lens formula

lens formula, in optics, a formula relating the distance (u) of an object from a lens, the distance (v) of the object’s image from the lens, and the focal length (f) of the lens.

The formula is1/u + 1/f = 1/v.The formula follows the thin lens approximation in which the thickness of the lens is much smaller than the radius of curvature of the surfaces of the lens. This form of the lens equation also follows the Cartesian sign convention in which light travels from the object in a positive direction. This means that u is always negative.

A convex lens is thicker at its center than at its edges; a concave lens is thicker at its edges than at its center. With a convex lens, when the object is farther from the lens than the focal length, the light converges at the focal length to form a real image. The focal length f is positive, as is the image distance v. When the object is closer to the lens than the focal length, the focal length f is positive, but the image is now a virtual image because the light seems to diverge from the focal length and the image distance v is negative. With a concave lens, the focal length f is negative. All images formed are virtual, and thus the image distance v is also negative.