We begin our treatment of optics by first considering geometrical optics. In the limit of small wavelengths, geometrical optics describes the direction in which light travels through space as it encounters materials with different indices of refraction. Initially the refractive index will simply be assumed to be a property of a material which describes the speed at which light propagates in that material. That will be sufficient to allow us to treat the theory of aberrations and to look into some basic aspects of telescope design. Next we will look at the physical origins of the refractive index and at the Fresnel coefficients, which are important in a number of contexts including the design of various spectroscopic devices. Then we will consider physical optics, the behavior of light in the regime of finite wavelengths where diffractive effects become important. This will include a look at the Airy pattern. Finally we will introduce the concepts of the point spread function and the modulation transfer function and use them to consider some general properties of imaging.

Geometrical optics

The properties of light propagation can often usefully be described by geometrical optics, an approximation which is valid in the limit of small wavelengths. The wavelength λ is assumed to be small compared with all relevant length scales, including the dimensions of any physical objects present. The media of propagation are described by various values of the refractive index n, which in general is wavelength dependent.