Charles. I do not quite comprehend in what manner reflection takes place at a convex mirror. Tutor. I will endeavour by a figure to make it plain: C D (Plate III. Fig. 19.) represents a convex mirror standing at the end of a room, before which the arrow A B is placed on one side or obliquely: where must the spectator stand to see the reflected image? Charles. On the other side of the room. Tutor. The eye E will represent that situation: the rays from the external parts of the arrow, A and B, flow convergingly along ▲ a and в b, and if no glass were in the way they would meet at P; but the glass reflects the ray A a along a E, and the ray B b along bɛ; and as we always transfer the image of an object in that direction in which the rays approach the eye, we see the image of A along the line E a behind the glass, and the image of B along E b, and, of course, the image of the whole arrow is at 6. By means of a similar diagram, I will show you more clearly the principle of the concave mirror. Suppose an object e (Plate. III. Fig. 20.) to be beyond the focus, F, and the spectator to stand at z, the rays e b and e d are reflected, and where they meet in E the spectator will see the image. James. That is between himself and the object. Tutor. He must, however, be far enough from it to receive the rays after they have diverged from E, because every enlightened point of an object becomes visible only by means of a cone of diverging rays from it, and we cease to see it if the rays become parallel or converging. Charles. Is the image inverted? Tutor. Certainly, because the rays have crossed before they reach the eye. You may see this subject in another point of view: let ry (Plate 111. Fig. 21.) be a concave mirror, and o the centre of concavity: divide o A equally in F, and take the half, the third, and the fourth, &c. of F o, and mark these divisions,,, &c. Let Ao be extended, and parts be taken in it equal to F o, 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, 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 1: 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? Tutor. Then the object and image will 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, . CONVERSATION XIV. Of Convex Reflection-Of Optical Delusions-O£ Anamorphoses. GHARLES. 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 ƒ be half the radius of convexity, and take a F, F 0, 0 B, &c, each equal a f. If incident rays flow from |