_Emily._ Then I do not understand why I should not see the whole of my person in a much smaller mirror, for a ray of light from my feet would always reach it, though more obliquely.

_Mrs. B._ True; but the more obliquely the ray falls on the mirror, the more obliquely it will be reflected; the ray would, therefore, be reflected above your head, and you could not see it. This is shown by the dotted line (fig. 3.)

Now stand a little to the right of the mirror, so that the rays of light from your figure may fall obliquely on it----

_Emily._ There is no image formed of me in the gla.s.s now.

_Mrs. B._ I beg your pardon, there is; but you cannot see it, because the incident rays, falling obliquely on the mirror, will be reflected obliquely, in the opposite direction; the angles of incidence, and reflection, being equal. Caroline, place yourself in the direction of the reflected rays, and tell me whether you do not see Emily's image in the gla.s.s?

_Caroline._ Let me consider.--In order to look in the direction of the reflected rays, I must place myself as much to the left of the gla.s.s, as Emily stands to the right of it.--Now I see her image, not straight before me, however, but before her; and it appears at the same distance behind the gla.s.s, that she is in front of it.

_Mrs. B._ You must recollect, that we always see objects in the direction of the last rays, which reach our eyes. Figure 4 represents an eye, looking at the image of a vase, reflected by a mirror; it must see it in the direction of the ray A B, as that is the ray which brings the image to the eye; prolong the ray to C, and in that spot will the image appear.

_Caroline._ I do not understand why a looking-gla.s.s reflects the rays of light; for gla.s.s is a transparent body, which should transmit them!

_Mrs. B._ It is not the gla.s.s that reflects the rays which form the image you behold, but the silvering behind it; this silvering is a compound of mercury and tin, which forms a brilliant metallic coating.

The gla.s.s acts chiefly as a transparent case, through which the rays find an easy pa.s.sage, to, and from, the quicksilver.

_Caroline._ Why then should not mirrors be made simply of mercury?

_Mrs. B._ Because mercury is a fluid. By amalgamating it with tinfoil, it becomes of the consistence of paste, attaches itself to the gla.s.s, and forms, in fact, a metallic mirror, which would be much more perfect without its gla.s.s cover, for the purest gla.s.s is never perfectly transparent; some of the rays, therefore, are lost during their pa.s.sage through it, by being either absorbed, or irregularly reflected.

This imperfection of gla.s.s mirrors, has introduced the use of metallic mirrors, for optical purposes.

_Emily._ But since all opaque bodies reflect the rays of light, I do not understand why they are not all mirrors.

_Caroline._ A curious idea indeed, sister; it would be very gratifying to see oneself in every object at which one looked.

_Mrs. B._ It is very true that all opaque objects reflect light; but the surface of bodies, in general, is so rough and uneven, that the reflection from them is extremely irregular, and prevents the rays from forming an image on the retina. This, you will be able to understand better, when I shall explain to you the nature of vision, and the structure of the eye.

You may easily conceive the variety of directions in which rays would be reflected by a nutmeg-grater, on account of the inequality of its surface, and the number of holes with which it is pierced. All solid bodies more or less resemble the nutmeg-grater, in these respects; and it is only those which are susceptible of receiving a polish, that can be made to reflect the rays with regularity. As hard bodies are of the closest texture, the least porous, and capable of taking the highest polish, they make the best mirrors; none, therefore, are so well calculated for this purpose, as metals.

_Caroline._ But the property of regular reflection, is not confined to this cla.s.s of bodies; for I have often seen myself, in a highly polished mahogany table.

_Mrs. B._ Certainly; but as that substance is less durable, and its reflection less perfect, than that of metals, I believe it would seldom be chosen, for the purpose of a mirror.

There are three kinds of mirrors used in optics; the _plain_, or _flat_, which are the common mirrors we have just mentioned; _convex_ mirrors, and _concave_ mirrors. The reflection of the two latter, is very different from that of the former. The plain mirror, we have seen, does not alter the direction of the reflected rays, and forms an image behind the gla.s.s, exactly similar to the object before it. A convex mirror has the peculiar property of making the reflected rays diverge, by which means it diminishes the image; and a concave mirror makes the rays converge, and under certain circ.u.mstances, magnifies the image.

