the coating than a lower-index lens (a consequence of the Fresnel equations). It is also generally easier and cheaper to coat high index lenses. Photolithography Antireflective coatings (ARC) are often used in microelectronic photolithography to help reduce image distortions associated with reflections off the surface of the substrate. Different types of antireflective coatings are applied either before (Bottom ARC, or BARC) or after the photoresist, and help reduce standing waves, thin-film interference, and specular reflections. Solar cells Solar cells are often coated with an anti-reflective coating. Materials that have been used include magnesium fluoride, silicon nitride, silicon dioxide, titanium dioxide, and aluminum oxide. Types Index-matching The simplest form of anti-reflective coating was discovered by Lord Rayleigh in 1886. The optical glass available at the time tended to develop a tarnish on its surface with age, due to chemical reactions with the environment. Rayleigh tested some old, slightly tarnished pieces of glass, and found to his surprise that they transmitted more light than new, clean pieces. The tarnish replaces the air-glass interface with two interfaces: an air-tarnish interface and a tarnish-glass interface. Because the tarnish has a refractive index between those of glass and air, each of these interfaces exhibits less reflection than the air-glass interface did. In fact, the total of the two reflections is less than that of the "naked" air-glass interface, as can be calculated from the Fresnel equations. One approach is to use graded-index (GRIN) anti-reflective coatings, that is, ones with nearly continuously varying index of refraction. With these, it is possible to curtail reflection for a broad band of frequencies and incidence angles. Single-layer interference The simplest interference anti-reflective coating consists of a single thin layer of transparent material with refractive index equal to the square root of the substrate's refractive index. In air, such a coating theoretically gives zero reflectance for light with wavelength (in the coating) equal to four times the coating's thickness. Reflectance is also decreased for wavelengths in a broad band around the center. A layer of thickness equal to a quarter of some design wavelength is called a "quarter-wave layer". The most common type of optical glass is crown glass, which has an index of refraction of about 1.52. An optimal single-layer coating would have to be made of a material with an index of about 1.23. There are no solid materials with such a low refractive index. The closest materials