A Fresnel lantern is a light which makes use of the Fresnel Lens, named after Augustin-Jean Fresnel. The lens has a stepped appearance, instead of a round, smooth one. This allows the lens to have a much greater curvature than would otherwise be practical.
Theatrical Fresnels are typically made in 8, 6 or 3 inch varieties, referring to the diameter of the lens, with lamps ranging in wattage from 150 W (typically with a 3-inch fresnel) to 2000W (with an 8-inch fresnel). Fresnel lenses can operate close to the light source and are very cheap to produce, so the lanterns tend to be small and cheap.
Unfortunately, Fresnels are not very efficient. The reflector cannot be larger than the lens aperture, and thus all the radiated light that is neither redirected forward by the spherical reflector behind the bulb or emitted directly through the lens is absorbed by the casing as waste heat.
The stepped lens gives the beam a very even spread of light, compared to an ERS, and this makes them useful for color washes or back- or top- lighting. They are best used at a medium throw. The lack of beam control can be combated by the use of barn doors.