Projects - Cengage Learning

Appendix C C-71
PROJECT
Snell’s Law and an Ancient Experiment
The “lifting” effect produced by refraction is the basis for one of the earliest
recorded experiments in optics, one which was known to the ancient Greeks. A
coin is placed in the bottom of an empty vessel and the eye of an observer is
placed in such a position that the coin is hidden below the edge of the vessel.
If water is poured into the vessel the coin appears to rise and come into view.
—Francis Weston Sears in Optics (Reading, Mass.: Addison-Wesley Publishing
Company, Inc., 1958)
In this group project you will learn some of the basic ideas of geometrical
optics, a subject first studied by the ancient Greeks, advanced by artists and
mathematicians of the Renaissance, and further developed by mathematicians
and physicists from the seventeenth through the twentieth and into the twentyfirst
century. Major contributors include Archimedes, Descartes, Fermat,
Huygens, Newton, Gauss, Hamilton, Fresnel, Einstein, and Born.
We now discuss some of the basic principles. The first one is the notion of
a light ray. When traveling through a uniform transparent medium (such as a
vacuum, water, plastic, or glass) light travels along straight line paths called
light rays.
The second principle is that light rays bend when passing from one
medium to another, for example, when passing from water to air. The amount
of bending is determined by the Law of Refraction, usually referred to as
Snell’s Law after its discoverer, Willebrod Snell (1580–1626). When a light
ray traveling in a transparent medium intersects the boundary with another
transparent medium, its direction changes as indicated in Figure A.
Incident ray
Normal line
Angle of incidence
Boundary
Angle of refraction
˙
First medium: index of refraction n
Point of incidence
Second medium: index of refraction nª
˙ª
Figure A
Refracted ray
Using the terminology introduced in Figure A we can state Snell’s Law in
two parts:
I. The incident ray, the refracted ray and the line normal (or perpendicular) to
the boundary at the point of incidence all lie in the same plane.
II. The angle of incidence and the angle of refraction are related by the
equation
n sin f n¿ sin f¿
The index of refraction of a vacuum is defined to be 1. For other materials
it may be determined empirically by precise measurement of angles. Air has