Lens

A lens is a transparent optical element that refracts light to form images. It typically consists of glass or plastic and has at least one curved surface. Lenses are designed to converge or diverge light rays; a converging lens has a positive focal length, while a diverging lens has a negative focal length. The bending of light follows Snell's law, and the focal length depends on the material's refractive index and the curvature of the surfaces. In the thin-lens approximation, 1/f ≈ (n−1)(1/R1 − 1/R2).

Common shapes include biconvex, planoconvex, biconcave, and planoconcave lenses. Planar-convex lenses are often used to minimize spherical aberration in focusing optics, while planoconcave lenses are used in beam projection. Lenses may be combined into achromatic doublets to reduce chromatic aberration by pairing glasses with different dispersion.

Materials range from crown and flint glasses to fused silica and plastics such as acrylic or polycarbonate. Many lenses receive anti-reflective coatings to improve transmission and reduce glare, and some are designed with aspheric surfaces to correct aberrations.

Applications span vision correction with eyeglasses and contact lenses, photography and cinematography, microscopes and telescopes, projection systems, and laser and optical instruments. Design choices balance focal length, aperture, aberration control, size, weight, and cost.

History notes: early lenses appeared in antiquity, with magnifying properties recognized in several ancient cultures. The understanding of image formation evolved through the work of Kepler, Descartes, and others, leading to modern manufacturing techniques that employ precision grinding, polishing, and coating to produce high-quality lenses.