Mirrors

Type of physical science: Classical physics

Field of study: Optics

A smooth surface that reflects light or other radiant waves is called a mirror. Aside from their everyday use as "looking glasses," mirrors are the heart of many optical instruments, astronomical telescopes, and solar concentrators because of their image-forming properties.

Overview

In its simplest form, a mirror is a device that reflects light. Although rough surfaces also act as reflectors, they break up a concentrated beam and scatter it diffusely and in many different directions. The term "mirror" is usually reserved for a smooth reflecting surface exhibiting specular reflection, in which a thin beam of light striking it remains substantially intact but is reflected in a single different direction. Parallel rays of light striking a perfectly flat mirror change direction on reflection but remain parallel to one another. Parallel rays striking a concave mirror (whose surface is curved toward the direction of the incoming rays) are bent toward one another so that they tend to converge. Parallel rays striking a convex mirror (whose surface is curved away from the direction of the incoming rays) are spread apart, or diverged.

Although the reflection of light off shiny metallic surfaces is most familiar, transparent materials may also act as mirrors. Whenever light passes through the interface between two media, causing the light to travel at different characteristic speeds, part of it is reflected and part is transmitted through the surface. This result explains why the surface of a still pond or a clean sheet of glass also behaves like a mirror, especially when there is a dark background behind it to diminish scattered glare. Both forms of reflection may be explained by the laws of electromagnetism. When a ray of light, or any form of electromagnetic radiation, strikes a smooth surface, the charged electrons in the surface atoms are stimulated to oscillate in step with the electric field of the incoming ray. These oscillating charges radiate individual electric fields, which produce constructive interference in only two directions--one reflected back into the medium from where the ray hit the surface and one refracted into the medium beneath the surface. If the surface is a good conductor, such as a shiny metallic coating, then almost all the energy in the light beam is reflected back and very little penetrates the surface. If the surface is between two transparent media, such as air and water or air and glass, only a small percentage of the light is reflected and most is transmitted through the surface.

The direction of the reflected ray is specified by the law of reflection, which states that the reflected beam will be in the plane containing the incoming ray and a line perpendicular to the surface and will make the same angle with the surface as the incoming ray. In other words, the component of the velocity of the incoming ray of light that is parallel to the surface is unaffected, while the incident perpendicular component of velocity is reversed in the reflected beam. Light is only one form of electromagnetic radiation, and smooth surfaces exhibit mirror reflection at radio, radar, infrared, and ultraviolet frequencies as well. Specular reflection occurs only if the surface is smooth over a region comparable to the wavelength of the incoming radiation. Thus, optical mirrors that reflect light whose crest-to-crest wavelength is about 500 nanometers (1 nanometer is one-millionth of a millimeter) must be polished smooth to accuracies better than one-thousandth of a millimeter. The mirrors used in radar or satellite television antennas, which use radio wavelengths on the order of millimeters, do not have to be visibly smooth, however, and indeed, can be constructed of wire mesh and still exhibit specular reflection at those wavelengths. Sound waves, although not electromagnetic, also obey the laws of reflection when bouncing off hard smooth surfaces, but their wavelengths are on the order of tens of centimeters to tens of meters. Therefore, parabolic microphones, such as the 1-meter dishes used by broadcasters at sporting events to pick up the sounds from the playing field, will focus high-pitched sounds but not long wavelengths of low frequencies.

Light rays from a point source which reflects from a flat mirror appear to come from a point as far behind the mirror as the source is in front of it. This point is called a virtual image because the light rays do not actually pass through it. The image of an extended object in a flat mirror also appears to be as far behind the mirror as the object is in front of it, a fact familiar to anyone who uses a looking glass, and appears to be the same size as the object. The image does differ from the object, however, in one curious aspect. When a person moves a right hand while looking into a mirror, the image appears to be moving its left hand. This reversion is caused not by the reflection of light from right to left in the mirror but by a front-to-back inversion of the image.

