Correct diopter formula?

In the articles section there is an article by Scheunemann that lists the correct diopter formula as:

D = 100cm / 3.03*r

where r is the radius of the dome in centimeters. However, searching through the archives the following formula often comes up:

D = 100cm / 4*r

Which one is strictly correct? (I have a feeling the first one is correct and the second an approximation but I want to verify that.)

Lanier

Dioptric Power = 1000/4xR assuming that the refractive index of seawater is 4/3 and that the dome port is of negligible thickness and of radius R (so focal length = -3R). R is in mm. This realigns focus at 4R from the centre of the Dome and gives a maximum focussing ability for lens/dome. As with most of these equations it assumes things that are not exactly so and alternatives can be tried and work well for specific requirements.