The main reason for curving only the inner surface of the lenses in the diving mask faceplate is so that the diver can see clearly when looking at objects straight ahead while underwater and in the air.
Consider light rays approaching the mask along a normal to the plane of the faceplate.
If curved surfaces were on both the front and the back of the diving lens on the faceplate, refraction would occur at each surface.
The lens could be designed so that these two refractions would give clear vision while the diver is in air.
When the diver is underwater, however, the refraction between the water and the glass at the first interface is now different because the index of refraction of water is different from that of air.
Thus, the vision would not be clear underwater.
By making the outer surface of the lens flat, light is not refracted at normal incidence to the faceplate at the outer surface in either air or water - all of the refraction occurs at the inner glass-air surface.
Thus, the same refractive correction exists in water and in air, and the diver can see clearly in both environments.