Mirrors with regularly curved surfaces have several useful properties. A concave ellipsoidal mirror will reflect diverging rays from a point source at the focus of the ellipse, so that all rays that strike the mirror pass through the other focus of the ellipse. This property is sometimes exhibited in "whispering chambers" formed by the walls of elliptical rooms. A concave paraboloidal mirror will converge all rays of light parallel to its axis, so that they pass through the focus of the parabola. Astronomical telescopes, radar reflectors, or other mirrors intended to image distant objects usually are made with a parabolic cross section because of this property. Spheroidal mirrors are easy to make and focus rays from a distance source somewhat like paraboloids, but they exhibit distortions called "spherical aberrations" which become worse for the parts of the image further from the optic axis of the mirror, as is evident in the reflections from round Christmas tree ornaments.

The same law that is used to locate the images formed by lenses can also be used for curved mirrors with one slight modification. A mirror has only one focal point. For a concave mirror, it is the point at which incoming parallel rays are brought to a focus, and the focal length f is the distance from this focal point to the mirror surface (approximately one-half of the radius of curvature of a spherical mirror). For a convex mirror whose surface curves away from the incoming light, the focal point is behind the surface, and the focal length is considered to be negative. If a point object is located a distance o from the mirror (distances in front of the mirror are considered to be positive), then the distance i from the mirror to the image of this point is determined by the equation 1/f = 1/o + 1/i. If the mirror is flat, then the focal length f is infinite and i = -o, illustrating the rule that the image appears to be as far behind a plane mirror as the object is in front of it. For a concave mirror with positive f, if the object is at infinity, then i = f and the image is located at the focal point. A convex mirror, on the other hand, which has negative f, will always appear to have an image behind the mirror surface (i will be negative) if the object is in front of the mirror. This image is also virtual, since the light rays do not actually pass through the image point.

Curved mirrors can be used to enlarge or diminish an optical image. A concave mirror enlarges the apparent size of nearby objects, a property utilized in facial makeup mirrors. As is demonstrated by side-mounted rearview mirrors in automobiles, the images from convex mirrors appear smaller than the object itself.

The size of the mirror affects both its ability to gather light and energy and its "resolving power," or ability to distinguish neighboring points in the image. A larger telescope not only can distinguish fainter objects than a smaller one but also can resolve smaller details in the image. The telescopes used by space surveillance satellites are said to be able to read an automobile license plate from an orbit that is 1,000 kilometers high. Radio telescopes must be much larger than optical instruments to achieve the same resolution, since radio wavelengths are much longer.

Applications

Although looking glasses once were so expensive to make that only the rich could afford them, they are now commonplace. Curved mirrors are often used in carnival fun houses to form humorously distorted images. "Half-silvered" mirrors, which transmit a small fraction of the light striking them to a dark room beyond, are used for secret surveillance. To the observer sitting on the lighted side, the device appears to be an ordinary mirror, since the eye cannot tell that the mirror is reflecting only 85 percent of the light striking it while allowing about 15 percent to pass through.

Astronomical needs have been responsible for most advances in reflective optics.

Reflecting telescopes can be designed with a compact, folded optical path and can be built for less money than lens instruments. Because larger instruments can gather more light and see deeper into space, a series of larger and larger mirrors, culminating in the 6-meter reflector at Mount Pastukhov in the Soviet Union, has provided more and more detail about the stars and galaxies outside the solar system. Practical limits on the flexing of glass mirrors with temperature changes and the mirror's own weight have changed the course of modern mirror design. Fused quartz, which changes dimension much less than glass, has become commonly used as a mirror backing. The Multiple Mirror Telescope near Tucson, Arizona, paved the way for other modern designs in Hawaii and Chile by utilizing several independent mirrors, aligned by laser beams to millionths of a millimeter, to form a much larger instrument. Telescopes have also been placed into space to eliminate the absorbing effect of the earth's atmosphere.

Mirrors are employed in many other optical instruments, such as the spectrometers that are used by chemists to analyze the light emitted or absorbed from excited atoms, because they do not absorb ultraviolet or infrared waves as glass lenses do. Many modern cameras and telescopes are designed with combinations of lenses and mirrors to reduce their size and increase their optical performance.

Parabolic radio reflectors can be used as receiving antennas for satellite television signals, as well as microwave relay stations. Automobiles act as unwitting radio mirrors when they bounce radar signals back to traffic police officers. The shift of frequency of the reflected wave from the moving mirror (called the Doppler effect) is used to determine whether a vehicle is traveling over the speed limit. A similar reflection of sound (sonar) waves from underwater objects is used to determine the depth of the sea bottom, the position of submarines, or even the location of schools of fish.

