Lens
A lens is a curved piece of transparent material that refracts light to converge or diverge it, forming images in eyes, cameras, and telescopes.
Definition
A lens is a curved piece of clear glass or plastic that bends light, and lenses can make things look bigger, smaller, closer, or clearer: a magnifying glass makes tiny print look large, and eyeglasses, cameras, microscopes, and eyes all use lenses, with a magnifying glass even able to focus sunlight into a hot spot because it gathers light across its whole surface and bends it all to one point. It is a transparent object with at least one curved surface that refracts light to form an image; a convex lens thicker in the middle bends parallel rays inward to a focal point while a concave lens thinner in the middle spreads rays outward, and depending on where the object sits, a converging lens can form a real image or a magnified virtual one. A thin lens obeys $1/f = 1/d_o + 1/d_i$ with magnification $m = -d_i/d_o$, $f$ positive for converging and negative for diverging lenses, and the focal length follows from the lensmaker's equation, $1/f = (n - 1)(1/R_1 - 1/R_2)$, so it depends on the material's index and surface curvatures; lens power in diopters is $P = 1/f$ with $f$ in meters, and real lenses suffer chromatic and spherical aberration, corrected with compound lens systems.
Example
A converging lens with focal length $10\ \text{cm}$ used as a magnifier with an object at $5\ \text{cm}$ produces a virtual, upright, enlarged image, while moving the object to $30\ \text{cm}$ makes the same lens project a real, inverted, smaller image on a screen $15\ \text{cm}$ behind it. A biconvex crown glass lens ($n = 1.52$) with $R_1 = +20\ \text{cm}$ and $R_2 = -20\ \text{cm}$ has $1/f = 0.52 \times (1/20 + 1/20) = 0.052\ \text{cm}^{-1}$, so $f \approx 19.2\ \text{cm}$, and an object $30\ \text{cm}$ away gives $d_i \approx 53.3\ \text{cm}$ and $m = -53.3/30 \approx -1.78$, a real, inverted image nearly twice the object's size.
Key Insight
The eye's own lens changes shape to focus; nearsighted people have eyes that focus too strongly and need diverging lenses, while farsighted people need converging lenses to add focusing power. A lens is really a device for equalizing travel time: its center is thickest so rays through the middle are slowed just enough to arrive at the focus in step with rays from the edge, which is Fermat's principle turned into glass.