C.3.2—Snell’s law

Write the boundary relationship

For a ray crossing from medium 1 to medium 2, Snell’s law is $n_1\sin\theta_1=n_2\sin\theta_2$. Each angle is measured between the ray and the normal, not between the ray and the surface.

Solve the geometry first

Draw or identify the normal at the boundary, label incident and refracted angles, then substitute the refractive indices and sines. If the question asks for speed, combine the result with $n=c/v$.

Check the bend

Entering a higher-index medium decreases speed and bends the ray toward the normal. Entering a lower-index medium increases speed and bends it away from the normal; the frequency remains fixed at a stationary boundary.

Common trap

Do not use the angle between a wavefront and the normal as if it were the ray angle. A wavefront is perpendicular to the ray, so convert the angle when the diagram labels wavefronts.