Tutorial : focal lengths - principal planes - thin lens

A lens is considered as a a thin lens when its center thickness is small enough to be neglected. It is a theoretical case which is however very useful. Here, we consider the case where the lens is in air or vacuum. The vertexes of the lens surfaces coincide. They coincide also with the object and image nodal points. The paraxial parameters are given by the simplified formulas below (the general formula is detailed in the section "Thick lens in the air") :

From the focal length formula, one can see that the lens type (positive or negative) can be easily deducted from its shape. Indeed, for instance, biconvex and plane-convex lenses are positive (f_i positive) while biconcave and plane-concave lenses are negative (f_i negative). A Lens with both convex and concave surfaces is positive if the radius of the convex surface is smaller than the radius of the concave one.

The image of a point at infinity through a positive lens is real, which means that the rays effectively intercept the image focal point while the image through a negative lens is virtual, which means that the rays never "physically" intercept the image focal point but only their directions do.