Mirrors are used to collect and focus the heat waves that are emitted by a military aircraft engine in order to guide heat-seeking missiles to their target. A more peaceful use of mirrors is to collect the rays of the sun for solar-heating purposes. Solar furnaces make use of large arrays of mirrors tracking the sun to achieve temperatures of thousands of degrees Celsius for research into the thermal behavior of substances. Solar telescopes such as the 152-centimeter McMath telescope at Kitt Peak National Observatory, Arizona, can take detailed pictures of sunspots or eruptions and can analyze the chemical elements on the sun by sending the light to a spectroscope. In fact, helium was discovered from its traces in sunlight before it was discovered on Earth.

A unique type of mirror is the corner reflector, formed by three surfaces at a 90-degree angle, which has the property of reflecting back any light striking it exactly in the direction from which it came. American astronauts planted several of these mirrors on the Moon, and by beaming lasers onto them from Earth-based telescopes and timing the return flash, the Moon's orbit has been determined to a fraction of a millimeter.

Mirrors for optical devices are made by grinding two pieces of glass together with successively finer grains of carborundum slurry between them until the overhanging piece is hollowed out to a spheroid of the approximate focal length needed. The surface is then smoothed and polished with "rouge," a fine mixture of oxides and water, until it has deepened into a paraboloid, or whatever other surface is desired. The mirror is then coated with evaporated aluminum to form a reflecting surface. A simple test with a pinhole light source and a razor blade is used to verify the final figure of the mirror to a fraction of the wavelength of light. The procedure is so simple that thousands of amateur astronomers have made their own telescopes.

Unfortunately, the mirror of the ill-fated Hubble Space Telescope that was sent into space in 1990 was tested with a spacer that was slightly out of position, causing unfortunate aberrations in the expensive instrument.

One interesting type of mirror is not made from a metallic reflector at all. If light coming from underneath the surface of glass strikes the surface at an angle greater than 42 degrees, then the laws of electromagnetism predict that the light will be 100 percent reflected, thus acting as a perfect mirror. The inverted image produced by the lens system in good binoculars is often turned right-to-left and rightside up with two 45-degree Porro prisms, which are more rugged than thin mirrors. This total internal reflection is also the secret of the optical fiber, which has denser glass coated onto the surface of a very pure and transparent glass fiber.

Almost all the energy that enters one end will be reflected from this interface and will emerge from the other end. Such "light pipes" have become common in the television and communications industry, since they can carry more information simultaneously than ordinary wires.

Context

The earliest mirrors were simply polished pieces of metal. Archimedes is supposed to have defended the port of Syracuse by setting the invading Roman ships afire with light reflected off his soldiers' shields, which would be the first recorded use of a solar-energy collector. The Romans spread the use of hand mirrors through the ancient world, but a full-size looking glass did not appear until about the first century A.D.

After Galileo used a pair of lenses to examine the sky in 1609, astronomers demanded larger and larger refracting telescopes, culminating in Christiaan Huygens' telescope, which was more than 60 meters long and had to be hoisted by a crane. The first reflecting telescope was probably invented by James Gregory about 1663, but his design was too advanced for the optical technology of his time and a simpler model by Sir Isaac Newton five years later became more popular and is still used by amateur astronomers. Astronomers were slow to abandon refractors until Sir William Herschel's 1.22-meter instrument in the late eighteenth century showed that a reflecting telescope could be more compact, cheaper, and of better optical quality than one using lenses. Newton's mirror was of speculum metal, a mixture of copper, tin, and arsenic, and when it tarnished, the entire mirror had to be reground. It was not until 1856 that a German astronomer, Carl August von Steinheil, suggested forming a reflecting coating by precipitating silver chemically onto a surface. The practice of evaporating an aluminum coating onto a mirror was developed in the early 1930's, in time to use it on the Hale 5-meter telescope.

Eighteenth and nineteenth century magicians were fascinated by the properties of mirrors and used them in spectacular disappearing acts that gave rise to the common saying, "It's all done with mirrors." In fact, many texts on optics in the 1800's presented magicians' mirror illusions as seriously as they did microscope lenses. In the 1880's, Henry Rowland improved the design of the spectrometer by inscribing the fine lines of a diffraction grating directly onto a concave mirror, so that a single optical element could both separate the light into its colors and focus it onto a photographic plate.

