Reflection And Refraction

Reflection and refraction occur as light passes from one medium to another of differing density. The characteristic bending of light rays that occurs provides insight into the physical properties of the refracting media and provides an example of the electromagnetic wave behavior of light.

Overview

When light strikes the surface of a medium such as water or glass, several phenomena occur. Some portion of the light may be absorbed and transformed to heat energy. The remaining light rays either are returned to the first medium (usually air) by reflection off the boundary surface or pass through the second medium with a change in direction called refraction.

Light falling on the surface of a liquid or solid is referred to as incident light. The angle of incidence is defined as the angle between the incident light ray and a line drawn normal, or perpendicular, to the surface of the medium. If the surface boundary is well defined and quite smooth, then the angle of reflection is equal to the angle of incidence. In addition, the incident light ray, reflected ray, and the normal to the boundary surface will all occur in a common plane. Frequently, however, the surface separating two media is rough and irregular, and light becomes scattered in numerous directions. This is referred to as diffuse reflection.

The ratio of the intensity of reflected light to the intensity of the incident beam is termed the "reflectivity" of the surface. The proportion of the light that is reflected is dependent on the angle of incidence, the smoothness of the surface, and the composition of the medium.

Metallic materials such as silver and aluminum are excellent reflectors, although aluminum is often favored for mirrors because of its resistance to tarnish.

Reflection not only returns light rays from a boundary surface but also may affect certain properties of the light. Associated with the propagation of light are electric and magnetic vibrations occurring in all directions within a plane perpendicular to the direction of light-ray travel. As an incident beam strikes a surface, the electromagnetic vibrations parallel to the surface reflect, while vibrations in other orientations are absorbed preferentially. The result is a reflected ray, which is said to be plane polarized. The effectiveness of the polarization is highly dependent on the angle of incidence and is better observed with nonmetallic surfaces. That explains why sunglasses equipped with Polaroid lenses are so effective at eliminating glare. The polarizing direction of the lenses is designed to cut off the dominant plane-polarized light produced by reflection off a road surface.

While light travels within a vacuum, it possesses a velocity of 3 x 10¹⁰ centimeters per second, or 300,000 kilometers per second. When light encounters a denser medium, velocity is reduced and may be accompanied by the bending, or refraction, of light rays.

Refraction explains the apparent bending of a pencil when placed in a glass of water. The velocity of light is equal to the wavelength multiplied by the frequency, as expressed by the following equation: c= ƒλ where c equals light velocity, f is frequency, and λ is the wavelength. As a result, if light velocity changes, then either the frequency, the wavelength, or both must change. Since frequency remains constant for a given color of light, it is the wavelength value that changes.

A measure of the change in light velocity caused by a particular medium is the index of refraction, which is defined as the velocity of light in a vacuum relative to the velocity in the medium. The index is usually expressed by the letter n, as in the following equation: n = V(vacuum)/V(medium) where V represents the velocity of light. Because the light velocity in any medium is always slower than that in a vacuum, the numerical value of the refractive index must always be greater than one. Most substances have indices of refraction in the range between 1.3 and 2.5.

If an incident light ray passes obliquely into a second, denser medium, the refracted ray will be bent toward a line drawn normal to the boundary surface. For light emerging from a dense medium, the light ray will be bent away from the normal line. The relationship between the angle of incidence, angle of refraction, and index of refraction was first discovered by Willebrord Snell, a Dutch astronomer, in 1621. Through experimentation, he found that, for any angle of incidence, the ratio of the sine of the incident angle to the sine of the angle of refraction was equal to the index of refraction, n. This is usually expressed as sin i/ sin r = n, where i and r are the angles of incidence and refraction, respectively. This relationship is referred to as Snell's law. One consequence of Snell's law is that for incident rays—which are normal to the medium boundary surface—where the angle of incidence will be 0 degree, the angle of refraction will also be 0 degree. A useful means of envisioning this relationship is to imagine a column of troops marching several abreast in step across a hard surface and into a muddy field. If the column marches directly along a line drawn perpendicular to the boundary of the field, the first soldiers entering the mud will all slow down together and tend to bunch up but not change direction. Yet, if the column enters the field at an oblique angle, then as the first soldiers to encounter the mud slow down the remaining soldiers in their row (who are still on the hard surface), they must swing around to remain in step and thus bend the column at the margin of the muddy field. The amount of bending that occurs will be greater for higher angles of incidence.

