Matrices used in physics

USE OF MATRICES IN STUDYING OPTICAL SYSTEM
Matrix approach helps understand how optical system works.Optical system has an input plane and output plane. Ray of light is determined by the distance that hits above or below the object axis and the slope of light r’.
Develop a working model-Ray matrices : Newtonian or Gaussian optics tell you where all rays that start from some object point will meet again to form an image (massively parallel). They tell you nothing about what rays are doing at points in the system that are not object or image points. This is a very useful approach for calculating images position and magnifications in the paraxial limit.
Ray matrices tell you the position and the slope of a single ray at a single plane (serial). The ray matrix approach is more flexible but serial rather than parallel ans is very well suited to using computers.

How to proceed?
We find the matrix to each element that comprise the optical system.
[M1], [M2], [M3], [M4], [M5].
[M1]=
[M2]= etc…
We multiply them together to get a single matrix. We multiply them in reverse order because the ray comes on the input plane first. Like this we find the ray matrix that helps us know what happens at every ray in the each plane

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Reference: http://www.youtube.com/watch?v=DLF5acjI51Q