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3. How does the density of air near the ground affect the bending (refraction) of light waves during a mirage?
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Light rays bend toward regions of higher refractive index. For air, refractive index n is almost proportional to density ρ (n − 1 ≈ K·ρ), so denser air has a slightly larger n.
How that produces a mirage:
- If the ground is very hot, the air near the ground is warmer and therefore less dense (lower n) than the air above. A vertical gradient with n increasing with height makes rays from the sky bend upward (away from the low‑n layer near the ground). Rays that would normally go straight to the ground are curved up into the observer’s eye, so the observer’s brain extrapolates the rays backward and sees a virtual image of the sky on the ground (an inferior mirage, the “puddle” effect).
- If the surface air is colder (denser, higher n) than the air above (a temperature inversion), n decreases with height and rays bend downward toward the denser layer. That can lift distant objects above their true position, producing a superior mirage.
Mathematically this follows from Snell’s law in a continuously varying medium (n(y) sin θ = constant) or from ray‑equations: the curvature of the ray is proportional to the transverse gradient of n. The absolute changes in n are tiny (n ≈ 1.0003 at STP) but over tens to hundreds of meters even small gradients produce visible bending, which creates the mirage.
How that produces a mirage:
- If the ground is very hot, the air near the ground is warmer and therefore less dense (lower n) than the air above. A vertical gradient with n increasing with height makes rays from the sky bend upward (away from the low‑n layer near the ground). Rays that would normally go straight to the ground are curved up into the observer’s eye, so the observer’s brain extrapolates the rays backward and sees a virtual image of the sky on the ground (an inferior mirage, the “puddle” effect).
- If the surface air is colder (denser, higher n) than the air above (a temperature inversion), n decreases with height and rays bend downward toward the denser layer. That can lift distant objects above their true position, producing a superior mirage.
Mathematically this follows from Snell’s law in a continuously varying medium (n(y) sin θ = constant) or from ray‑equations: the curvature of the ray is proportional to the transverse gradient of n. The absolute changes in n are tiny (n ≈ 1.0003 at STP) but over tens to hundreds of meters even small gradients produce visible bending, which creates the mirage.
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