Power of a Lens

The power of a lens is defined as the reciprocal of its focal length, expressed in metres: $P=\frac{1}{f\,(\text{in metres})}.$ Power measures how strongly, and in which sense, a lens converges or diverges a beam of light -- a short-focal-length lens bends light sharply and so has a large power, while a long-focal-length lens bends light only gently and has a small power. The SI unit of power of a lens is the dioptre, symbol D, defined as the power of a lens of focal length exactly $1\ \text{m}$ ($1\ \text{D}=1\ \text{m}^{-1}$); this is also the unit an optician writes on a spectacle prescription. Because the sign convention makes the focal length of a convex (converging) lens positive and that of a concave (diverging) lens negative, the power of a converging lens comes out positive and the power of a diverging lens comes out negative -- so the sign of a lens's power alone, without needing to say "convex" or "concave" at all, already tells its type; an optician's prescription of "$+2.0\ \text{D}$" thus specifies a converging lens (used to correct hypermetropia, or long-sightedness) while "$-3.5\ \text{D}$" specifies a diverging lens (used to correct myopia, or short-sightedness). Defining power as the reciprocal of focal length, rather than working with focal length directly, is what makes the next sub-sectio …