_Emily._ We have a convex mirror in the drawing-room, which forms a beautiful miniature picture of the objects in the room; and I have often amused myself with looking at my magnified face in a concave mirror. But I hope you will explain to us, why the one enlarges, while the other diminishes the objects it reflects.

_Mrs. B._ Let us begin by examining the reflection of a convex mirror.

This is formed of a portion of the exterior surface of a sphere. When several parallel rays fall upon it, that ray only which, if prolonged, would pa.s.s through the centre or axis of the mirror, is perpendicular to it. In order to avoid confusion, I have, in fig. 1, plate 18, drawn only three parallel lines, A B, C D, E F, to represent rays falling on the convex mirror, M N; the middle ray, you will observe, is perpendicular to the mirror, the others fall on it, obliquely.

_Caroline._ As the three rays are parallel, why are they not all perpendicular to the mirror?

_Mrs. B._ They would be so to a flat mirror; but as this is spherical, no ray can fall perpendicularly upon it which is not directed towards the centre of the sphere.

_Emily._ Just as a weight falls perpendicularly to the earth, when gravity attracts it towards the centre.

_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 pa.s.s 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.

You will now easily understand the nature of the reflection of concave mirrors. These are formed of a portion of the internal surface of a hollow sphere, and their peculiar property is to converge the rays of light.

Can you discover, Caroline, in what direction the three parallel rays, A B, C D, E F, are reflected, which fall on the concave mirror, M N, (fig.

3.)?

_Caroline._ I believe I can. The middle ray is sent back in the same line, in which it arrives, that being the direction of the axis of the mirror; and the two others will be reflected obliquely, as they fall obliquely on the mirror. I must now draw two dotted lines perpendicular to their points of incidence, which will divide their angles of incidence and reflection; and in order that those angles may be equal, the two oblique rays must be reflected to L, where they will unite with the middle ray.

_Mrs. B._ Very well explained. Thus you see, that when any number of parallel rays fall on a concave mirror, they are all reflected to a focus: for in proportion as the rays are more distant from the axis of the mirror, they fall more obliquely upon it, and are more obliquely reflected; in consequence of which they come to a focus in the direction of the axis of the mirror, at a point equally distant from the centre, and the surface, of the sphere; and this point is not an imaginary focus, as happens with the convex mirror, but is the true focus at which the rays unite.

_Emily._ Can a mirror form more than one focus, by reflecting rays?

_Mrs. B._ Yes. If rays fall convergent on a concave mirror, (fig. 4,) they are sooner brought to a focus, L, than parallel rays; their focus is, therefore, nearer to the mirror M N. Divergent rays are brought to a more distant focus than parallel rays, as in figure 5, where the focus is at L; but what is called the true focus of mirrors, either convex or concave, is that of parallel rays, and is equally distant from the centre, and the surface of the spherical mirror.

I shall now show you the real reflection of rays of light, by a metallic concave mirror. This is one made of polished tin, which I expose to the sun, and as it shines bright, we shall be able to collect the rays into a very brilliant focus. I hold a piece of paper where I imagine the focus to be situated; you may see by the vivid spot of light on the paper, how much the rays converge: but it is not yet exactly in the focus; as I approach the paper to that point, observe how the brightness of the spot of light increases, while its size diminishes.

_Caroline._ That must be occasioned by the rays approaching closer together. I think you hold the paper just in the focus now, the light is so small and dazzling--Oh, Mrs. B., the paper has taken fire!

_Mrs. B._ The rays of light cannot be concentrated, without, at the same time, acc.u.mulating a proportional quant.i.ty of heat: hence concave mirrors have obtained the name of burning mirrors.

_Emily._ I have often heard of the surprising effects of burning mirrors, and I am quite delighted to understand their nature.

_Caroline._ It cannot be the true focus of the mirror, at which the rays of the sun unite, for as they proceed from so large a body, they cannot fall upon the mirror parallel to each other.

_Mrs. B._ Strictly speaking, they certainly do not. But when rays, come from such an immense distance as the sun, they may be considered as parallel: their point of union is, therefore, the true focus of the mirror, and there the image of the object is represented.

Now that I have removed the mirror out of the influence of the sun's rays, if I place a burning taper in the focus, how will its light be reflected? (Fig. 6.)

_Caroline._ That, I confess, I cannot say.