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In binoculars with Schmidt–Pechan or Uppendahl roof prisms, mirror coatings are added to some surfaces of the roof prism because the light is incident at one of the prism's glass-air boundaries at an angle less than the critical angle so total internal reflection does not occur. Without a mirror coating most of that light would be lost.
Another variant of the Porro prism of the second type with the same function is the Porro–Abbe prism; a two prisms variant that reduces the lateral beam axis offset by 23% compared to a traditional double Porro prism system in binoculars.
They are typically used to erect the image in binoculars or single-lens reflex cameras – without the prisms the image would be upside down for the user. Reflective prisms use total internal reflection to achieve near-perfect reflection of light that strikes the facets at a sufficiently oblique angle.
A Schmidt–Pechan prism is a type of optical prism used to rotate an image by 180°. These prisms are commonly used in binoculars as an image erecting system. The Schmidt–Pechan prism makes use of a roof prism section (from the German: "Dachkante", lit. roof edge ).
Binoculars diagram showing an Abbe–Koenig prism. An Abbe–Koenig prism is a type of reflecting prism, used to invert an image (rotate it by 180°). They are commonly used in binoculars and some telescopes for this purpose. The prism is named after Ernst Abbe and Albert Koenig.
An Uppendahl prism is an erecting prism, i.e. a special reflection prism that is used to invert an image (rotation by 180°). The erecting system consists of three partial prisms made of optical glass with a high refractive index cemented together to form a symmetric assembly and is used in microscopy as well as in binoculars technology.