Mirages: bending light over a warm or cold layer of air
A mirage is not a trick of the eye — it is refraction. Air of different temperature has slightly different density, and light curves toward the denser (cooler) air. Trace a ray through a temperature layer and you can watch inferior mirages, superior mirages, Fata Morgana, and even light ducting around the curve of the Earth.
What you are looking at
The diagram is a side view. An eye sits on the left; a distant object (the dot on the pole) sits on the right at the distance you choose. Faint lines are a fan of light rays leaving the eye; the bold lines are the rays that actually reach the object — each one is a separate image the eye sees. The shaded band on the far left shows how the air's refractivity changes with height, and the gently curving line is the surface of the Earth falling away with distance.
Inferior mirage
Over a hot road or desert, the air right at the surface is hottest and thinnest, so its refractivity rises with height. Rays skimming the ground curve upward, and the eye sees an inverted image below the real object — the famous "wet road" or shimmering desert pool, which is really an inverted reflection of the sky.
Superior mirage & looming
When a warm layer sits over cold ground or sea (a temperature inversion), refractivity drops with height and rays curve downward. Objects beyond the horizon can be lifted into view (looming), stretched (towering), or stacked into the shifting cliffs of a Fata Morgana.
The horizon is farther than it looks
Because rays bend gently downward in ordinary air, they follow the Earth's curve a little — so the horizon sits farther away than straight-line geometry predicts. The standard way to bookkeep this is the effective Earth radius: refraction acts like a planet roughly four-thirds the true radius, pushing the horizon out by a few percent.
Ducting & the Novaya Zemlya effect
If the inversion is strong enough that rays bend downward as sharply as the Earth curves, light becomes trapped in a duct and can travel far beyond the normal horizon. This is how explorers have reported seeing the Sun while it was geometrically below the horizon — the Novaya Zemlya effect — and it is a cousin of the brief green flash at sunset.
Try it
- Pick Hot road and lower the observer — the inverted inferior image appears near the surface.
- Pick Cold sea and push Refraction strength up — extra images fold in as a superior mirage develops.
- Pick Strong inversion — rays duct along the surface and reach objects far past the ordinary horizon.
The diagram uses a paraxial ray-tracing model of a horizontally layered atmosphere over a spherical Earth — the same physics textbooks use to explain terrestrial refraction. It is a teaching model, not a forecast of any particular day's sky.