Our previous studies of optical systems were based on two premises.

We assumed a paraxial system.

This means we employed a first order optical theory. Check the article just linked for a good overview of whats paraxial optics and whats first order optical theory. Such assumptions are fraught with various types of aberrations which we studied in detail in lecture-I and lecture-II.

We assumed that our lenses are thin.

This we did for simplicity. In Physics when we assume a simple situation we are not evading the actual complexity of the situation, we are just postponing this to the happy hour, howsoever you define it. Some people go by the Friday happy hour rule. It gives a good substratum on which a disposition can be carried out. Later one develops the nuances and fits it into the substratum and if things are carried out with caution and skill one gets a very effective overview of the pedagogy.

Let us now delve into the complexity of the optical system as a next step from its simple substratum of a thin lens. Our analysis needs to be modified for applying optical principles to optical systems when we consider thick lenses. In our last lecture we studied the method of matrices in understanding optical ray tracing. Let us now apply this method to the case of thick lens and see what power it unleashes.

# Category: matrix

## Matrix formulation in Geometrical Optics.

In this lecture, we will discuss about one of the most interesting and powerful methods in Geometrical Optics. As we have discussed, geometrical optics is that segment of optics in which we are limited to a situation when the wavelength of light is negligible eg λ is insignificant compared to the size of the objects light interacts with. As a consequence light can be considered as rays or geometrical straight lines and the nuances of light as wave undulations can be postponed to a happy hour.

Ray Tracing.

Any general optical system has a ray which can be traced through two basic types of traversal of the ray: Translation and Refraction. The law of refraction is thus the central tool for ray-tracing. A ray can be described in an optical system by its coordinates which we will define soon. Our goal is to find the matrix which governs the displacement of the ray from one coordinate to another coordinate of the ray as the ray travels from one geometric point to another.