MIRROUB, in catoptrics, any polished body impervious to the rays of light, and which reflects them equally Mirrours were anciently made of me tal: but at present they are generally smooth plates of glass, tinned or quicksil vered on the back part, and called look ing-glasses. The doctrine of mirrours depends wholly on that fundamental law, that the angle of reflection is always equal to the angle of incidence. See OPTICS.
Parallel rays falling directly on a plane speculum are reflected back upon them selves; if they fall obliquely, they are re flected in the same angle and parallel as they fell. Hence there is no such thing, properly speaking, as a focus belonging to a plane speculum, neither real nor vir tual. The focus of parallel rays is called the solar focus ; because in that the image of the sun is formed, and of all objects very remote. But the focus of any object, situated near the mirrour, will have its distance from the vertex more or less than half the radius ; the rule in all cases being as follows : " Multiply the distance of the object into the radius of the mir rour, and divide the product by the sum of the radius, and twice the distance of the object ; the quotient will be the focal distance of a convex mirrour." Again, for a concave mirrour, the same product of the radius into the distance of the object, divided by the difference of radius and twice the distance of the ob jest, will give the focal distance. And here we are to observe, that as twice the distance of the object is lesser or greater than the radius, so the focus will be posi tive or negative, that is, behind the glass or before it.
The image of the object is formed in the focus proper to its distance, and, since the writers on optics demonstrate, that the angles under which the object and its image are seen from the centre or vertex of the mirrour are always equal, it follows, that the image will be always in proportion to the object as the focal distance to the 'object's distance. The position of the object will be always erect at a positive focus, or behind the specu lum diminished by a convex, and magnifi ed by a concave one. Hence, since a convex has but one, viz. an affirmative fo cus; so it can never magnify any object, however posited before it.
The position of the image in a negative focus, or that before the glass, will be ever inverted; and, if nearer the vertex than the centre, it will be less; if further from it, it will be greater than the object: but in the centre It will be equal to the object and seem to touch it.
The image formed by a plane specu. lum is erect, large as the life, at the same apparent distance behind the glass as the object is before it, and on the same side of the glass with the object. Those
properties render this sort of mirrour of most common use, viz, as a looking glass.
If the rays fall directly, or nearly so, on a plane mirrour, and the object be opaque, there will be but one single image formed, or at least be visible, and that by the second surface of the specu lum, and not by the first, through which the rays do most of them pass.
But if the object be luminous. and the rays fall very obliquely on the speculum, there will be more than one image form ed to an eye placed in a proper position to view them. The first image, being formed by the first surface, will not be so bright as the second, which is formed by the second surface. The third, (mirth, &c. images are produced by several re flections of the rays between the two sur faces of the speculum ; and, since some light is lost by each reflection, the images from the second will appear still more faint and obscure to the eighth, ninth, or tenth, which can scarcely be discern ed at all.
Mirrours may be divided into plane, concave, convex, cylindrical, conical, pa rabolical, and elliptical.
The properties of cylindrical mirrours are, 1. The dimensions of objects corres ponding lengthwise to the mirrour are not much changed, but those correspond ing breadthwise have their figures alter ed, and their dimensions lessened, the further from the mirrour ; whence arisen a very great distortion. 2, If the plane of the reflection cut the cylindric mirrour through the axis, the reflection is per formed in the same manner as in a plane mirrour; and if parallel to the base, the reflection is the same as in a spherical mirrour ; if it cut it obliquely, the reflec tion is the same as in an elliptic mirrour. Hence, as the plane of reflection never passes through the axis of the mirrour, except when the eye and objective line are in the same plane ; nor parallel to the base, except when the radiant point and the eye are at the same height; the reflection is therefore usually the same as in an elliptic one. 3. If a hollow cylin dric mirrour be directly opposed to the sun, instead of a focus of a point, the rays will be reflected into a lucid line parallel to its axis, at • distance somewhat less than a fourth of its diameter. Hence arises a method of drawing anamorpho rks, that is, wild deformed figures on a Wane, which appear well proportioned 4lien viewed in a cylindric mirrour.
In an elliptic mirrour, if a ray strike on it from one of its focuses, it is reflect ed into the other. Parabolic mirrours, as all the rays they reflect meet in one point, make the best burning-glasses.