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Telescope Types
I'm trying to buy a gravitational lens for my camera, but I can't tell if the manufacturers are listing comoving focal length or proper focal length.
Title text: I'm trying to buy a gravitational lens for my camera, but I can't tell if the manufacturers are listing comoving focal length or proper focal length.

Explanation

This comic shows diagrams of a number of different types of telescope, some real and others made up by Randall. It includes both refracting and reflecting designs; see 1791: Telescopes: Refractor vs Reflector for the important (according to Randall) differences between them.

Type Real? Refractor/Reflector Description
Prime Focus Yes Reflector A telescope design where the observer/receiver is situated at the focal point of a single mirror. Rare in optics, but a common design in radio telescopes.
Herschelian Yes Reflector A telescope design much akin to Prime Focus but with the mirror tilted so that the observer does not block incoming light. Named after astronomer William Herschel.
Newtonian Yes Reflector Newtonian telescopes employ a second, flat mirror along with the primary parabolic mirror.
Galilean Yes Refractor What might usually come to mind when picturing a telescope. A long tube that uses lenses rather than mirrors (making it a refracting telescope) to magnify images.
Keplerian Yes Refractor An improvement on Galilean telescopes, using a convex lens rather than a concave one at the eyepiece (as shown in the diagram). It does however invert images.
Gregorian Yes Reflector Uses two concave mirrors, the secondary being placed beyond the primary's focal point. The image is reflected back through a hole in the primary mirror. Unique among reflectors in that the image is not inverted.
Cassegrain Yes Reflector Similar to prime focus, but uses a secondary mirror to reflect light through a hole in the primary mirror to the observer (situated at the rear)
Cardboard tube Yes, but not as a (functional) telescope Neither Children may sometimes use tubes, particularly the cardboard middles from paper rolls, as a play 'telescope'. Looking through a tube can give an illusion of magnification by removing distractions and focusing your attention on the object in view, but it doesn't actually magnify the object being viewed.
Kaleido Yes, but not as a telescope ReflectorrotcelfeR A kaleidoscope is similar in form to the stereotypical 'ship's telescope', being a tubular object that you look in to one end of. However, it isn't really a telescope, because you can't use it to magnify arbitrary objects of interest. The non-viewing end is closed, and you view patterns created by many fragmented reflections of tiny objects contained at the end, rather than remote objects. The mirrors are also usually flat, so there's no magnification.
Liquid Mirror Yes Reflector A telescope with the same design as Prime Focus, using a rotating pool of reflective liquid (most commonly mercury) as a mirror. The diagram adds a straw so that someone can drink the liquid. This would not improve telescope performance or end well for the drinker.
Narcissian Yes, but not as a telescope Reflector This is like a prime focus telescope, but the focus is outside the end of the telescope where the viewer is located, so they can only see themselves, magnified by the concave mirror. This is inspired by the myth of Narcissus, who fell in love with his reflection in a pool of water. A House of Mirrors (a typical attraction at a funfair) might feature such a 'telescope', because it is basically a concave mirror.
Gravitational Yes Refractor Using the gravitational effect of very large objects on the light passing around them to gain a magnified (if distorted) view of objects beyond them. These are formed naturally by large stars (particularly black holes) and galaxies, which can't be constructed on Earth[citation needed]. There are proposals to launch missions to the very far reaches of the Solar System to "construct" a Solar gravitational lens telescope, but the masses and distances involved are not compatible with consumer camera hardware. In the title text, Randall makes a pun on whether the listed focal length of a gravitational lens is measured in the comoving or proper reference frame — that is, whether the expansion of the universe (between the place and time of the lens's creation or construction and Randall's decision to purchase) has been factored out or not. At the cosmological scales between stars and galaxies, where gravitational lensing is most relevant, this is a useful distinction to make, but stars are not for sale (by any legitimate commercial entity) and so nobody would be advertising any focal length in either reference frame for any purchaser.
Geological No Reflector This 'telescope' employs a single mirror to show the observer the 2003 movie "The Core". As a telescope it would not be useful, not least because it cannot be pointed at anything in the sky. Its relevance to real geology is also dubious.

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