MIRROR, an optical instrument which produces images of objects by reflection. In ancient times it was merely a polished sheet of metal, and was called a speculum; in modern times a mirror is a sheet of polished glass silvered at the back.
If an object CD (fig. I) is placed in front of a plane mirror AB, every ray such as CP, starting from a point C on the object and striking the mirror, will proceed after reflection along a line PQ, which if produced will pass through the point E, found by dropping a perpendicular CM on the mir ror and producing it to a distance ME be hind the mirror equal to the distance MC.
For it is obvious that the triangles CAD and EAD will always be equal, and there fore that the angles at P which the rays CP and PQ make with the mirror will be equal. Thus to an eye at Q the appearance will be exactly the same as if the light had come from this point E, wherever the eye may be, so long only as the line EQ cuts the surface of the mirror. The image formed by a plane mirror is therefore optically perfect, and free from all aberration.
The image of a solid object is not however a solid of the same shape as the object. For instance the image of a man's face may be imagined to be obtained by making a rubber mask of the face, and then everting it. The image will only be the same shape as the object if the face is perfectly symmetrical, right and left. (See LIGHT.) Combination of Two Plane Mirrors.—If a beam of light, ABCD (fig. 2), is reflected in succession from two plane mirrors which are parallel to one another, as all the angles which they make with the normals to the mirrors are obviously equal to one another, the path of the light after the second reflection must be parallel to the original one AB.
This final direction will therefore not be altered however the mir rors are turned about, provided only that the mirrors are kept parallel to one another. But the beam itself is displaced parallel to itself by an amount which depends upon the separation of the mirrors and the angle of incidence of the beam. Moreover any near object PQ seen by reflection will appear in a position P'Q', found by drawing lines PP', DD', QQ', from PQ parallel to the common normal NN', and twice its length. By rotating the pair of mirrors round any
axis parallel to PQ, the image P'Q' can be made to describe the surface of a cylinder of which PQ is the axis.
If in fig. 2, we suppose the mirror B to remain still, and we rotate the mirror C by an angle w, the ray CD will be turned through an angle 2W, and the emergent beam will make this angle 2w, with the incident beam. This angle between the two beams is therefore independent of the angle of incidence of the original beam upon the first mirror, and will be unaffected by any movement or rotation of the pair of mirrors, so long as the angle between the mirrors is kept unchanged, and the line of intersection of their planes is kept parallel to itself.
A very important use of this property is made in the con struction of the common sextant (q.v.).
Two mirrors at right angles yield some interesting effects. An object P (fig. 3) will give images PA and PB after one reflection in OA and OB respectively, and (if the angle AOB is exactly a right angle), a single image Q after two reflections. This image can be constructed by drawing lines from the several points of the object P, through 0 the line of intersection of the mirrors, and producing them to an equal length. It is then obvious that this image will not be affected by rotating the pair of mirrors about 0. If the mirrors are set up in a vertical plane, with the line of intersection vertical, a person looking at himself in them, will find his right hand H reflected over to H' on the left of the image as he sees it. If he moves to one side, the image moves to the opposite side, so that he can always see it while he remains within the angle AOB.