The following experiments are stated by Mr. Ferguson in his “Lectures on select Subjects,” &c. “If a fire be made in a large room, and a smooth mahogany table be placed at a good distance near the wall, before a large concave mirror, so placed that the light of the fire may be reflected from the mirror to its focus upon the table; if a person stand by the table, he will see nothing upon it but a longish beam of light: but if he stand at a distance toward the fire, not directly between the fire and mirror, he will see an image of the fire upon the table, large and erect. And if another person who knows nothing of the matter beforehand should chance to come into the room, and should look from the fire toward the table, he would be startled at the appearance; for the table would seem to be on fire, and by being near the wainscot, to endanger the whole house. In this experiment there should be no light in the room but what proceeds from the fire; and the mirror ought to be at least fifteen inches in diameter. If the fire be darkened by a screen, and a large candle be placed at the back of the screen, a person standing by the candle will see the appearance of a very fine large star, or rather planet, upon the table, as bright as Venus or Jupiter. And if a small wax taper—whose flame is much less than the flame of the candle—be placed near the candle, a satellite to the planet will appear on the table; and if the taper be moved round the candle, the satellite will go round the planet.”
Many other illustrations of the effects of concave specula might have been given, but I shall conclude this department by briefly stating some of the general properties of speculums.
1. There is a great resemblance between the properties of convex lenses and concave mirrors. They both form an inverted focal image of any remote object, by the convergence of the pencil of rays. In those instruments whose performances are the effects of reflection, as reflecting telescopes, the concave mirror is substituted in the place of the convex lens. The whole effect of these instruments, in bringing to view remote objects in heaven and on earth, entirely depends on the property of a concave mirror in forming images of objects in its focus. 2. The image of an object placed beyond the centre, is less than the object; if the object be placed between the principal focus and the centre, the image is greater than the object. In both cases the image is inverted. 3. When the object is placed between the focus and the mirror, the image situated behind the mirror is greater than the object, and it has the same direction: in proportion as the object approaches the focus, the image becomes larger and more distant. These and similar results are proved by placing a lighted candle at different distances from a concave mirror. 4. An eye cannot see an image in the air except it be placed in the diverging rays; but if the image be received on a piece of white paper, it may be seen in any position of the eye, as the rays are then reflected in every direction. 5. If a picture drawn according to the rules of perspective, be placed before a large concave speculum, a little nearer than its principal focus, the image of the picture will appear extremely natural, and very nearly like the real objects whence it was taken. Not only are the objects considerably magnified, so as to approach to their natural size, but they have also different apparent distances, as in nature, so that the view of the inside of a church appears very like what it is in reality, and representations of landscapes appear very nearly, as they do from the spot whence they were taken. In this respect a large concave speculum may be made to serve nearly the same purpose, as the Optical Diagonal Machine, in viewing perspective prints. 6. The concave speculum is that alone which is used as the great mirror which forms the first image in reflecting telescopes; and it is likewise the only kind of speculum used as the small mirror, in that construction of the instrument called the Gregorian Reflector.
Quantity of light reflected by polished surfaces.
As this is a circumstance connected with the construction of reflecting telescopes, it may not be improper, in this place, to state some of the results of the accurate experiments of M. Bonguer on this subject. This philosopher ascertained that of the light reflected from mercury, or quicksilver, more than one-fourth is lost, though it is probable that no substances reflect more light than this. The rays were received at an angle of eleven and a half degrees of incidence, measured from the surface of the reflecting body, and not from the perpendicular. The reflection from water was found to be almost as great as that of quicksilver; so that in very small angles it reflects nearly three-fourths of the direct light. This is the reason why so strong a reflection appears on water, when one walks, in still weather, on the brink of a lake opposite to the sun. The direct light of the sun diminishes gradually as it approaches the horizon, while the reflected light at the same time grows stronger; so that there is a certain elevation of the sun in which the united force of the direct and reflected light will be the greatest possible, and this is when he is twelve or thirteen degrees in altitude. On the other hand, light reflected from water at great angles of incidence is extremely small. When the light was perpendicular, it reflected no more than the thirty-seventh part which mercury does in the same circumstances, and only the fifty-fifth part of what fell upon it in this case.
Using a smooth piece of glass, one line in thickness, he found that, when it was placed at an angle of fifteen degrees with the incident rays, it reflected 628 parts of 1000 which fell upon it; at the same time, a metallic mirror which he tried in the same circumstances, reflected only 561 of them. At a less angle of incidence much more light was reflected; so that at an angle of three degrees, the glass reflected 700 parts, and the metal something less, as in the former case. The most striking observations made by this experimenter relate to the very great difference in the quantity of light reflected at different angles of incidence. He found that for 1000 incident rays, the reflected rays, at different angles of incidence, were as follows.
| Angles of incidence | Rays reflected by water | Rays reflected by glass |
|---|---|---|
| 5° | 501 | 549 |
| 10 | 333 | 412 |
| 15 | 211 | 299 |
| 30 | 65 | 112 |
| 50 | 22 | 34 |
| 70 | 18 | 25 |
| 90 | 18 | 25 |
With regard to such mirrors as the specula of reflecting telescopes, it will be found, in general, that they reflect little more than the one half of the rays which fall upon them.
Uncommon appearances in nature produced by the combined influences of Reflection and Refraction.
The reflection and refraction of the