Notes:

To understand how liquid crystals can be used to correct the eye's optical system, it helps to review how ordinary lenses focus light. When a plane wave of light enters the optically dense medium of the lens, the light slows down. This property of transparent materials to slow the propagation of light is summarized by its "refractive index". The higher the refractive index the more light is slowed down, or retarded. All lenses have one or more curved surfaces, which cause some parts of the wavefront to enter the lens material before other parts and begins to slow down sooner. As a result, the flat wavefront becomes curved as it propagates through the lens. When the wavefront emerges from the lens some parts pick up speed first because they enter the air first where the refractive index is lower. Eventually the entire wavefront escapes the lens with a curved shape that causes it to focus to a point. Thus, a perfect lens is one which reshapes the plane wave into a perfect spherical shape which will focus down to a perfect point. In reality the focus is never a perfect point because of diffraction effects, but for the eye diffraction is not a major limiting factor except when the pupil is very constricted.

Focusing of light by a lens is analogous to a marching band of musicians traveling across an open field. The musicians all march to the same beat and their cadence (i.e. temporal frequency of light oscillation) never varies. The curved surface separates the dry marching field where the musicians have a long stride (i.e. wavelength is relatively long) from a muddy field where the musicians must shorten their stride to avoid slipping (i.e. the wavelength of light is reduced). Since the musicians near the middle enter the muddy field first, that part of the line slows down first. As time progresses, more and more of the marching line enters the slower medium but because the interface is curved, those musicians furthest from the centerline stay on dry land the longest and therefore travel the furthest before they too must enter the slower field. By the time the entire marching line has passed into the new medium, the end of the line has advanced further than the center and so the line is curved. So it is with light. The incident wavefront is delayed more near the centerline than at the edges and thus the wavefront becomes curved.