Abstract

The matrix optics formalism is applied to show that a simple Gaussian equation is enough to relate object and image distances in an optical system consisting of an arbitrary number of thick lenses in cascade immersed in air. First, the case of a single thick lens was studied. Applying sequentially the optical matrixes corresponding to refraction and displacement of the optical ray, and imposing certain conditions on the behavior of the bunch of rays being refracted by the lens, there were found characteristic parameters such as focal distance, back and front focal points, and principal planes. Then the equation relating object and image distances is found, which, after a coordinate transformation, becomes the well-known Gaussian equation, usually used to describe the more idealized case of thin lens. Further, the formalism is extended to compound systems of two, three and N thick lenses in cascade. It is also found that a simple Gaussian equation is sufficient to relate object and image distances no matter the number of lenses.

Key words: Matrix optics, thick lenses, back focal length, front focal length, principal planes, focus, multi-lenses system.