Reflection of Light

Reflection of Light

 

a phenomenon exhibited when light (optical radiation) is incident on the interface of one medium with a second medium; the interaction of the light with the material of the second medium results in the appearance of a light wave that is propagated from the interface back into the first medium. At least the first medium here must be transparent to the incident and reflected radiation. Bodies that are not self-luminous become visible as a result of the reflection of light from their surfaces.

The spatial intensity distribution of reflected light is determined by the ratio of the dimensions of surface (interface) to the wavelength λ of the incident radiation. If the irregularities are small in comparison with λ, specular, or regular, reflection of light occurs. When the dimensions of the irregularities are commensurate with or exceed λ—as in the case of rough surfaces and mat surfaces—and the distribution of the irregularities is disordered, the reflection of light is diffuse. Mixed reflection of light, in which part of the incident radiation is reflected specularly and part diffusely is also possible. If irregularities with dimensions of approximately λ or greater are distributed in an orderly manner, the distribution of reflected light has a special character close to that observed when light is reflected from a diffraction grating. The reflection of light is closely connected with refraction phenomena, which occur when the reflecting medium is completely or incompletely transparent, and with absorption phenomena, which occur when the medium is incompletely transparent or is opaque.

Specular reflection. Specular reflection of light is characterized by a definite relationship between the positions of the incident and reflected rays: (1) the reflected ray lies in a plane that passes through the incident ray and the normal to the reflecting surface, and (2) the angle of reflection ψ is equal to the angle of incidence φ (Figure 1). The intensity of the reflected light is characterized by the reflection coefficient and depends on φ, the polarization of the incident beam of rays, and the relation between the refractive indices n2 and n1 of the second and first media. This dependence is quantitatively expressed for a dielectric reflecting medium by the Fresnel equations. In particular, it follows from the equations that when the light is incident along a normal to the surface, the reflection coefficient is independent of the polarization of the incident beam and is equal to (n2n1)2/(n2 + n1)2. In the very important special case of normal incidence of light on the interface between air and glass (nair ≈ 1.0 and nglass = 1.5), the reflection coefficient is approximately 4 percent.

Figure 1. Specular reflection of light: (N) normal to the reflecting surface (interface), (φ) angle between the incident ray and the normal (angle of incidence), (Ψ) angle between the reflected ray and the normal (angle of reflection); φ = Ψ. (Ep), (Rp), (Rs), and (Rs) amplitude components of the electric vectors of the incident and reflected waves with vibrations lying, respectively, in and perpendicular to the plane of incidence. The arrows indicate selected positive directions of vibration amplitudes.

The character of the polarization of reflected light changes with φ and is different for components of the incident light that are polarized parallel (the ρ component) and perpendicular (the s component) to the plane of incidence (Figure 2). Here, the plane of polarization is, as usual, taken to be the plane of vibration of the electric vector of the light wave. For angles φ equal to the Brewster angle, the reflected light becomes completely

Figure 2. Relationship between the angle of incidence ψ and the reflection coefficients rp and rs of the components of the incident wave that are polarized, respectively, parallel and perpendicular to the plane of incidence. Curves 1 refer to the case n2/n1 = 1.52, and curves 2 to the case n2/n1 = 9. The upper scale refers to the case n2/n1 = 1/1.52.

polarized perpendicular to the plane of incidence, and the ρ component of the incident light is completely refracted into the reflecting medium. If this medium strongly absorbs light, the refracted ρ component traverses a very short path in the medium. This characteristic of specular reflection is made use of in a number of polarization devices. For φ greater than the Brewster angle, the reflection coefficient for dielectrics increases with φ toward a limit of 1, regardless of the polarization of the incident light.

In general, in specular reflection, as is clear from Fresnel’s equations, the phase of the reflected light changes discontinuously. At normal incidence to the interface (φ = 0), the phase of the reflected wave is shifted by π when n2 > n1, and it remains unchanged when n2 < n1. The phase shift during reflection when φ ≠ 0 may differ for the ρ and s components of the incident light, depending on whether φ is greater or less than the Brewster angle and also on the ratio of n2 and n1.

Reflection from the surface of an optically less dense medium (n2 < n1) when sin φ ≥ sin n2/n1 is total internal reflection, in which all the energy of the incident beam of rays is returned to the first medium. Specular reflection from surfaces of strongly reflecting media, such as metals, is described by equations similar to the Fresnel formulas with the extremely important difference that n2 becomes a complex quantity whose imaginary part characterizes the absorption of the incident light. Absorption in a reflecting medium results in the absence of a Brewster angle and in values of the reflection coefficient higher than for dielectrics. Even at normal incidence the coefficient may exceed 90 percent—thus the extensive use of smooth metallic and metal-plated surfaces in mirrors.

The polarization characteristics of light waves reflected from an absorbing medium also differ—as a result of other phase shifts of the ρ and s components of the incident waves. The character of the polarization of reflected light is so sensitive to the parameters of the reflecting medium that many optical methods used to investigate metals are based on this phenomenon.

Diffuse reflection. Diffuse reflection of light is the scattering of light in all directions by the uneven surface of the second medium. The spatial distribution and intensity of the reflected radiation flux differ in each specific case and are determined by the relation between λ and the dimensions of the irregularities, by the distribution of the irregularities over the surface, by the conditions of illumination, and by the properties of the reflecting medium. The limiting case of the spatial distribution of diffusely reflected light is not strictly realized in nature and is described by Lambert’s law. Diffuse reflection of light is also observed from media whose internal structure is inhomogeneous. Such a structure results in the scattering of light within the medium and in the return of part of the light to the first medium. The regularities of the diffuse reflection of light from such media are determined by the character of the processes of single and multiple scattering of light within the media. Both the absorption and the scattering of light may display a strong dependence on λ. A consequence of this fact is alteration of the spectral composition of diffusely reflected light, which, for illumination by white light, is visually perceived as the coloring of bodies.

REFERENCES

Landsberg, G. S. Optika. 4th ed. Moscow, 1957. (Obshchii kurs fiziki. vol. 3.)
Born, M., and E. Wolf. Osnovy optiki. 2nd ed. Moscow, 1973. (Translated from English.)
Ditchburn, R. Fizicheskaia optika. Moscow, 1965. (Translated from English.)
Minnaert, M. Svet i tsvet ν prirode. Moscow, 1958. (Translated from English.)
Brekhovskikh, L. M. Volny ν sloistykh sredakh. Moscow, 1957.
Tolansky, S. Udivilel’nye svoistva sveta. Moscow, 1969. (Translated from English.)

N. A. VOISHVILLO

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