength and scale
- Reflection: occurs at any scale; detailed angular/phase behavior depends on surface properties. Specular vs diffuse reflection depends on surface roughness relative to wavelength.
- Refraction: depends on wavelength via dispersion (n = n(λ)), so different wavelengths bend by different amounts (prism dispersion).
- Diffraction: strongest when obstacle/aperture size is comparable to wavelength; negligible when wavelength ≪ object size (geometrical optics limit).

Effects on frequency, wavelength, phase, and amplitude
- Frequency: remains the same for reflection and refraction (in lossless media); for diffraction the local frequency is unchanged.
- Wavelength: unchanged by reflection, changes in refraction (λ2 = λ1 n1/n2).
- Phase: reflections may introduce phase shifts (π phase shift on reflection from a medium of higher refractive index). Refraction may alter phase accumulation through travel in new medium. Diffraction patterns arise from interference of components with different path lengths/phase.
- Amplitude/energy: incident energy is partitioned into reflected and transmitted (and possibly absorbed); Fresnel equations give reflection/transmission coefficients. Diffraction redistributes energy angularly, creating maxima and minima.

Special phenomena and limits
- Total internal reflection: if n1 > n2 and incident angle > critical angle θc = arcsin(n2/n1), all energy is reflected.
- Brewster’s angle: at a certain angle of incidence, reflected light is fully polarized (no p-polarized reflection).
- Resolution/diffraction limit: diffraction limits the smallest resolvable detail (e.g., Rayleigh criterion for imaging systems).
- In the short-wavelength limit (λ ≪ features), reflection and refraction are well described by rays; diffraction becomes negligible.

Typical examples / applications
- Reflection: mirrors, radar echoes, sound echo off a cliff, radio reflections from ionosphere.
- Refraction: lenses, prisms, optical fibers (guided by total internal reflection after refraction at entry), atmospheric refraction causing stars to appear displaced.
- Diffraction: single- and double-slit experiments, optical diffraction gratings, x-ray diffraction for crystal structures, radio waves bending around buildings/terrain, resolving power of telescopes (Airy disk).

When to expect each to dominate
- Reflection dominates when impedance mismatch at an interface is large or for high-angle incidence (or in TIR).
- Refraction governs transmission across interfaces and design of lenses and prisms.
- Diffraction dominates when features (apertures, obstacles, slits) are on the order of the wavelength or when coherent interference effects are important.

Summary comparison (short)
- Reflection: bounce back at interface; governed by angle equality; frequency constant; may introduce phase shift.
- Refraction: bending into another medium due to speed change; governed by Snell’s law; wavelength changes; dispersion possible.
- Diffraction: bending and spreading around edges/apertures due to wave nature; strongest when sizes ~ λ; produces interference patterns and limits resolution.

If you want, I can show sketches or work out example problems: Snell’s-law refraction through a two-interface slab, single-slit diffraction pattern calculation, or compute Fresnel reflection coefficients for a particular pair of media.