Chapter 1
Physical Basis of Geometrical Optics
As mentioned, the subject of geometrical optics is based on the laws
of reflection and refraction. The laws of reflection state:

The reflected ray lies in the plane of incidence.

The angle of reflection equals the angle of incidence.
The plane of incidence is the plane
containing the incident ray and the normal
to the reflecting surface constructed
at the point where the incident ray
strikes the surface. The angle of
reflection is the angle between the normal
and the reflected ray; the angle of
incidence is the angle between the normal
and the incident ray.
The laws of refraction state that for
a refracting surface between two
transparent media:

The refracted (or transmitted) ray
lies in the plane of incidence, and
 n sin
=
n ' sin
',
(Snell's law),
where
is the angle of incidence and
'
is the angle of refraction, the angle
between the normal to the surface and the
refracted ray, and n and n ' are the
indices of refraction of the media on either
side of the refracting surface.
The index of refraction of a medium is defined
as the ratio of the speed of
light in vacuum to the speed of light in the medium.
In first order theory, which essentially involves
the first term in the
series expansion for the sine of the angle, Snell's
law is used in the
form
n
= n '
'.
A better approximation than the
first order theory involves
higher order terms in the expansion which gives
rise to the third and fifth
order theories. The results of the higher order
theories are usually expressed
in terms of the defects in the image formed by
spherical refracting surfaces,
the socalled monochromatic aberrations.
In what follows we shall concentrate on the
subject of refraction, on the
basis of first order theory, leaving the
subject of reflection to be treated later
as a special case.