thin lens

A magnifying glass held over a page enlarges the print, held up to the Sun it can burn a dot into paper, and held far from your eye it flips the distant world upside down. A thin lens is a piece of transparent material, usually glass or plastic, with two curved surfaces that bends light by refraction to bring it together or spread it apart. It is the workhorse of optics, and it answers the question: how can a single shaped piece of glass gather scattered light back into a sharp image?

Light bends at each surface of the lens according to Snell's law, and the two surfaces are shaped so all the bending adds up to steer parallel rays to a single point. A converging (convex) lens is thicker in the middle, it brings parallel light to a real focal point on the far side and has a positive focal length. A diverging (concave) lens is thinner in the middle, it spreads parallel light so it appears to come from a focal point on the near side and has a negative focal length. The word thin means the lens is thin enough compared with its focal length that we can ignore its thickness and treat all the bending as happening at one central plane, a simplification that makes the neat thin-lens equation 1/f = 1/d_o + 1/d_i work.

Thin lenses are the beating heart of nearly every optical device: cameras, microscopes, telescopes, projectors, eyeglasses, and the lens inside your own eye. Combine two or more and you can build almost any instrument. An honest caveat: the thin-lens idealization ignores lens thickness and assumes rays stay near the central axis and are close to one colour. Real thick lenses suffer aberrations, spherical aberration blurs off-axis rays and chromatic aberration (from dispersion) fringes edges with colour, which is why quality lenses are actually stacks of several elements.