Bending of light occurs in both prisms and lenses. Give reasons why prism does not form images ?
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Prisms have certain advantages but I wouldn't say unilaterally that they are better. Perhaps one of the biggest advantages is that the prism reflects by total internal reflection, which is very close to 100% reflection whereas the metalized mirror might achieve 95 or 96% reflection. This advantage is offset by the fact that the prism has two entrance faces, each of which can suffer a few percent loss unless a very sophisticated anti-reflection (AR) coating is used. If you're going to use a sophisticated AR coating on the prism that you could consider a very sophisticated reflection coating on the mirror that could get your reflectivity above 99%. So using modern coatings the mirror and the prism are about at parity.
In order for mirrors or prisms to reflect without distortion both of them need to be very robustly made. Prisms are inherently robust whereas mirrors are only robust if they are made very thick. Of course in a high-quality Periscope made of mirrors they would be made thick and very flat.
The AR Coatings on the prism are likely to be more environmentally robust than the metallic reflecting coatings on a mirror. This is because the AR coatings are dielectric and are more robust to corrosion than metals. Of course if the coating on the mirror is also dielectric, which would be necessary to achieve the greater than 99% reflectivity, then this advantage becomes moot.
The final issue is maintaining critical alignment by mounting. The prism is inherently robust and with three optical surfaces it is easy to register optically and mechanically. The mirror has only one optical surface but if it is made robustly it can also be optically registered and mounted.
Finally, if the periscope is short, the prisms can be optically cemented to each other for alignment, the way they are optically cemented in binoculars. But most periscopes have a significant distance between the two bends in the optical path so this advantage seldom applies to periscopes.Traditionally periscopes have been made with prisms but there is no reason that a high quality periscope could not also be made with high-quality first-surface mirrors. Such a telescope may have certain advantages over its prism-based counterpart, such as lower weight if weight is a concern such as for aerospace.
I once designed a periscope for use inside a nuclear reactor. This was a very long, very high performance periscope with multiple bends in the optical path. This periscope used mirrors for all of the bends in the optical path. The only prism was the derotation prism in the rotating head.
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