Thin Lens Equation: 1/f = 1/u + 1/v relates focal length (f), object distance (u), and image distance (v). This equation applies to both thin lenses and spherical mirrors.
Magnification: m = v/u = h'/h where h' is image height and h is object height. Negative magnification indicates inverted image; |m| > 1 means enlarged image.
Lens Power: P = 1/f (in diopters when f is in meters). Used in optometry for prescribing corrective lenses. Positive power converges light (farsightedness correction); negative power diverges light (nearsightedness correction).
Real vs Virtual Images: Real images form where light rays actually converge (can be projected on screen), with positive v. Virtual images form where rays appear to diverge from (cannot be projected), with negative v.
Sign Convention (New Cartesian): Distances measured from lens/mirror center. Direction of incident light is positive. Object distance usually negative (left side). Real image v is positive (right side); virtual image v is negative (left side).
Applications: Cameras, telescopes, microscopes, eyeglasses, contact lenses, magnifying glasses, projectors, binoculars, and all optical instruments rely on lens equations for design and analysis.