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- why is there no market for an Amici mirror as technically it is possible ?
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Two-mirror solutions do exist, and have ben used many times before, e.g.. in periscopes and in big binocular telescopes where prisms would be impossibly large.
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- why do binoculars not use mirrors as 4 mirrors have less light loss than 4 prisms ?
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They don't - 2 mirrors are sufficient to produce an erect image and without left-right reversal.
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- why do binoculars with 90º viewing angle not use Amici prisms (or mirrors) ? Less weight and light loss.
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Porro prisms suffice, and the cost of manufacture is very low. Historically, after WWII many of the plants that made pentaprisms for SLR film cameras could crank out Porro prisms for next to nothing and small roof prisms weren't much harder. Roof prisms are still used in the small binoculars and Zeiss, Leica also make larger but rather expensive pairs. Porro prisms in particular provide a very useful aspect for the average binoculars in the range 20-70mm aperture where, for mechanical reasons, it was desirable to make the spacing of the optical axes of the two objectives somewhat larger than the inter-pupillary distance between your eyes - and the binoculars also had to provide an easy way to adjust for variations between users with different IPD. The traditional binocular design with Porro prisms provides an elegant way to do this - and achieve a very compact length as well. In comparison roof-prism binoculars are quite a bit longer and heavier, and due to the fact that most peoples eyes are about 70mm apart this poses an upper aperture limit on any design that uses co-axial optics (such as roof prisms).
Amici prisms aren't a solution for binoculars.
As indicated below total internal reflection is a very useful thing, better than a mirror. In addition they are easier to keep clean, and better yet, the surfaces do not deteriorate with time the way first-surface mirrors do. If commercial binoculars were based on mirrors they would have a relatively short life in the hands of most owners before the mirrors are so degraded as to be useless, whereas the life of prism binoculars is limited only by the time for fungus to set in, or corrosion or mechanical misadventure (dropped) to ruin the assembly.
Large prisms however pose several issues:
- mass, which increases as the cube of the dimensions;
- passing the convergent beam through a long optical path in glass between plane surfaces introduces spherical aberration. The objective must be designed to compensate for this, or alternatively mirrors can be used (which contribute no spherical aberration).
- manufacturing cost, which increases as the 5th power of the dimension, due to the difficulties in maintaining accurate angles, while making large optically flat surfaces.
The other bit of history is that until the 1950's the vast majority of binoculars were sold to the military - in Japan, the US and europe. Small size and light weight were high priorities - whether it be the army footsoldier in the trenches who had to carry everything, aircraft (every pound of weight mattered) or warships (size and weight). The Porro prism design was always preferred because it was the most compact and lightest. The same applies even now if you are bushwalking or backpacking.
You have a wee bit to learn about optics, and prisms in particular, Grasshopper.
