Yes,  Snell's law can be verified from wave theory. From the right-angled triangle AA'P',

\(\sin\left(i\right)=\frac{PP'}{AP'}=\frac{ct}{AP'}\)

Where c is the velocity of light in the air.

From the right-angled triangle AA'P',

\(\sin\left(r\right)=\frac{AA'}{AP'}=\frac{vt}{AP'}\)

Where v is the velocity of light in the denser medium.

Now, \(\frac{\sin\left(i\right)}{\sin\left(r\right)}=\frac{ct}{vt}=\frac cv=\mu\)

∴ \(\mu=\frac{\sin\left(i\right)}{\sin\left(r\right)}\) 

Which is the Snell's law.