Conc.ive and Convex Mirrors.

655

its rounded surface with the direction or obliquity which, according to the required relation of the angles of incidence and reflection, fits it to reflect the light to the eye, and hence every wave in that extent is sending its momentary gleam, creating a long patterning of reflected light over the waters. Summer visitors from the interior of a country to a southern coast, as from London to Brighton, often express wonder at the great difference of climate, or the heat and light encountered when they walk along the cliffs, forgetting that in the reflection from the sea, they have almost a double sun.

"Mirrors may be plane, convex, or concave; and certain curvatures will produce images by reflection, just as lenses produce images by refraction; in consequence there are reflecting telescopes and microscopes, as there are refracting instruments of the same names.'

888. While a plane surface reflects light, so that what is called the image in it of a known object in front, may readily be mistaken for the reality, convex or concave mirrors reflect as if every distinct point of them were a separate exceedingly small plane mirror, and their effects on light depend on the relative inclination of the different parts. The forms of importance are the regularly spherical and the parabolic concave, and convex mirrors. These produce on light, effects similar to those of lenses, only the concave mirror answers to the convex lens, and the convex mirror to the concave lens. It is the concave mirror, as a speculum, which gathers the light to form the images in the most powerful telescopes that exist, as those of Herschel, Lord Rosse, and others. Admirable as is the refracting telescope, it still falls short in certain respects of the telescope acting by reflection.

In a hollow sphere, or part of a sphere with polished internal surface, if rays radiate from the centre in all directions, they reach every part perpendicularly, and therefore are thrown back to the centre. Thus, if A B (fig. 220) were part of a concave spherical mirror, of which C were the centre, rays Issuing from C would, in obedience to the law that "the angles of incidence and reflection are equal,” again meet at C.

B

Fig. 220.

It can be proved also, that any ray parallel to the axis of the

656

Reflection from Curved Surfaces.

mirror, falling upon such a mirror, will be reflected inwards so as to

D

с

Fig. 221.

a

Ն

c

cut the axis half-way between the

mirror and its centre, viz., at D, the

centre being C; and that as all parallel rays meet after reflection in the same point, that point becomes a focus, as already explained for lenses, and there, when the mirror is held

towards the sun, an image of the sun will be formed, as in the focus of a lens. This point is called the focus, or the principal focus of the mirror.

For the same reason that parallel rays, when reflected, meet in the focus, so will rays, issuing from the focus towards the mirror, become parallel, after reflection, as seen above (fig. 221); and if they be then caught in a second and opposite mirror, as represented at p. 433, corresponding effects will follow.

889. Now, as already explained for a lens, in whatever direction a pencil or cone of rays may fall upon a concave mirror, they are equally brought to a focus somewhere in the line of the central ray of the pencil, and when the rays fall on the mirror with a certain obliquity from one side of its axis, as from A (fig. 222), the central

ray of that being A d, and the axis of the mirror being C d, their focus will be with the same obliquity on the opposite side of the axis as here shown at a, in the direction da, following the central ray

in its reflection, and therefore the mirror will form an inverted image of any object placed before it, just as a lens does; and the image will be near or distant and large or small, according to the divergence of the approaching rays, exactly as happens with lenses. Thus, the camera obscura, magic lantern, telescopes, and microscopes, may all be formed by mirrors. Moreover, concave mirrors magnify, and convex mirrors minify, like lenses of the opposite names. The two subjects, therefore, of images by refraction and by reflection, run so nearly parallel, that it would be useless repetition here to enter upon the detailed consideration of the latter, and it may be sufficient to show, further, why a concave mirror magnifies, and why a convex mirror minifies.

Concave and Convex Mirrors.

657

A concave mirror magnifies because a ray of light nearly parallel

from C, and the light from B similarly appears to come from D, so that the cross. A B, by the reflection, seems to the eye to be of the greater dimensions, C D.

890. In a convex mirror, again, for corresponding reasons, the cross, A B (fig. 224), reflected, appears only as C D, and therefore smaller than the reality.

A convex mirror or silvered globe hanging from the wall, is a common ornament in apartments, exhibiting a pleasing miniature of the room and its contents. If placed opposite to a window it gives a pleasing landscape view, in a reduced form, of all that is in front of the house.

C

Fig. 224.

A

The cornea of the human eye is a convex mirror, which portrays most perfect miniatures of a window or any bright object. It is the image of the window, or of the sun in the convex mirror of the eyeball, which painters usually represent by a white spot, sometimes without knowing what it represents; and a similar luminous spot or line must be made when they have to picture almost any of the pieces of furniture which have rounded polished surfaces, such as bottles, glasses, or smooth pillars.

