John M. Pierce's Telescope Making Articles

These articles are reproductions from the magazine of the '30s, Everyday Science and Mechanics.

In the present article, some miscellaneous facts about telescope making are presented

Part 12

Many amateur telescope makers who have tried to use their telescope on terrestrial objects have been puzzled by noticing that the focal point for fairly near objects is not the same as for the stars and planets. Possibly they were not even to pull the eyepiece enough to focus on nearby objects.

The telescope, like the camera, requires a longer extension for near than for far objects. Stars and planets, however, all have the same focus because they are all distant objects. The focal length of a mirror for distant objects is equal to half its radius of curvature. To find the position of the focal points for nearer objects we must use the law of conjugate foci (given at the end of this article), which applies equally to mirrors or lenses.

We will consider a mirror of 100 inch radius of curvature. This give a value of F of 48 inches (note: John Pierce made an error here as the real number is 50 inches) or 4 feet. If we observe an object at 25 ft., 100 ft., 1000 ft.. and infinity, and mote the different focal distances, we find that, for objects as near as 25 ft., the eyepiece has to be extended as much as 0.76 ft., or about 9 inches farther than for the stars. Objects 100 ft. distant require an extension of 0.17 ft. or about 2 inches; while objects 1000 ft. away require an extension of about 0.2 of an inch.

Objects nearer than 25 ft. will require still longer extension. The focus for an object at 96 inches (2F) (note: again an error between focal length and radius of curvature) is at this same distance (96 inches). This condition is fulfilled when we test a mirror at it's center of curvature with a lamp and a knife-edge. An object at the primary focus has its focal point at infinity; the rays from the objective lens or mirror being parallel rays that meet only at an infinite distance. Objects nearer than the primary focus have no real focal point, the rays form the lens or mirror being diverging rays.

Magnitude of a Star.
The magnitude of a star is its measure of brightness. Each magnitude represents a difference in brightness of 2 1/2 times: - a first magnitude star delivers to us 2 1/2 times as much light as one of the second magnitude. This does not mean that the first magnitude star is actually any larger or intrinsically brighter than those of higher magnitudes. It may merely be nearer. A 4 inch aperture telescope should show 12th magnitude stars. To see those of the 13th magnitude requires a telescope whose objective lens or mirror has 2 1/2 times the area of a 4 inch. Hence, to see a 13th magnitude star we must have a mirror slightly more than 6 inches in aperture.

A 10 inch telescope should show stars of the 14th magnitude; a 16 inch those of the 15th magnitude, and to see 16th magnitude stars requires a telescope of 24 inches aperture. Of course this applies to stars that we can see visually with the telescope. Much fainter stars can be photographed, the limit for any given telescope depending upon the length of photographic exposure.

The stars cross our sky at the rate of 360 degrees in 24 hours, or 15 seconds of arc, in one second of time. To find the actual angular aperture of a telescope with a certain eyepiece, time the passage of the star across the field of view; then multiply this time in seconds by 15 which will give the aperture of the telescope in seconds of arc.

For example, suppose we time the passage of a star, from the time it first appears on one side of the eyepiece, until it disappears on the opposite side and find it 47 seconds; 15 x 47 seconds is 705 seconds or 11 3/4 minutes of arc.

To find the apparent angular aperture multiply this by the power of the telescope. Suppose this was 48 inch focus mirror used with a 1/2 inch eyepiece; the power would be 48 divided by 1/2 or 96x. The apparent aperture then would be 95 x 11 3/4 arcminutes or 1128 arcminutes or 18.8 degrees.

Light Grasp and separating power.
A telescope has three functions. The one we usually think of is it's power to magnify; this makes possible our seeing details on the moon and planets that would be impossible otherwise. This magnification would be of little value if it were not for another power of the telescope, that of gathering in all the light from an object which falls on its objective or mirror and putting it into the image; thus a bright enlarged image is made possible. The opening or aperture in the human eye is rarely more than 1/8 inch in diameter. A 6 inch aperture telescope receives and uses about 2000 times as much light. This makes it possible to see and photograph very faint stars and nebulae. Thus the light grasp of a telescope depends on its aperture or size. It also depends on the reflecting quality of the mirror.

Figuring Your Mirror
A very accurate, yet simple way, of parabolizing to the degree desired is to place the testing lamp at a considerable distance from the mirror with the knife edge at the corresponding conjugate focus of the mirror. You then figure your mirror by polishing as needed to give the flat appearing shadow that indicates the perfect sphere when tested at the center of curvature in the usual way. Fig. 2 shows such a setup. The prism is place in the cone of rays to bring the focus to one side, where we can setup our knife-edge and make our observations of the Foucault shadows without getting the head in the way. The prism will, of course, leave a blind spot at the center of the mirror, but as this area is covered anyway by the telescope diagonal or prism, this will make no difference. The prism should be set about 4 inches inside the lesser conjugate focus of the mirror.

	Formula for Conjugate Foci:
		1/F = 1/f + 1/f'
	F = focal distance for distant objects = 1/2 radius of curvature
	f = Distance from lens or mirror to object
	f' = distance from lens or mirror to the image formed.
A larger telescope magnifies distances, but not the apparent diameter of stars.

Method of testing a telescope mirror; see previous articles for fuller instructions.