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Many websites say this is because the effective focal length of the objective is increased by making the secondary mirror convex. This allows a Cassegrain telescope to be shorter than a similarly powered Newtonian.
What I don't understand is that if the focal length is made longer, how come the telescope doesn't have to be made longer too? Could someone explain how the focal length is increased and how this leads to shorter telescopes?
Basically, the light has a longer way to go after hitting the secondary mirror in a Cassegrain than in a Newton telescope.
In a Newton telescope (top image), the light hits the primary mirror and goes through the telescope tube once. In a Cassegrain telescope (bottom image), the light hits the primary mirror and goes through the entire length of the tube twice.
The focal length of a telescope is the distance between the telescope's primary mirror and the point where the light rays come together in focus. This is how far the light has to go after hitting the primary mirror before reaching the eyepiece.
Since the light goes a longer distance within a Cassegrain telescope than a Newton telescope of the same length, the focal length of the primary mirror can be made longer. Conversely, for two telescopes with the same focal distance, the Cassegrain will be shorter than the Newton telescope.
You can imagine the Cassegrain telescope folding the focal length in two, whereas the Newton telescope leaves the focal length stretched out flat.
In this image, light has a longer path to go in the bottom (Cassegrain) telescope than in the top (Newton) one. Even though they are the same size, the bottom telescope has a longer focal length.
This would make it seem that a Cassegrain can have a focal length twice the length of the tube, whereas a Newton can have a focal length roughly the length of the tube. In fact, Cassegrain have an extra trick up their sleeve to increase the focal length, and can have a focal length equal to five times the length of the tube.
The secondary mirror of a Cassegrain telescope is convex, and has its own focal length. The effective focal length of the primary mirror + the secondary mirror can thus be made longer than that of the primary mirror alone.
The Focal Length is not really the distance the light travels from the objective. The Focal Length is the diameter of the aperture divided by the tangent of the angle at which light rays from the edge of the objective converge at the telescopes focal point. The curved secondary mirror of a Cassegrain telescope decreases that angle, and thus increases the effective focal length.
