Math 150

Projects

Snell's Law

Steve Wilson

 

Snell's Law says that if a particle, like a ray of light or a billiard ball, is reflected off a flat surface like a mirror or the rail of a pool table, the angle of incidence is congruent to the angle of reflection. In the figure,

 

this is to say that /TPE is congruent to /BPO. Snell's Law is a low of physics, and laws of physics are usually established empirically, i.e. after observing a large number of experiments, physicists posit an explanation for the results. However, Snell's Law can be derived mathematically from the following considerations.

 

The line from the eye, E, to P, the point of reflection on the mirror, will go, it extended, to O' the reflection of the object, O, in the mirror.

 

This follows from Newton's observation, "Nature follows the path of least resistance." Since PO' is the reflection of PO in the mirror, the distance from E to O through P is the same as the distance from E to O' through P, and the shortest distance between two points is a straight line.

 

To get to O', the reflection of O in the mirror, go from O perpendicular to the mirror, and then proceed along this line the same distance on the other side of the mirror.