The coefficient of refraction, n, has already been defined as the ratio of the velocity of light in a vacuum to the velocity in a medium. In turn, the velocity of light is equal to the wavelength multiplied by frequency. Because frequency remains constant during refraction, the index of refraction could be defined alternatively as the ratio of the wavelength of light in a vacuum relative to the wavelength of light in a medium. As a result, each portion of the visible light spectrum will have its own distinct angle of refraction. This property is referred to as "dispersion" and is best observed with an ordinary glass prism. A ray of sunlight is often referred to as white light. It is composed of a range of wavelengths of light from approximately 4,000 angstroms to 7,600 angstroms. The various colors that the human eye perceives lie within very narrow bands of this overall visible light spectrum. The shortest wavelengths correspond to red, while progressively longer wavelengths encompass orange, yellow, green, blue, and violet. When white light is refracted, the differing wavelengths of these component colors result in differing indices of refraction and, hence, varying angles of refraction as well. The angle of refraction for the shorter-wavelength colors is somewhat larger than those of the longer-wavelength colors. The result of dispersion is the characteristic spectrum of colors produced by either a prism or raindrops in the case of rainbows.

Both reflection and refraction usually occur whenever light strikes a boundary between two media. The quantity of light reflected depends on the properties of the media and the angle of incidence. Generally, the proportion of incident light that is reflected increases as the angle of incidence increases. When this angle has become great enough, all incident light will be reflected. The particular angle of incidence at which total reflection first occurs is called the critical angle. One feature of the critical angle is that the angle of refraction is equal to 90 degrees, which indicates that no light ray actually travels within the denser medium but, instead, a ray is directed along the boundary plane separating the media.

Applications

The theories of reflection and refraction have broad applications in both everyday objects, such as mirrors or eyeglasses, and scientific fields, such as crystallography and microscopy.

The most common utility of reflection is in the manufacture of planar, or flat, mirrors.

To an observer, the image of an object reflected in a mirror appears to originate at some point behind the mirror surface. The image will appear to be as far behind the mirror as the object is in front of it. The size of the reflected image will also equal the size of the actual object. Because the eye places the image at a point where light rays converge when extended past the plane of the mirror, the image is not real and is referred to as a virtual image.

In some applications, mirrors are designed that are spherical in shape. Those that have their reflective surface on the interior of the sphere are concave mirrors, while those with coated exterior surfaces are convex mirrors. Spherical mirrors are described further by their radius of curvature and their principal axis. The principal axis is a line through the center of the mirror, which also corresponds to a diameter of the complete sphere. Rays of incident light that are parallel to the principal axis will all reflect through a common point on the principal axis called the principal focus. The distance between the mirror and the principal focus is referred to as the focal length. For a truly spherical concave mirror, only those light rays that are close to the principal axis will reflect through the principal focus. Rays farther away from the center region of the mirror will reflect through points that are closer to the mirror surface. The resulting image is less sharp as a result of this phenomenon, which is called spherical aberration.

In telescopes, which use concave mirrors to gather light over a large area, the problem of spherical aberration is solved by constructing the curvature of the mirror in the shape of a parabola rather than a true sphere.

Incident light parallel to the principal axis and falling on the surface of a convex mirror reflects back in a way that causes the rays to diverge away from the mirror surface. The reflected rays will appear to have originated at a principal focus, which extends behind the mirror and thus forms a virtual image. Objects viewed with a convex mirror will appear enlarged.

Refraction plays an important role in the design of lenses for eyeglasses, telescopes, and microscopes. Transparent materials of a particular index of refraction, such as glass or plastic, are used to cause light rays to either converge or diverge to form an image of some object. Typically, lenses are disk-shaped, with either two curved surfaces or one surface flat and the other curved. The curved portion of a lens may be either concave or convex. All rays that pass through a lens are refracted, with the exception of the ray that passes through the center point, which is called the optical center. Diverging lenses create virtual images that are upright and smaller than the actual object. A convergent lens causes light rays to converge at the principal focus, which is behind the lens. The size of the image will depend on the distance of the object relative to the focal length of the lens and the amount of lens curvature.

