_Mrs. B._ In order, therefore, that rays may fall perpendicularly to the mirror at B and F, the rays must be in the direction of the dotted lines, which, you may observe, meet at the centre O of the sphere, of which the mirror forms a portion. Now, can you tell me in what direction the three rays, A B, C D, E F, will be reflected? _Emily._ Yes, I think so: the middle ray, falling perpendicularly on the mirror, will be reflected in the same line: the two outer rays falling obliquely, will be reflected obliquely to G and H; for the dotted lines you have drawn are perpendiculars, which divide the angles of incidence and reflection, of those two rays. _Mrs. B._ Extremely well, Emily: and since we see objects in the direction of the reflected ray, we shall see the image L, which is the point at which the reflected rays, if continued through the mirror, would unite and form an image. This point is equally distant, from the surface and centre of the sphere, and is called the imaginary focus of the mirror. _Caroline._ Pray, what is the meaning of focus? _Mrs. B._ A point at which converging rays, unite. And it is in this case, called an imaginary focus; because the rays do not really unite at that point, but only appear to do so: for the rays do not pass through the mirror, since they are reflected by it. _Emily._ I do not yet understand why an object appears smaller, when viewed in a convex mirror. _Mrs. B._ It is owing to the divergence of the reflected rays. You have seen that a convex mirror, by reflection, converts parallel rays into divergent rays; rays that fall upon the mirror divergent, are rendered still more so by reflection, and convergent rays are reflected either parallel, or less convergent. If then, an object be placed before any part of a convex mirror, as the vase A B, fig. 2, for instance, the two rays from its extremities, falling convergent on the mirror, will be reflected less convergent, and will not come to a focus, till they arrive at C; then an eye placed in the direction of the reflected rays, will see the image formed in (or rather behind) the mirror, at _a b_. _Caroline._ But the reflected rays, do not appear to me to converge less than the incident rays. I should have supposed that, on the contrary, they converged more, since they meet in a point. _Mrs. B._ They would unite sooner than they actually do, if they were not less convergent than the incident rays: for observe, that if the incident rays, instead of being reflected by the mirror, continued their course in their original direction, they would come to a focus at D, which is considerably nearer to the mirror than at C; the image, is, therefore, seen under a smaller angle than the object; and the more distant the latter is from the mirror, the smaller is the image reflected by it.