Build the refracted angle from wavefront timing

A plane wave reaches a flat interface at incidence angle 30° to the normal. Its speed in the second medium is half its speed in the first.

What is sin of the refracted angle to the normal?

Organize the givens & assumptions

θ1 = 30°
v2/v1 = 1/2

Isotropic media and a stationary plane interface, incident plane wave and transmitted wavefront; ray directions are normal to the wavefronts. Both speeds refer to the same frequency.

A $\frac{\sqrt3}{4}$
B $\frac14$
C $1$
D $\frac12$

Try it on paper first. Free sample problems in every collection include the complete reasoning: find one in this collection →