Grote Reber built a 9-meter dish in his backyard in Wheaton, Illinois, in the 1930's, which became the first reflecting radio telescope. Larger metal reflectors were developed for radar use in World War II, and after the war, a huge 76-meter steerable parabolic radio telescope was constructed at Jodrell Bank in England. It was surpassed twenty years later by a 100-meter dish in Bonn, Germany. A large radio mirror, fully 305 meters across, was formed by lining a natural depression in Arecibo, Puerto Rico, with metal mesh. Instruments with even greater resolving power can be formed by combining the signals from several reflectors spaced a considerable distance apart. The Very Large Array of radio telescopes south of Albuquerque, New Mexico, incorporates twenty-seven large parabolic mirrors, which can be spaced along a Y-shaped track forming a mirror effectively 43.5 kilometers across. Using sophisticated electronic timing techniques, radio telescopes on different continents can work together to form an array effectively the size of the earth, enabling radio sources to be pinpointed with a resolution rivaling that of optical telescopes.

Principal terms

FOCAL LENGTH: the distance from the surface of a mirror to its focal point

FOCAL POINT: the point at which parallel rays reflected by a concave mirror are brought to a focus, or from which parallel rays reflected by a convex mirror appear to radiate

IMAGE: the result of rays of light from an object being brought to a focus by a mirror or lens

REAL IMAGE: an optical image that can be focused on a screen

RESOLUTION or RESOLVING POWER: the ability of an optical device to image small details in an object

SPECULAR REFLECTION: a coherent, mirrorlike change in the direction of light or electromagnetic rays when they strike a smooth surface

VIRTUAL IMAGE: an image that can be seen only by looking into the rays that are reflected by a mirror

Bibliography

Barlow, Boris V. THE ASTRONOMICAL TELESCOPE. London: Wykeham, 1975. A semitechnical review of telescope design.

Gluck, Irvin D. IT'S ALL DONE WITH MIRRORS. Garden City, N.Y.: Doubleday, 1968. An interesting nontechnical survey of the uses of mirrors in history from the looking glass to solar collectors. Contains many suggestions for home experiments and projects.

Hayes, Donald S., Russell M. Genet, and David R. Genet, eds. NEW GENERATION SMALL TELESCOPES. Mesa, Ariz.: Fairborn Press, 1987. Descriptions of small telescope designs, many of which employ both mirrors and lenses.

Howard, N. E. STANDARD HANDBOOK FOR TELESCOPE MAKING. New York: Thomas Y. Crowell, 1959. Describes how to make a telescope mirror.

Jenkins, F. A., and H. E. White. FUNDAMENTALS OF OPTICS. 3d ed. New York: McGraw-Hill, 1957. A standard textbook at the third-year college level. See part 1 on geometrical optics. Most introductory physics textbooks contain an abbreviated treatment of mirrors.

Levi, Leo. APPLIED OPTICS. New York: John Wiley & Sons, 1960. A technical guide to the design of optical systems from lamps to rangefinders. Chapters 8 and 9 discuss plane and curved mirrors.

Miczaika, G. R., and William M. Sinton. TOOLS OF THE ASTRONOMER. Cambridge, Mass.: Harvard University Press, 1961. Contains a good description of the use of mirrors and lenses in astronomical instruments, although somewhat dated.

Muirden, James. BEGINNER'S GUIDE TO ASTRONOMICAL TELESCOPE MAKING. London: Pelham Books, 1975. Details how to grind, polish, and mount a telescope mirror. Muirden has written a series of good books on amateur astronomy.

Welford, W. T. THE OPTICS OF NON-IMAGING CONCENTRATORS: LIGHT AND SOLAR ENERGY. New York: Academic Press, 1978. A good, but technical, reference to the design of solar collector mirrors.

Woodbury, David O. THE GLASS GIANT OF PALOMAR. New York: Dodd, Mead, 1939. A fascinating, nontechnical account of the conception and construction of the famous Hale 5-meter telescope, including many details of the process of mirror casting and grinding.

Reflection off the surface of a concave mirror

Reflection off the surface of a convex mirror

Reflection and Refraction