### 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:
1. The reflected ray lies in the plane of incidence.
2. 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:

1. The refracted (or transmitted) ray lies in the plane of incidence, and
2. 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 so-called 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.