A physics teacher created this video showing how to make a penny "disappear" by placing a Pyrex beaker over it and filling it up with water, asking why and how this illusion worked. On IO9, Esther Inglis-Arkell explains how the effect is achieved — it's all down to the strange motion of light in water.
So when the penny is at the bottom of the beaker, there's only one sharp turn that the light from the penny has to make, from the pyrex dish to the air. The water-to-pyrex transition is comparatively mild, with little bending. The penny is distorted, but it's visible. When the wet penny is beneath the dish, but under another layer of water, the light also only has one sharp turn — back into the air at the end of its journey. Before that it only travels through water and pyrex, which have similar indices of refraction, and so it isn't bent much.
When the penny 'disappears,' though, it is taking two sharp turns, the massive turns between the pyrex and the air both at the bottom of the beaker and at the side. And, because of the way light bends, both turns are in the same direction, away from the eye of the viewer. Imagine the beaker full of water like an immense piece of rectangular carpeting on the concrete floor, and the light like a person on roller skates. (No, seriously, this will help.) The viewer is on the right side of this carpet. In order for them to see the penny, just under the bottom of the carpet, the light has to get from the penny to them.