These notes discuss the use of matrices to describe systems in geometrical optics. As you will see, the techniques are powerful. We will limit ourselves to paraxial ray tracing which means that we will consider optical systems whose elements have a common optical axes and the light rays we'll be dealing with are all nearly parallel to the the optical axis. This means that we will be dealing with angles which are small enough so that the approximations:
are valid. We want to describe this system:
The angles are exaggerated in this drawing. We want to describe the parameters of the emergent ray in terms of that of the incident ray. By making the small angle assumption we are effectively making the assumption that we can write:
or in matrix form:
OK - that's the starting point. Now we will show how to write the matrix for different optical elements and then we'll show some examples.
