(...If you feel (or even better - can prove) that anything I’ve written here is actually illogical, incorrect or that the values I’m using are inaccurate, please don’t hesitate to let me know...Otherwise, I’d love to hear if you agree with me...If so, we could discuss...)
In almost all circumstances, the images which fall on a persons retina are inverted. Because we don’t see our world upside-down however, the obvious conclusion is that the ‘act of seeing’ (perhaps for want of better terminology) does not take place at the retina, but in our brain, once it has somehow re-inverted the image - so that we see it upright. I think most people would accept a corollary to this theory: if the image formed on the retina was upright, then what we actually ‘see’ must be inverted - as the brain has ‘learnt’ to invert everything we see. But how can this corollary be tested? Very simply actually!
The reason that the image formed on our retinas is inverted is because of the refraction which occurs when light passes from air into the cornea and aqueous humour at the front of the eye, and also when light passes through the biconvex lens.
If the refractive power of the cornea/aqueous humour is removed, however, the refractive power of the lens is not enough to invert the image by itself. The value I’ve been able to obtain for the refractive power of the lens is 20 diopters at maximum (which means that parallel rays striking it would be focused at a distance of 5 cm - 1/20 meters - behind it).
A very simple way to remove the refractive power of the cornea/aqueous humour is to replace air with water. The reason this works is because water and the aqueous humour have almost exactly the same refractive index - that of water is usually given a value between 1.33 and 1.34; that of the aqueous humour is 1.336. What about the cornea? Well, the cornea has a refractive index of about 1.38, but this is irrelevant, as the opposite sides of the cornea can be considered as parallel for the purposes of this experiment (unlike the biconvex lens). Parallel rays travelling from water to the aqueous humor can therefore be considered as behaving as demonstrated in the attached "fig1.gif"
Because the refraction occuring between the two mediums (water and the aqueous humor) in this instance is effectively negligible, rays which are parallel at the cornea can be considered to be still parallel at the lens (see attached "fig1.gif").
Values I’ve been able to gather for the refractive power of the lens vary - anywhere from 10 (or even below) to 20 diopters. Therefore, parallel rays striking the lens will be focused 5-10 cm behind the lens. The distance from the lens to the retina, however, is only 1.4-1.7 cm. The image of the object in the water, therefore, is upright on the retina. According to the prevailing theory of visual awareness, we should therefore see the object upside-down, as our brain is supposed to invert whatever image is formed on the retina.
Try the experiment yourself! Take any object small enough so that the rays of light reflected off it into your eyes are parallel when the object is held at an arms length (or less) from your eyes, and which also has two easily-distinguishable sides (e.g. one side red; the other side white). Now submerge yourself in either fresh water or salt water (your bath; the sea; whatever - the difference between the refractive index of the two mediums is negligible - and no, this is not a joke ).
Now simply hold the object out in front of you (at a distance which ensures that the rays reflected off it into your eyes are parallel). It is difficult to see under water - quite a strain on the eyes in fact - but if the object you are using has two easily-distinguishable sides, you will see the image upright, although, according to the prevailing theory of visual awareness, it should be inverted. Note that you don’t even see a diminished image of the object (which is the very least you would expect).
(....These are my own original ideas, and I can readily verify this...don’t do anything silly like claim them as your own....)
EDIT (May 7th 2004): This is sooooh embarassing , but it turns out that my argument is inherently flawed. See THIS thread to see where I went wrong.