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A typical camera lens employs a set of simple lenses organized in groups to form an image. In addition to lenses, a reflex lens uses mirrors (a mirrors-and-lenses optical system is called catadioptric, a word you can use to impress your friend). In practice, certain lenses groups are substituted by two mirrors that are used to fold the optical path in three. You can recognize them from their short and chubby shape, and from the fact that the front lens has an opaque insert in the centre: this is the back of the secondary mirror. This design makes sense only for long focal lenght lenses (I would say telephoto lenses, but then mturner would have me killed by rabid optical scientists, because no reflex lens is a telephoto lens!), and it replicates an optical design widely used in telescopes. I have read that the catadriotric design is less susceptible to chromatic aberration - but of course, not completely immune; there are still some lenses in a reflex lens.

Reflex lenses have a fixed f stop, because there is no place in the optical path for a diaphragm. They are never too bright; a typical lens would be a 500 mm f8. There is either a filter drawer or the back lens has a threaded collar that allows application of filters; ND filters are the only way to reduce the amount of light coming in. Keep in mind that a dark, extreme telephoto lens is an absolute bastard to focus; that's why nature photographers normally shun reflex lenses.

On the plus side, reflex lenses are lighter and cheaper than regular ones. How much cheaper? Extremely. A Nikon 500 mm f8 reflex lens costs, new, less than one thousand dollars. There is no non-catadioptric Nikon lens beyond 400 mm that consts less than four thousand dollars (new).

Because of the lens design, bokeh is very peculiar; the lens maps out of focus points to rings, which produces strange doughnut-studded backgrounds.

I have only seen reflex lenses with focal lengths ranging from 500 to 2000 mm. I have a vague memory of seeing a shorter one, but I cannot remember clearly.