Thermal Mirage: Heat Refraction / Optical Distortion
Optics, Waves & Sound arc, page 118 of 193. Back to The Pixelated Physics Universe
Who they are
Meet Thermal Mirage. That shimmering puddle on a hot road is not water. It is sky. Hot air over a road has a lower refractive index, so skylight bends upward into your eye and looks like water. This is an inferior mirage, and it only works for rays within about half a degree of the road. Thermal Mirage wears it in pixel art on a unisex tee.
Thermal Mirage is a character of the Optics, Waves & Sound arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Hot air over a road is thinner, so light travels slightly faster in it. Skylight skimming the road bends up into your eye, and you see the sky below the horizon. It only works for rays within about half a degree of the road.
$$ \begin{gathered} n\cos\alpha = \text{constant}\quad\text{(stratified air)} \\ n - 1 = K\rho \propto \frac{p}{T},\qquad n - 1 \approx 2.9\times10^{-4}\ \text{at STP} \\ \alpha_{\max} \approx \sqrt{2\,\Delta n} \approx 0.4^{\circ}\ \text{for}\ \Delta T \approx 30\ \mathrm{K} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $n$ | refractive index of air | 1 |
| $\alpha$ | angle of the ray above the horizontal | rad |
| $K$ | Gladstone–Dale constant | m³/kg |
| $\rho$ | air density | kg/m³ |
| $p$ | pressure | Pa |
| $T$ | absolute temperature | K |
| $\Delta n$ | refractive-index difference between cooler air above and hot air at the road | 1 |
| $\alpha_{\max}$ | steepest ray angle that can still be turned back by the hot layer | rad |
Sources
- Feynman Lectures on Physics Vol. I Ch. 26: Optics: The Principle of Least Time
- Ciddor (1996) Refractive index of air: new equations for the visible and near infrared, Appl. Opt. 35, 1566
Crossovers
Thermal Mirage meets Turbulorn (Astronomical Seeing). Thermal Mirage bends light through air whose refractive index changes with temperature. Turbulorn's seeing is the same physics in a turbulent atmosphere, which blurs stars and limits telescopes.
Thermal Mirage meets Slithera (Atmospheric Dispersion). Thermal Mirage's air bends light by temperature. Slithera's air bends it by wavelength, spreading a star's image into a short spectrum near the horizon.
Thermal Mirage meets Nimbryn (Mie Scattering Clouds). Nimbryn's cloud droplets are comparable to or larger than the wavelength, so Mie scattering whitens all colours equally. Thermal Mirage bends light without scattering it, through gradients in the air's refractive index. Both shape what an observer sees of the sky.
Wear the lore
- Thermal Mirage – Heat Refraction / Optical Distortion Physics T-Shirt
- Related infographic poster: Snell's Window – Plate 025 Physics Poster
Concept keywords: Heat Refraction / Optical Distortion, Thermal Mirage, Optics, Waves & Sound, physics lore, Pixelated Physics