Imagine shining a laser beam through a prism, as shown in Figure 4.10. Snell's Law can be applied to calculate how the light ray bends after it enters and exits the prism. Note that for the upright prism, a ray pointing slightly upward becomes bent downward. Recall that a larger refractive index inside the prism would cause greater bending. By placing the prism upside down, rays pointing slightly downward are bent upward. Once the refractive index is fixed, the bending depends only on the angles at which the rays enter and exit the surface, rather than on the thickness of the prism. To construct a lens, we will exploit this principle and construct a kind of curved version of Figure 4.10.

Figure 4.10: The upper part shows how a simple prism bends ascending rays into descending rays, provided that the incoming ray slope is not too high. This was achieved by applying Snell's law at the incoming and outgoing boundaries. Placing the prism upside down causes descending rays to become ascending. Putting both of these together, we will see that a lens is like a stack of prisms that force diverging rays to converge through the power of refraction.

Figure 4.11: A simple convex lens causes parallel rays to converge at the focal point. The dashed line is the optical axis, which is perpendicular to the lens and pokes through its center.

Steven M LaValle 2020-01-06