Q.Why do stars twinkle?

Refraction and Snell's Law

When light crosses the boundary between two transparent media its speed changes, so the ray bends at the surface. The bending is governed by Snell's law, which relates the angle of incidence $i$ (measured from the normal) in medium 1 to the angle of refraction $r$ in medium 2:

Here $n = c/v$ is the (absolute) refractive index of a medium, always $\geq 1$ for ordinary matter.

Which way does it bend?

• Going into a denser medium ($n_2 > n_1$): light slows down, $\sin r < \sin i$, so the ray bends toward the normal.
• Going into a rarer medium ($n_2 < n_1$): the ray bends away from the normal.
• At normal incidence ($i=0$) the ray passes straight through, and a ray never bends past the normal for ordinary media.

Across a stack of layers (e.g. air $\to$ turpentine $\to$ water), apply Snell's law at each interface in turn. Since $n_{air} < n_{water} < n_{turpentine}$, a ray descending from air bends toward the normal on entering the turpentine and then away from the normal on entering the (less dense) water. …