How to make a flat lens

“LENS” IS THE Latin word for lentil. And it is indeed true that the shape of bi-convex lenses—the familiar sort used as magnifying glasses—resembles those leguminous seeds. But that resemblance may soon be a thing of the past. For a group of engineers at Columbia University, in New York, led by Nanfang Yu, has worked out how to make magnifying lenses that are flat, and thinner than a hair.A lens works by slowing down a light wave as it traverses one of the lens’s faces (the speed of light in glass is about two-thirds of that in air). Slowing a wave changes its direction, a process called refraction. The angle through which it is refracted depends on its angle of incidence to the refracting surface—an angle that, on a curved surface, varies continuously. When the light leaves the lens it picks up speed again, and thus goes through a second refraction. The trick of the lensmaker’s art is to grind the two surfaces into such shapes that the sum of all this refraction brings the light passing through the lens to a focus.