Nope, the speed of light isin't a constant. It varies with the material being travelled through. (Ok, it's a bit more complicated than that, but for our purposes, we'll treat it as though it's just a property of the material)
The commonly quoted speed of 186000 miles/sec is the speed in a vacuum.
When light crosses from a material where it has one speed to a material with another speed, it bends. The amount of bending is characterized by a value called the "index of refraction".
For vacuum, this value is 1, by definition. For air, its close enough that you can generally call it 1. For water, the value is (I believe, doing this from memory) 1.33 . (Coincedentally, diamond also has the same IOR; if you put a diamond underwater, it will "disappear". A trick occasionally used in crime movies/novels). For glass it has yet another value (depending on the type of glass).
The exact amount of bending depends on the values of the IOR for the two materials (the one being left, and the one being entered). The closer the two values are, the less
bending will take place.
The amount of bending that occurs is also affected by the angle at which the light hits the surface. Look up "Snell's Law" to get the full math. (it's only basic trigonometry, nothing too scary).
So lenses work by controlling both the angle the light hits the surface of the lens at (i.e. the lens' shape), and the Index of Refraction of the material the lens is made of.
As for the short-sited question...
Imagine parallell rays of light travelling through the air.
When they enter your eye, they bend towards each other slightly, and with correct vision, will meet each other at the same point that they hit the back of your eye (the retina). I.e. the image is in-focus at the point where you can sense it.
If you're short-sited, your eye bends the light too much, so rays that are parallell in the air cross before they reach
the back of your eye. But for things that are close, the light coming from them isin't quite parallell, but is diverging slightly. So when your eye bends it, they don't get bent quite as far and you're able to form a focussed image on your retina.
Now move underwater. The water has a larger IOR than air, and is closer to the IOR that the lens of your eye has. So the light gets bent less in general. So the rays from a distant object now get focussed further back in your eyeball, and if your lucky, might even meet each other at your retina, giving the effect of correct vision.
For lots more about this, check in the chapters on Optics in most physics textbooks.
Jamie
