thicklens

A thick lens, sometimes written as thicklens in some contexts, is an optical element in which the separation between its two refracting surfaces is not negligible relative to its focal length. In such lenses, the paraxial imaging properties cannot be described by a single focal length as in thin-lens theory; instead, they are described by an effective focal length and two principal planes.

The lens has two principal planes, typically denoted H1 and H2, which are separated by the lens thickness. The front focal point lies at a distance from H1 (the front focal length, FFL) and the back focal point lies at a distance from H2 (the back focal length, BFL). The relationship among object distance, image distance, and focal properties is described by the thick-lens equation and can be computed using ray-transfer (ABCD) matrices or the standard thick-lens formula that involves the lens index, surface curvatures, and thickness. In air, the refractions at the two surfaces are determined by their radii and the refractive index of the lens material.

Practical considerations include the fact that thick lenses are common in camera objectives, microscope objectives, and other precision optics. By distributing curvature over multiple surfaces and adjusting spacing, designers can better control aberrations and achieve desired imaging performance. Manufacturing often uses glasses with specific dispersion properties, and aspheric surfaces may be employed to further reduce aberrations. The imaging behavior of a thick lens is typically analyzed by tracing paraxial rays or using matrix methods to determine the effective focal length, principal planes, and focal points.

In summary, thick lenses require more complete description than thin lenses, using principal planes, focal lengths, and matrix-based ray tracing to predict focus, magnification, and aberrations in optical systems.