I have thought of this question due to personal experience. I am short-sighted, and over the last three years my short-sightedness has worsened. Taking a lifeguard certificate again now that I did already three years ago, I noticed while diving that I have almost no vision anymore when trying to find and collect some training rings, that I had no problem to visually identify three years ago. In all cases, I am not wearing any goggles while diving.
So, I came to think whether short-sightedness has an effect that adds to the effect of the eyes being covered by water and the cornea having almost no refraction. This process is explained in other questions here, but I claim that my set of closely related questions is different, not only due to the inclusion of short-sightedness.
I then tried out my normal glasses under water and noticed no effect at all, not positive, not negative. I am now confused as to why the glasses have no effect, but the short-sightedness that they should correct does have a worsening effect. In this, I am assuming, without being able to justify it, that the glasses should have the same effect under water as above water, because, as the water touches them from both sides, the light should have a different path inside the length (less bending at entry and exit), but that the light rays exiting the glasses under water should be parallel to the light rays that would exit it in air. But what is instead the mechanism at work here that renders air-glasses useless under water?
Second, I notice that, when wearing swimming goggles, my short-sightedness is alleviated under water. This means that I can see better under water with swimming goggles and without any contact lenses or corrective glasses than I can above water without glasses or lenses. A quick search on the web found other questions of short-sighted people that noticed this effect, but I could not identify how this is working out for normal-sighted or far-sighted people. How does this work?
Then I pondered, as contact lenses are swimming on the eye, but, when underwater, have also contact with water instead of the air they are designed for, do contact lenses have an effect under water (ignoring the risk of them swimming away quickly)?
Finally, what would be the dimensions of a pair of glasses that actually work under water (be it for normal-sighted or short-sighted persons), when we, in turn, ignore their performance in air? How thick and large would they be?