Spherical Aberration: Descartes’ Solution

Philosophical Context: Optics

For those unclear about what spherical aberration is, and attempting to follow Spinoza’s comments about Descartes below, it is the tendency of rays at the edge of a spherical lens to refract at a focal length shorter than those near the axis:

This tendency is corrected by a hyperbolic lens, as theorized by Rene Descartes, which in its progressive sloping, sends the rays to one mathematical point.

It was Spinoza’s thought, probably working from the theories of mathematician Johannes Hudde, that light rays gathered at what he called a “mechanical point” and not a mathematical point. So spherical aberration was considered inconsequential, a fact of working with lenses and light. (A practical mid-century address of spherical aberration in telescopes was the use of much larger, flatter lenses, with longer focal lengths, making telescopes sometimes reach lengths over 30 ft.)

Unfortunately, for the greater part of the 17th century this spherical aberration effect was confused with, and assumed to be the cause of, chromatic aberration which produced a bluish halo at the edges of images, and which is, in most cases, more disruptive than spherical blurring. Not until Newton discovered the spectrum components of light from 1670 – 72 was it theoretically realized that the one was not the other. Even Christiaan Huygens, as he worked to resolve spherical aberration solely with spherical lenses, probably thought that he was resolving what was latter understood to be chromatic, as he was somewhat deflated by Newton’s discovery: