Mirror

I

Introduction

Mirror, optical device, commonly made of glass, with a smooth, polished surface that forms images by the reflection of rays of light (see Optics). The ways in which mirrors form images depend on the laws of reflection, in particular that the angle of incidence equals the angle of reflection, and for both plane and curved mirrors, the principles are the same. There are two types of curved mirror: concave and convex. A concave mirror is curved inward, with the reflective surface facing the centre of curvature. A convex mirror curves outward, with its centre of curvature behind its reflective surface.

Depending on which type of mirror is used, and the position of the source of the light, two types of image can be formed: real and virtual. Real images are those which it is possible to cast on to a screen, whereas virtual images are images which cannot be cast on to a screen but are nevertheless perceived by the eye. The actual positions of images may be calculated using the mirror formula:

1/v + 1/u = 1/f = 2/r

where u is the distance of the object from the mirror, v is the distance of the image, f the focal length of the mirror, and r its radius of curvature (see below). To use this formula, it is essential to observe the convention that real object or image distances are positive, and virtual object or image distances are negative.

II

Concave Mirror

In a concave mirror, rays of light parallel to the mirror’s principal axis (an imaginary line passing at right angles through the centre of the mirror) fall at an angle θ to the normal (an imaginary line perpendicular to the tangent at the point on the surface where the light hits the mirror)are therefore reflected at an angle θ also. The rays then pass through the principal focus. A ray of light through the centre of curvature and along the principal axis hits the mirror at its centre, or pole, and is reflected back along this axis towards the principal focus. The distance between the pole and the principal focus is the mirror’s focal length. The distance between the mirror’s pole and the centre of curvature is the mirror’s radius of curvature. It can be shown by geometry that, for small angles, and thus for small mirrors, the focal length is half the radius of curvature.

Concave mirrors are used in a variety of optical devices, such as microscopes (for increasing the illumination of slides or specimens), astronomical telescopes (mirrors can be made with much bigger apertures than lenses, so reflecting telescopes can give higher resolutions than refracting ones), and slide projectors (to increase the light falling on to the slide). A specialized form of concave mirror has a parabolic shape. With a light source placed at the focus of the parabola, a parallel beam of light can be reflected from the mirror, and this is used to make powerful lights such as searchlights.

III

Convex Mirror

For convex mirrors, the principal focus is the point from which rays striking the mirror parallel to the principal axis appear to come after reflection. This point is behind the mirror surface. The same mirror formula can be used as for a concave mirror, except that in this case, the focal length must be given a negative value. An image seen in a convex mirror is always virtual and erect, and is nearer to the mirror and smaller than the object. Rear-view driving mirrors, and the large mirrors erected near blind corners such as driveways, are usually convex mirrors because they have a large field of view and produce a diminished, erect image.

IV

History

Mirrors made of brass are mentioned in the Bible, and mirrors of bronze were in common use among the ancient Egyptians, Greeks, and Romans. Polished silver was also used by the Greeks and Romans to produce reflections. Crude types of glass mirror were first made in Venice in about 1300. By the end of the 17th century, mirrors were made in Britain, and the manufacture of mirrors developed subsequently into an important industry in the other European countries, and in the United States.