You can use this cutaway telescope to show the parts of the telescope and describe their functions.

Shown above is a Celestron 10 telescope, which has had a portion of the main tube removed to show the parts inside. Optical telescopes come in a variety of designs, which generally fall into one of two categories. Refracting telescopes use a system of lenses to gather incoming light and to form an image, and are based on the priciples illustrated in demonstration 80.51 -- Telescope. Reflecting telescopes use a set of mirrors to gather incoming light and to form the image. Several types of reflecting telescopes are available. The one in this demonstration is a Schmidt-Cassegrain telescope. A Cassegrain telescope consists of a tube, at the rear of which sits a curved (concave) primary mirror, which reflects the light entering the tube back toward the opening of the tube, where it would normally focus at a point outside the tube, called the prime focus. A (convex) secondary mirror, which sits in the center of the opening of the tube, reflects the light back through a hole in the center of the primary mirror, to focus at a point outside the rear of the tube. This point is called the Cassegrain focus. An eyepiece, or ocular, placed at its focal distance behind the Cassegrain focus allows you to see the image produced by the telescope. You can also place a camera at the Cassegrain focus. The telescope then acts as a long telephoto lens. Some telescopes are designed to allow removal of the secondary mirror and attachment of a camera to do photography at the prime focus.

What differentiates the Schmidt-Cassegrain telescope from the Cassegrain telescope is the addition of an optic called a corrector plate. This is a lens that spans the opening of the telescope, and which has a central hole in which to mount the secondary mirror. The corrector plate is designed to remove spherical aberrations introduced by the primary mirror because its curvature deviates slightly from that of a parabolic surface. The corrector plate is a refractive optic, so the Schmidt-Cassegrain design contains both reflective and refractive optics. Such a system is called a catadioptric system. (The eyepiece, which is refractive, does not enter into this nomenclature; a Cassegrain telescope is not considered a catadioptric system.) The photograph below has the various parts of the telescope labeled.

 

The optics of the telescope

The body of the telescope is a tube, which holds the mounts for the optics, and encloses the optical path. Light enters the open end of the tube through a corrector plate, which, as noted above, removes spherical aberrations introduced by the primary mirror because of its non-ideal curvature. After passing through the corrector plate, the light is reflected by the primary mirror back toward the open end of the telescope. The secondary mirror, mounted in the center of the corrector plate, reflects the light back down the tube, through a hole in the primary mirror. A baffle tube extending from the hole in the primary mirror blocks stray light from the optical path. Attached to the rear of the telescope tube is the rear cell, which provides a mount for external optics. The visual back, which attaches to the rear cell, receives any optic that has standard tubulation, in this case, that with 1-1/4″ o.d. Some telescope optics have 2″ tubulation. While it would be possible to insert an eyepiece directly into the visual back, this would require you to place your head directly behind the rear of the telescope tube, which in many, if not most, cases, would make viewing very uncomfortable, or even impossible. For this reason, one normally inserts an optic called a star diagonal into the visual back. This is usually a flat, highly reflective mirror, set at 45° to the axis of the telescope tube. The one mounted to this telescope is a right-angle prism, with its long face set at 45° to the telescope tube axis. The star diagonal on this telescope is missing the tube that receives the eyepiece. This would go on the face that is 90° to the face that is attached to the visual back. The star diagonal allows you to view on an axis that is perpendicular to the telescope axis, and also to rotate that axis to whatever direction makes viewing most comfortable.

With an eyepiece inserted directly into the visual back (no star diagonal), you would see an inverted image; it would be upside down and flipped left to right. A star diagonal inserted between the visual back and the eyepiece reflects the image through 90° in one plane, and thus erects the image in that plane. For example, with the star diagonal as shown in the photograph above, if there were a tube with an eyepiece attached at the opening, if you looked through the eyepiece with your head oriented vertically, that is, forehead near the rear of the tube and chin toward the dust cap, you would see an erect image, flipped from left to right.

