Think of a marching band crossing from a paved road into deep mud; they slow down and their steps shorten (wavelength), but the number of steps they take per minute (frequency) stays the same to maintain their rhythm.

Remember 'V-W-C' (Velocity and Wavelength Change, Frequency constant) for refraction.

Snell's law is defined by the relation $\frac{\sin i}{\sin r} = \frac{n_2}{n_1} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}$, where $n$ is the refractive index, $v$ is speed, and $\lambda$ is wavelength. Since the frequency $f$ is related to speed and wavelength by $v = f \lambda$, and the ratio of speed to wavelength must remain constant for the frequency to be conserved, $f$ remains invariant during refraction.

In any optics question regarding refraction, immediately remember that frequency is the only property that does NOT change; velocity, wavelength, and direction are all subject to change.