B.2      Ray optic concatenation of lenses

Fig. B-2 Single lens in ray optics approximation

For a single lens (Fig. B-2), the distance s is given by

where f is the focal length (imaging equation). For a parallel entering light (r = ¥), s = f. Negative distance are possible for virtual converging points.

Fig. B-3 Two cascaded lens in ray optics approximation (left) and screen placed after the last lens (right)

For two cascaded lenses (Fig. B-3), we have the following relations

For the case with the screen, the spot size L is given by

We note that in the case presented in Fig. B-3, the parameters s_m, r_m and f_m are negative. It is possible to use these equations in a recursive way for an arbitrary number of lenses.