The Celestron 10 has an entrance aperture of 10 inches, and a focal length of 135 inches (3400 mm), which corresponds to a photographic speed of f/13.5. The magnification achieved by the telescope is the ratio of the focal length of the telescope to that of the objective, or:

M = f_telescope/f_eyepiece

For example, with an eyepiece whose focal length is 40 mm, the magnification is 3400 mm/40 mm = 108, and with a 10-mm eyepiece, it is 340. The field of view depends on the apparent field of view of the eyepiece, which is typically around 46° (but varies according to the design of the eyepiece), and equals the magnification divided by the apparent field of view of the eyepiece:

FOV = FOV_eyepiece/M

For the cases above, the 40-mm eyepiece gives a field of view of about 0.42°, and the 10-mm eyepiece gives a field of view of about 0.14°. For reference, both the moon and the sun subtend an angle of about 0.5°.

Mounting and aiming the telescope

The telescope tube is mounted between the tines of a fork, the bottom of which is fastened to a clock drive. If the telescope were in use, the base that contains the clock drive would be mounted on a wedge, adjusted so that the long axis of the fork sits at an angle with respect to vertical that corresponds to the latitude of the location where it is being used (for Broida Hall this is 34°24′50″, or 34.4139°). That is, the wedge is set to the complementary angle of the latitude (so for Broida Hall it should be set to about 55.6°). The wedge sits on the (level) head of a tripod or other stand. This type of mount is called an equatorial mount. To use the telescope (in the northern hemisphere), one sets the base of the wedge level, and points the tines of the fork north. When the telescope is set this way, the central axis of the fork sits parallel to the earth’s axis of rotation. (Note that if the telescope were at the equator, the fork would have to be set horizontal and pointing north to be parallel to the earth’s axis, and that as we moved the telescope northward, we would have to raise the fork, until at the north pole it would be vertical.) The clock drive turns the fork in the opposite direction to that of the earth, at the same speed. With this arrangement, when you point the telescope at a particular object, as the earth turns, the clock drive rotates the fork in the opposite direction, and the telescope continues to point to that object.

Whether we wish to look at objects whose locations in the sky are known, or to note the locations of objects that we are observing for the first time, we need some way of defining positions in the sky – a system of celestial coordinates. Whereas we use the coordinates of latitude and longitude to designate the locations of points on the earth’s surface, we use an analogous system to locate objects in the sky. This system is based on the concept of the celestial sphere, an imaginary spherical surface to which celestial objects appear to be attached as they move across the sky (see demonstration 92.06 -- Celestial globe). As the note above regarding the clock drive on the telescope mount implies, the motion of objects across the sky is due to the earth’s rotation. We think of the celestial sphere as sharing the same axis of rotation as the earth, but rotating from east to west. The north celestial pole is above earth’s north pole, the south celestial pole is above the south pole, and the celestial equator is on the same plane as the earth’s equator. In the northern hemisphere, celestial objects appear to move in circular paths about a point that is very close to the star Polaris, which is also known as the Pole Star or North Star. Polaris is so named, because it sits above the north pole, almost in line with the earth’s axis of rotation. The two coordinates we use to locate objects in the sky are right ascension (RA) and declination (dec). Right ascension is analogous to longitude, and declination is similar to latitude. An object’s declination is the angle of its position with respect to the celestial equator. Declination is measured in degrees north or south of the celestial equator, and is positive north of the celestial equator and negative south of it. The celestial equator is at a declination of 0°, the north celestial pole is at +90° and the south celestial pole is at -90°. Since the celestial sphere is rotating with respect to the Earth (or vice versa), right ascension is measured in time relative to a specific reference point, in hours (^h), minutes (^m) and seconds (^s), and it increases toward the east. The reference point for zero right ascension is by convention taken as the position of the sun in the sky at the instant of the vernal equinox.

