Thin lens

A thin lens is an idealisation in which the lens thickness is negligible compared to the focal length and the object/image distances, so that rays can be treated as bending once at a single plane rather than twice at two separated surfaces. Under this approximation, a thin lens in air with focal length f obeys the thin-lens equation 1/f = 1/s_o + 1/s_i, relating the object distance s_o (measured from the lens to the object) and the image distance s_i (measured from the lens to the image). Magnification is m = −s_i/s_o, with sign encoding orientation (negative = inverted).

The focal length itself is given by the lensmaker's equation 1/f = (n − 1)(1/R₁ − 1/R₂), where n is the glass index and R₁, R₂ are the signed radii of curvature of the two surfaces (positive for a convex-toward-incoming-light surface, negative for concave). A biconvex lens with both radii equal in magnitude and n ≈ 1.5 has f ≈ R — a useful rule of thumb. Thin-lens analysis is the starting point for every optical system; real lenses are then corrected for aberrations (spherical, chromatic, coma, astigmatism, field curvature, distortion) by combining multiple thin-lens elements with carefully chosen indices and curvatures. The Kepler telescope, the microscope, the camera lens, and the spectacles on your face are all built from thin-lens formulas as a first approximation.