Prentice's equation and generalizations

The purpose of this note is to clarify confusion over the range of applicab ility of Prentice's equation for the calculation of prismatic effects in le nses. Making use of the concept of the ray transference in Gaussian and lin ear optics, the paper obtains generalized forms of Prentice's equation that apply in various situations. Redefinition of prismatic deviation as change in reduced direction of a ray makes Prentice's equation valid for thin sys tems in media of any index of refraction. In particular, the equation then holds for a single refracting surface. It does not hold in general for thic k systems, although there are some special cases in which it does apply. Th e appropriate equation is presented for thick systems in general. The corre ct form of power to use in the equations is equivalent power and not back-v ertex power. A generalized form of Prentice's equation applies to astigmati c systems, including single refracting surfaces and thin lenses. An analog of Prentice's equation gives the transverse displacement of a ray across a system as a function of the incident-reduced direction of the ray.