It has been a mathematical amusement to calculate what kind of distortion, mirrors of unusual forms must produce, and then to make distorted drawings, which, when reflected from such mirrors, will produce in the eye the natural form of the objects.

891. When a concave mirror is used for a telescope, the image formed in front of it, to be examined through the magnifying eyeglass, may be viewed in various ways,—first, as in Herschel's telescope, by the spectator turning his back to the real object and looking in at the mouth of the telescopic tube, near to the edge of which the image is thrown by a slight inclination of the mirror at its bottom :-or, secondly, as in the Newtonian telescope, through

658

Reflecting Telescopes.

an opening in the side of the tube after being reflected by a small plane mirror placed diagonally in the centre of the tube :—or, thirdly, as in the Gregorian telescope, through an opening cut in the centre of the principal mirror or speculum, after being reflected towards that opening by a smaller mirror placed in the centre of the tube with its face towards the observer: this last arrange ment is that preferred for small telescopes, because the spectator, while seeing the image, is also looking in the direction of the object.

Reflecting telescopes have the advantage of being perfectly achromatic, that is, of producing the images quite free from coloured or rainbow edges; for compound light is reflected, although not refracted, entire, all the colours following the one law of equal angles of incidence and reflection.

Herschel's large telescope had a mirror of 48 inches in diameter, and, therefore, to form images, collected about 150,000 times more light than can enter the pupil of an unassisted eye, forming, with that light, at a focal distance of 40 feet, a large image admirably distinct. It was with this telescope that, in the obscurity of remote space, Herschel discovered the immense planet rolling along, which in honour of his royal patron, he called the Georgium Sidus, but which now, by the decision of the scientific world, is called Uranus; *—and with this he discovered moons, before unseen, of other planets, and he unravelled many of the celestial nebulæ and clustered stars of the milky way, and, in a word, unveiled, vastly more than had before been done, the system of the boundless universe.

Other steps of advancement have been made since Herschel's time. Lord Rosse constructed a reflecting speculum nearly twice as large as Herschel's; and M. Foucault, of the French Institute, has succeeded with admirable skill in forming good specula or mirrors of glass coated with metal. Lord Rosse's reflector was six feet in diameter. For its magnifying power, as contrasted with some of the largest refracting achromatic telescopes, see note at foot of page 646.

892. Total reflection.-Although the external surface of glass reflects but a small part of the light which falls upon it-being

* From the Greek ovpavos, signifying the firmament or boundary of Heaven. The planet Neptune has since been discovered at a still greater distance from the sun.

The Camera Lucida.

E

659

therefore a feeble mirror, still, curiously, if light, which has entered a piece of glass, fall very obliquely upon the back or internal surface of it, instead of passing out there, it is more perfectly reflected than it would be by the best metallic mirror. Thus, light from A (fig. 225), entering a piece of glass at B, is entirely reflected at

E

B

Fig. 225.

C

C, on the internal back of the piece, and escapes at D towards E. The Camera Lucida.-It is this fact which enabled Dr. Wollaston to devise that beautiful little instrument called by him the Camera Lucida. The letters, A G C (fig. 226), indicate a piece of glass with a vertical surface, C, and a horizontal surface between C and A. The light entering from an object or scene, F, falls on the oblique surface, D, from which it is reflected to the oblique surface, A, from which it is reflected again to the eye at E, enabling that to see clearly the object at F. The wide pupil of the eye at E can also see past the corner of the glass at A, the sheet of paper on the table below it, B, and at the same time the objects at F, if traced on the paper. With a lead-pencil that appearance can be made permanent, and a correctly-drawn outline of the scene is at once obtained. This instrument for assisting draughtsmen is still simpler than the camera obscura. Other modifications of it have since been contrived.

Fig. 226.

as

893. The same fact of the internal surface of a transparent mass becoming a mirror, furnished at last the explanation of that apparition, so admired before it was understood, and not less admired since, of the rainbow, or arc in the heaven, as in France and elsewhere it is named—an object which the poets of nature have seemed almost to worship for its beauty.

The Rainbow.-When a partial shower of rain falls on the side of a landscape opposite to that where the sun is shining, there appears in the shower this marvellous arch, red at its external border or confine, and then successively orange, yellow, green, &c. (in the order of the colours of the prismatic spectrum described in Art. 812), towards its inner border. Its centre is directly opposite to the sun, or at the end of a straight line supposed to pass from the sun through the eye of the spectator to a point below the opposite horizon. The diameter of the circle of which the bow is a part, is of nearly 84° of