Tutorial : focal lengths - principal planes - refracting surface

A spherical dioptre is a spherical surface interfacting two transparent media. The primary and secondary principal planes coincide with the plane tangent to the dioptre and perpendicular to the optical axis. According to the Snell-Descarte law and applying a first order approximation for small angles, the effective back and front focal length are respectively given by the relations : .
R is the dioptre radius. n₀ and n₁ are the refraction indexes respectively of the object space and of the image space.

Note that according to the definition given in the section "Focal lengths and other parameters", the front and back focal lengths are f_t = f and f_b = f_i.