Lens Simulation

You may have noticed in the last simulation, a wave that passes all the way through a piece of material with parallel sides (for instance light through a flat slab of glass) leaves the material at the same angle that it entered. The wave un-bends when it exits the material by the same amount that it bent when entering. This is only true if the sides of the material are parallel, however. In the simulation below we have convex and concave lenses where the sides of the glass are not parallel (except near the center). In this case parallel rays of light end up exiting in different directions. This is the basis for any optical device that uses lenses, for example cameras, binoculars, microscopes, glasses, eyes of various animals, etc.

At each surface the waves obey the law of refraction (Snell's law) but the result is that parallel rays that enter are not parallel when they exit. Although our example is for light it should be kept in mind that the same behavior occurs for other types of waves when they enter a medium where their speed is different (as in the previous refraction of sound in a balloon filled with Carbon Dioxide).

For this simulation we use the thin lens approximation which assumes the lens thickness is small compared to the curvature of the lens. This allows us to approximate the bending as if it occurs all at once at the middle line of the lens (instead of some bending at each surface which in fact is what happens).

The object (a candle) in the simulation can be moved using the mouse. White arrows show where the light rays actually travel. The purple lines are imaginary extensions of the real light rays. Our brain/vision system assumes light always travels in a straight line and does not bend. For light that does bend due to refraction, our brain interprets the light as following the purple paths and constructs and image based on this information. The units of height, h, and distance, d, are arbitrary (cm, inches, etc.)