The second major type of telescope is the reflecting telescope. The reflecting telescope was invented by Newton and considered an improvement on Galileo's design. Most reflecting scopes still use Newton's design. Reflecting scopes use a wide concave mirror at the back of the tube to bring light to a focal point in front of the mirror which is then usually reflected sideways toward the eyepiece by a flat, angled mirror. There are also compound scopes that work like reflecting scopes but there is a hole in the center of the concave mirror and the mirror at the foal point reflects light back through the hole where it is magnified by an eyepiece at the end of the tube. Below are diagrams of both reflecting and compound telescopes.
Now for some pros and cons. Refractor tubes are usually longer and skinnier, thus have smaller apertures (and cost more per unit of aperture length); while reflectors are wider and shorter with larger apertures (and less cost per unit of aperture length). Because of this, refractors are usually more expensive and better for observing close planets while reflectors are better for observing deep sky objects like galaxies and nebulae.