The vernal equinox is when the sun crosses the celestial equator from south to north, which occurs on or about March 21, when it is spring in the northern hemisphere. It is so called, because at that point in the earth’s orbit, the plane in which the earth’s axis lies is perpendicular to the line between the earth and the sun, and the periods of night and day are equal. (At the opposite point in the orbit is the autumnal equinox, which occurs when the sun crosses the celestial equator from north to south on September 21.) The earth’s rotation causes it to bulge slightly at the equator. As a result, except near the equinoxes, the gravitational force between the earth and the sun exerts a torque about the center of the earth, pulling the bulging equator toward the plane of the ecliptic. The moon’s orbit lies at an angle of 5° to the ecliptic, so it, too exerts a torque in the same direction. This torque causes the earth’s axis to precess slowly. Because of this precession, the equinoxes drift westward by 50.3 arc seconds per year, or about 0.14 arc seconds per night. For this reason, astronomers use the location of the equinox at some standard year, which is updated every 50 years. The last two standard equinoxes are from 1950 and 2000; the next one will be for 2050. (Some people refer to these as “epochs,” which is not right. The epoch is the year during which one observes the position of an object; the equinox is the reference frame for the equinox that one uses to make the measurement. See, for example, https://srmastro.uvacreate.virginia.edu/astr313/lectures/coordchange/coordchange.html or http://mingus.mmto.arizona.edu/~bjw/mmt/spectro_standards.html#:~:text=What's%20the%20difference%20between%20equinox,star%20was%20at%20year%202015.5..)

Since the earth rotates through 360° in 24 hours, in one hour it rotates 15°, in one minute it rotates 0.25° (15 arc minutes, or 15′), and in one second it rotates 0.0042° (15 arc seconds, or 15″).

Around the circumference of the plate on which the fork is mounted, is a dial with a scale marked in hours, with a mark every five minutes, and longer marks on the quarter and half hours. This dial is moveable, so that you can set it to the time of day or whatever reference you wish. As the telescope sits in the photograph, hidden behind the bottom of the fork is a lock. When you release the lock, the fork is free to rotate about its long axis. You can then use the scale to set the position of the yoke to the desired right ascension, and then tighten the lock. The fork is now fixed to the clock drive and rotates with it. The knob on the side of the base allows you to make fine adjustments to the right ascension setting of the telescope.

Around the pivot at the end of each tine on the fork is a dial with a scale around its circumference, marked in degrees. At the top of the fork tine on the left in the photograph, is a lock. Releasing that lock allows you to rotate the tube about the pivot. You can then use the scale to set the telescope tube to the desired declination. The knob at the bottom of that fork tine allows you to make fine adjustments to the declination setting.

As noted above, to align the telescope (in the northern hemisphere), you would set it so that the base of the wedge (top of the tripod or other stand) sits level, and the long axis of the fork points to the north. With the tube in line with the fork, it should then point to Polaris (or close to it). It is also possible to use other stars whose locations you know to align the telescope. Many telescopes have computer control, so that after you set the telescope up, the computer allows you to choose reference stars to which to point the telescope, and from the settings required to align the telescope with those stars, and the coordinates stored in memory, the computer can calculate a calibration that then allows you to point the telescope at any object you choose.

Mounted to the side of the telescope tube is a small telescope called a finder scope. Because this telescope has a relatively wide angle of view, if you set the telescope so that it points in a direction that is close to the coordinates of a particular object, that object should appear somewhere in the field of the finder scope. If you then use the fine adjustments to center the object in the finder scope, you will see it in the main telescope. (This is actually the technique one uses to find reference stars for calibration of the telescope. The telescope moves to an alignment star, you center it in the finder scope, and then you center it in the main telescope. You then repeat the process for another alignment star.) If you cannot see the object in the finder scope, it is much easier to find by looking through the finder scope as you move the telescope, than it would be if you searched for it while looking through the main telescope.

The dust cap allows you to protect the corrector plate and secondary mirror mount when the telescope is not in use.

References:

1) Chaisson, Eric and McMillan, Steve. Astronomy Today, Third Edition (Upper Saddle River, New Jersey: Prentice-Hall, Inc., 1999), pp. 8-12, 178, 386-387.
2) https://science.nasa.gov/learn/basics-of-space-flight/chapter2-2/