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and mark these divisions , , , &c. Let Ao be extended, and parts be taken in it equal to F 0, at 2, 3, 4, &c. Now if any of the points 1, 2, 3, 4, &c. be the focus of incident rays,
the correspondent points 1, , , , &c. in o F will be the focus of the reflected rays, and vice versa.
James. Do you mean by that, if incident rays be at or, or ļ, the reflected rays will be at 2, 3, 4?
Tutor. I do: place a candle at 2, and an inverted image will be seen at : now place it at 4, and it will also move back to : these images may be taken on paper held in those respective places.
Charles. I see the farther you proceed one way with the candle, the nearer its inverted image comes to the point r.
Tutor. True: and it never gets beyond it, for that is the focus of parallel rays after reflection, or of rays that come from an infinite distance.
James. Suppose the candle were at o?
coincide: and as the image of an object between F, and a concave speculum, is on the other side of the speculum, this experiment of the candle and paper cannot be made.
I will now just mention an experiment that we may hereafter make. At one end of an oblong box, about two feet long, and 15 inches wide, is to be placed a concave mirror; near the upper part of the opposite end a hole is made, and about the middle of the box is placed a hollow frame of pasteboard that confines the view of the mirror. The top of the box next the end in which the hold is made is covered with a glass but the other half is darkened. Under the hole are placed in succession different pictures, properly painted, which are thrown into perspective by the mirror, and produce a beautiful appearance.
Of Convex Reflection-Of Optical Delusions
CHARLES. You cannot, I see,
make the same experiment with the candle, and a convex mirror, that you made yesterday with the concave one.
Tutor. Certainly, because the image is formed behind the glass : but it may, perhaps, be worth our while to consider how the effect is produced in a mirror of this kind. Let a b (Plate 111. Fig. 22.) represent a convex mirror, and a f be half the radius of convexity, and take a F, F 0, 0 B, &c, each equal a f. If incident rays flow from
2, the reflected rays will appear to con from behind the glass at .
James. Do you mean if a candle be pla ced at 2, the image of it will appear to be formed at behind the glass?
Tutor. I do: and if that, or any other object, be carried to 3, 4, &c. the image will also go backward to j, , &c.
Charles. Then, as a person walks towards a convex spherical reflector, the image appears to walk towards him, constantly in creasing in magnitude, till they touch each other at the surface.
Tutor. You will observe that the image, however distant the object, is never farther off than at f; that is, the imaginary focus of parallel rays.
James. The difference then between convex and concave reflectors is, that the point f in the former is behind the glass, and in the latter it is before the glass as F.
Tutor. Just so: from the property of diminishing objects, spherical reflectors are
not only pleasing ornaments for our best rooms, but are much used by all lovers of picturesque scenery. “ Small convex reflectors,” says Dr. Gregory, “ are made for the use of travellers, who, when fatigued by stretching the eye to Alps towering on Alps, can, by their mirror, bring these sublime objects into a narrow compass, and gratify the sight by pictures which the art of man in vain attempts to imitate.”*
Concave mirrors have been used for many other and different purposes; for by them, with a little ingenuity, a thousand illusions may be practised on the ignorant and credulous.
Charles, I remember going with you to see an exhibition in Bondstreet, which you said depended on a concave mirror ; I was desired to look into a glass, I did so, and started back, for I thought the point of a dagger would have been in my face. I look
* See Economy of Nature. Vol. I. p. 26. 2d Edition.