One of the most important measurable physical properties of transparent crystalline substances, such as minerals, is their refractive index. Gems such as diamonds are valued because of their high refractive index, which contributes to their characteristic sparkle. Because of the effects of dispersion, the index of refraction is always measured with a monochromatic light source. Transparent minerals may be divided into two general classes: the isotropic and the anisotropic groups. Isotropic minerals belong to the isometric crystal class. These substances possess the highest symmetrical arrangement of atoms within their crystal lattices. As a result, light rays will have a single velocity that remains constant along any crystallographic direction within the mineral. Isotropic minerals are characterized by a single index of refraction value.

Common examples include diamond, fluorite, garnet, and halite.

Anisotropic minerals possess lesser levels of symmetry, and as a result, the velocity of light varies with different crystallographic directions. The difference between the lowest and highest refractive index values for a mineral is referred to as birefringence. The passage of light through an anisotropic mineral is very complex. Typically, the light is split into two distinct rays, which are polarized at right angles to each other. Because the rays are polarized in different planes of vibration, each ray will have slightly differing velocities and hence differing indices of refraction. The rays are referred to as the ordinary and the extraordinary ray. The presence of two distinct rays results in the phenomenon of double refraction, which is well exhibited in the mineral calcite. If a clear calcite crystal is placed over a figure, such as a dot on a page, the image will appear doubled.

Context

The laws of reflection and refraction were known empirically long before there were adequate theories to explain the nature of light itself. The law of reflection was known to Euclid, the famous Greek mathematician best known for his work in geometry. Snell's law, the mathematical expression for the relation of the angle of incidence to the angle of refraction, was not published until 1621. Even before the recognition of Snell's law, Galileo, the Italian astronomer, had constructed the first telescope in 1609. Galileo's telescope was of a design called a refractor and used a convex objective lens that caused parallel light rays to bend and converge at a focal point behind the lens. In 1672, the reflector telescope was invented. Light rays are reflected by a parabolic-shaped mirror and brought to a focus in front of the mirror on the principal axis. A third type of telescope is known as the catadioptric system, which uses a combination of lenses and mirrors. The brightness and magnifying power of a telescope are proportional to the light-gathering area of its lens or mirror.

By the early seventeenth century, the microscope had also been invented. The simplest sort of microscope is the magnifying glass, which consists of a double convex lens with a short focal length. When an object is placed within focal length distance to the lens, an enlarged upright image results. The compound microscope consists of two such lenses placed at either end of a hollow metal tube. The upper lens serves as an eyepiece, while the lower lens is the objective. The naturalist Antoni van Leeuwenhoek experimented with more than two hundred microscope designs.

The laws of reflection and refraction also played a role in the debate on the nature of light. In the early 1600s, Rene Descartes, the French mathematician and philosopher, proposed the corpuscular theory of light. Descartes believed that light consisted of streams of tiny particles. Such an interpretation was consistent with reflection but could not account for refraction. Dutch physicist Christiaan Huygens set forth in 1678 a wave theory of light. Huygens did not know what type of wave motion might be involved or have any idea of the electromagnetic nature of light, but his ideas did account for such phenomena as refraction and diffraction. Diffraction refers to the bending of light observed near the edges of opaque objects.

Huygens described light wave motion by constructing complex geometric diagrams in which all points on a wavefront were considered to be point sources for the production of outward-moving secondary waves. Experiments on diffraction conducted in the early 1800s led to the dominance of the wave theory. By 1864, James Clerk Maxwell had discovered that light was a portion of the electromagnetic spectrum. The debate between corpuscular versus wave theory, however, was not resolved entirely. The discovery of the photoelectric effect, in which light falling on a metal surface causes a positive charge to develop at the surface, seemed to require a particulate component of light. The modern view, in which light is considered to possess a dual nature—particulate and electromagnetic wave behavior—was established in 1905 when Albert Einstein proposed the existence of light quanta, or photons.

Principal terms

ANISOTROPIC: having properties, such as light velocity, that vary with direction

BIREFRINGENT: exhibiting a range of refractive index values

DISPERSION: an expression for the variability of the index of refraction with the wavelength of light

FREQUENCY: the number of oscillations that occur during a unit time, such as the hertz, which is one oscillation per second

INDEX OF REFRACTION: the ratio of the velocity of light in a vacuum to light velocity in a particular medium

ISOTROPIC: having properties, such as light velocity, that are constant in all directions

MONOCHROMATIC LIGHT: light of one specific wavelength

WAVELENGTH: the distance between successive wavecrests, often expressed in either angstrom units or nanometers

Bibliography

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