Ok so here's the shader for a smooth eye surface. In the above images, I used this on 7_EyeSurface and 7_Tear.

If you don't like the tear at all (many people don't) then use the invisible shader on it instead. 

For artistic reasons, I increased the IOR to 1.4 - this gives slightly more obvious reflections without being ridiculous. The actual IOR of water is 1.33. I assume tears are close to that, but perhaps salt increases the IOR? In which case, my 1.4 is probably dead on.

We also possibly have a thin-film effect bouncing light between cornea and water surface, which may increase the reflection amount. So it's sensible to go higher if you like.

If you love glassy shiny eyes, go way higher - try 1.5 or 1.6. (Glass is 1.54) If you go above 1.6 it looks crazy like silicon eyes. Don't do that.

The way this is working is that the Fresnel_Blend node gives us a proportion for how much light is reflected. The complement of that is refracted. It turns out that when you plug something into Transparency, the value is assumed to be an opacity which is multiplied with other things - in particular with Alternate_Diffuse. The complement of what is plugged in is transmitted. 

Voila !

Note: My node names are sometimes adding or removing _ - this is because VSS generated them. Learn your nodes and the _ will never bother your understanding.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)