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, CD, 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 others falling obliquely will be reflected obliquely to GH; for the dotted lines you have drawn are perpendiculars, which divide their angles of incidence and reflection.

Mrs. B. Extremely well, Emily; and since we see objects in the direction of the reflected ray, we shall see the image at 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 a 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 converts, by reflection, 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 incidentrays. 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 less 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, AB, CD, EF, which fall on the concave mirror MN, (fig. 3.) are reflected ?

Caroline. I believe I can. The middle ray is sent back in the same line, as it is in 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 reffecting 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 fig. 5. where the focus is at L; but the true focus of mirrors, either convex or concave, is that of parallel rays, which is equally distant from the centre, and the surface of the sphere.

I shall now show you the reflection of real 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 becoming 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 !

862. Upon what does the obliquity depend with which parallel rays fall upon the surface of a concave mirror?-863. What is the focus of a concave mirror? - 864. What is the relative position of the focus to a concave mirror? - 865. Is the focus of a concave mirror real, or only imaginary as ir the convex mirror? -866. Will the focus be in the same place whether the rays fall parallel or converging upon the mirror? -867. Which is most distant from the mirror?-868. Which figure illustrates this?-869. Which will form the more distant focus from the mirror, divergent or parallel rays?-870. Which figures illastrate this?

Mrs. B. The rays of light cannot be concentrated, without, at the same time, accumulating a proportional quantity 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 under

stand 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 a point, they must fall divergent upon the mirror.

Mrs. B. Strictly speaking, they certainly do. But when rays come from such an immense distance as the sun, their divergence is so trifling, as to be imperceptible; and 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.

Mrs. B. The ray which falls in the direction of the axis of the mirror, is reflected back in the same line; but let us draw two other rays from the focus, falling on the mirror at Band F; the dotted lines are perpendicular to those points, and the two rays will therefore be reflected to A and E.

Caroline. Oh, now I understand it clearly. The rays which proceed from a light placed in the focus of a concave mirror fall divergent upon it, and are reflected parallel. It is exactly the reverse of the former experiment, in which the sun's rays fell parallel on the mirror, and were reflected to a focus.

Mrs. B. Yes: when the incident rays are parallel, the reflected rays converge to a focus; when on the contrary, the incident rays proceed from the focus, they are reflected parallel. This is an important law of optics, and since you are now acquainted with the principles on which it is founded, I hope that you will not forget it.

Caroline. I am sure that we shall not. But, Mrs. B., you said that the image was formed in the focus of a concave mirror; yet I have frequently seen glass concave mirrors, where the object has been represented within the mirror, in the same manner as in a convex mirror.

Mrs. B. That is the case only, when the object is placed between the mirror and its focus; the image then appears magnified behind, or, as you call it, within the

mirror.

Caroline. I do not understand why the image should be larger than the object.

Mrs. B. It proceeds from the convergent property of the concave mirror. If an object, A B, (fig. 7.) be placed between the mirror and its focus, the rays from its extremities fall divergent on the mirror, and on being reflected, become less divergent, as if they proceeded from C: to an eye placed in that situation the image will appear magnified behind the mirror at ab, since it is seen under a larger angle than the object.

You now, I hope, understand the reflection of light by opaque bodies. At our next meeting, we shall enter upon another property of light no less interesting which is called refraction.

CONVERSATION XVI.

ON REFRACTION AND COLORS.

Transmission of Light by Transparent Bodies; Refraction; Refraction of the Atmosphere; Refraction of a Lens; Refraction of the Prism; Of the Colors of Rays of Light Of the Colors of Bodies.

MRS. B.

THE refraction of light will furnish the subject of today's lesson.

Caroline. That is a property of which I have not the faintest idea.

877. Where must the object be placed in regard to a concave mirror, in order that the image appear behind the mirror ? 878 Why does the image in a concave mirror appear larger than the object?-879. How is this illustrated by the figure?