The Practical Astronomer / Comprising illustrations of light and colours--practical descriptions of all kinds of telescopes--the use of the equatorial-transit--circular, and other astronomical instruments, a particular account of the Earl of Rosse's large telescopes, and other topics connected with astronomy

by Thomas Dick

CHAPTER III.

ON THE OPTICAL ANGLE, AND THE APPARENT MAGNITUDE OF OBJECTS.

In order to understand the principle on which telescopes represent distant objects as magnified, it may be expedient to explain what is meant by the angle of vision, and the apparent magnitudes under which different objects appear, and the same object, when placed at different distances.

figure 40*.

The optical angle is the angle contained under two right lines drawn from the extreme points of an object to the eye. Thus AEB or CED (fig. 40*.) is the optical or visual angle, or the angle under which the object AB or CD, appears to the eye at E. These two objects, being at different distances, are seen under the same angle, although CD is evidently larger than AB. On the retina of the eye, their images are exactly of the same size, and so is the still larger object FG.

figure 41.

The apparent magnitude of objects denotes their magnitude as they appear to us, in contradistinction from their real or true magnitude, and it is measured by the visual angle; for whatever objects are seen under the same or equal angles appear equal, however different their real magnitudes. If a half-crown or half-dollar be placed at about 120 yards from the eye, it is just perceptible as a visible point, and its apparent magnitude, or the angle under which it is seen, is very small. At the distance of thirty or forty yards, its bulk appears sensibly increased, and we perceive it to be a round body; at the distance of six or eight yards, we can see the king or queen’s head engraved upon it; and at the distance of eight or ten inches from the eye it will appear so large, that it will seem to cover a large building placed within the distance of a quarter of a mile, in other words, the apparent magnitude of the half-crown held at such a distance, will more than equal that of such a building, in the picture on the retina, owing to the increase of the optical angle. If we suppose A (fig. 41.) to represent the apparent size of the half-crown at nine yards distance, then we say it is seen under the small angle FED. B will represent its apparent magnitude at 4½ yards distant under the angle HEG, and the circle C, its apparent magnitude at 3 yards distant, under the large angle KEI.

figure 42.