Snell's law

Printed on the AP Physics 2 sheet. Subscript 1 is always the side the light starts on, subscript 2 the side it ends on, and both $\theta$ are measured from the normal.

The rule in words, which is what qualitative questions want. The product $n\sin\theta$ is conserved across the boundary, so the bigger index has to carry the smaller angle.

• Low index into high index: $\theta$ must shrink, so the ray bends toward the normal.
• High index into low index: $\theta$ must grow, so the ray bends away from the normal.
• $\theta_1 = 0$ gives $\theta_2 = 0$. A ray along the normal passes straight through.

That single sentence, bigger $n$ takes the smaller angle, replaces memorising two cases and never inverts under pressure.

When the algebra returns $\sin\theta_2 > 1$, you have not made an arithmetic slip. There is no refracted ray: the light is entirely reflected back into medium 1, which is total internal reflection. It can only happen going from higher index to lower.

Snell's law governs the boundary, not the path length, so a slab of glass with parallel faces shifts a ray sideways and returns it to its original direction: the two bends are equal and opposite. Topic 13.3 works the numbers.