Question

How does the density of air near the ground affect the bending (refraction) of light waves during a mirage?

Answer 1

Light rays bend in air whenever the refractive index changes with position. Near the ground the refractive index n of air is directly tied to its density (Gladstone–Dale relation: n − 1 ∝ ρ), and density near the surface is mainly set by temperature (ρ ∝ 1/T at roughly constant pressure). So vertical changes in temperature produce vertical gradients in density and therefore in refractive index, and those gradients continuously refract light.

Key points

- Light bends toward regions of higher refractive index (toward denser air). In a stratified atmosphere this produces smoothly curved ray paths rather than a single discrete refraction.
- If the air near the ground is hotter and therefore less dense (n smaller near the surface), rays from the sky entering the hot layer bend away from the ground (bend upward). That produces the common inferior mirage (apparent patch of “water” or inverted image of the sky).
- If the air near the ground is colder and denser (n larger near the surface), rays bend down toward the ground and distant objects can appear lifted or inverted above the horizon (a superior mirage, e.g. looming or Fata Morgana).
- The amount of bending depends on the vertical gradient dn/dz (how rapidly n changes with height), not the absolute value of n. Strong, shallow gradients near the surface are needed for a noticeable mirage; the absolute refractive-index changes are small (n ≈ 1.0003 in air), so ordinary weak gradients produce negligible bending while steep near-ground gradients produce the visible effect. Turbulence and layered structure determine the shape and stability of the mirage.

You can also view the phenomenon from Snell’s law in differential form: in a horizontally stratified medium (n = n(z)) rays follow curved paths determined by d/ds(n dr/ds) = ∇n, so the curvature of the ray is set by the vertical refractive-index gradient.