Essay: Dioptrics

Overview
Published alongside the Discourse on Method in 1637, Descartes' Dioptrics builds a mechanistic science of light and vision that weds geometry to physical explanation. It rejects scholastic species and qualities in favor of simple mechanical principles, showing how lines, angles, and surfaces govern the behavior of light in air, water, glass, the eye, and instruments such as telescopes and microscopes.

Nature and Propagation of Light
Descartes treats light not as a material efflux but as a tendency to motion transmitted through a subtle medium that fills space. A point source establishes a pressure-like action communicated instantaneously along straight rays, much as a push at one end of a taut stick is felt at the other. Rays mark directions of this action; they travel rectilinearly in uniform media and change direction only at boundaries where the medium’s resistance differs.

Reflection and Refraction
At a surface, part of the action is reflected and part transmitted. Reflection is governed by equality of angles, derived mechanically by considering the rebound of particles. Refraction, bending in a new medium, follows a precise quantitative rule. Descartes shows that the ratio of the sines of the angles of incidence and refraction is constant for a pair of media, expressing what is now called the sine law. He justifies it by assuming that the component of the light’s tendency parallel to the surface remains unchanged while the overall speed differs between media. Although he held that light moves faster in denser media, a point later reversed, the geometric law he formulates is correct and predictive.

The Eye and the Formation of Images
The treatise offers a lucid account of the eye as an optical system. The cornea and aqueous humors begin the refraction; the crystalline lens provides the principal focusing; the image is formed inverted on the retina. Descartes confirms this by experiments with animal eyes and with camera obscuras, showing that an external scene is depicted point-for-point upon the inner surface. The iris regulates the aperture, and thus brightness and sharpness, by limiting peripheral rays that would otherwise blur the image. Accommodation is explained as a mechanical adjustment that alters focus, which he attributes to changes in the position and action of the eye’s parts relative to the retina, anticipating later discussions even if the detailed mechanism was not yet correct. Sensation itself is not in the image but in the mind, mediated by the optic nerve, a point he marks while deferring full physiology.

Geometric Optics and Lens Design
With the sine law in hand, Descartes turns to lenses and imaging. Spherical lenses focus imperfectly because peripheral rays converge at different points, spherical aberration. He proposes aspherical surfaces that would refract all rays from a point to a point, deriving curves, later called Cartesian ovals, that solve this problem exactly for given media and object-image positions. He sketches how such profiles could improve telescopes and microscopes by yielding sharper, brighter images, and he analyzes compound systems through ray construction and proportionality, establishing a general method for tracing rays through successive refractions.

Method and Experiment
Throughout, simple mechanical analogies and carefully chosen experiments anchor the geometry. Water-filled globes, glass panes in various orientations, and dissected eyes serve to display laws in action. The argumentative style reduces complex phenomena to a few intelligible assumptions about contact action, resistance, and rectilinear propagation, then builds back up by measured construction.

Legacy
Dioptrics codifies a mathematical physics of light: the sine law of refraction, the retinal image theory of vision, and the ideal of designing instruments by geometry rather than rule of thumb. Even where later science amended his physical hypotheses, his synthesis of mechanism with geometric analysis set the terms for seventeenth-century optics and for the engineering of lenses for seeing farther and seeing more clearly.