special relativity - Doppler Shift when Light Travels Through Two Different Mediums

When considering the Doppler shift, the 'canonical equation' is

$$f=\frac{c+vr}{c+vs}f_0$$

However, this equation seems to run into trouble in the following situation: A light source inside water is moving at a speed $v$ towards a receiver outside the water. Can we modify the above equation to deal with a transition between two media? Or is there a completely different formula that applies here?