thumb|Spectral reflectance curves for [[aluminium (Al), silver (Ag), and gold (Au) metal mirrors at normal incidence]]

The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic structure of the material to the electromagnetic field of light, and is in general a function of the frequency, or wavelength, of the light, its polarization, and the angle of incidence. The dependence of reflectance on the wavelength is called a reflectance spectrum or spectral reflectance curve.

Mathematical definitions

Hemispherical reflectance

The hemispherical reflectance of a surface, denoted , is defined as

<math display="block">R = \frac{\Phi_\mathrm{e}^\mathrm{r{\Phi_\mathrm{e}^\mathrm{i,</math>

where is the radiant flux reflected by that surface and is the radiant flux received by that surface.

Spectral hemispherical reflectance

The spectral hemispherical reflectance in frequency and spectral hemispherical reflectance in wavelength of a surface, denoted and respectively, are defined as This can be greater than 1 for a glossy surface illuminated by a source such as the sun, with the reflectance measured in the direction of maximum radiance (see also Seeliger effect).

Spectral directional reflectance

The spectral directional reflectance in frequency and spectral directional reflectance in wavelength of a surface, denoted and respectively, are defined as

Reflectivity

thumb|Fresnel reflection coefficients for a boundary surface between air and a variable material in dependence of the complex refractive index and the angle of incidence

For homogeneous and semi-infinite (see halfspace) materials, reflectivity is the same as reflectance.

Reflectivity is the square of the magnitude of the Fresnel reflection coefficient,

which is the ratio of the reflected to incident electric field;

as such the reflection coefficient can be expressed as a complex number as determined by the Fresnel equations for a single layer, whereas the reflectance is always a positive real number.

For layered and finite media, according to the CIE, reflectivity is distinguished from reflectance by the fact that reflectivity is a value that applies to thick reflecting objects. When reflection occurs from thin layers of material, internal reflection effects can cause the reflectance to vary with surface thickness. Reflectivity is the limit value of reflectance as the sample becomes thick; it is the intrinsic reflectance of the surface, hence irrespective of other parameters such as the reflectance of the rear surface. Another way to interpret this is that the reflectance is the fraction of electromagnetic power reflected from a specific sample, while reflectivity is a property of the material itself, which would be measured on a perfect machine if the material filled half of all space.

Surface type

Given that reflectance is a directional property, most surfaces can be divided into those that give specular reflection and those that give diffuse reflection.

For specular surfaces, such as glass or polished metal, reflectance is nearly zero at all angles except at the appropriate reflected angle; that is the same angle with respect to the surface normal in the plane of incidence, but on the opposing side. When the radiation is incident normal to the surface, it is reflected back into the same direction.

For diffuse surfaces, such as matte white paint, reflectance is uniform; radiation is reflected in all angles equally or near-equally. Such surfaces are said to be Lambertian.

Most practical objects exhibit a combination of diffuse and specular reflective properties.

Liquid reflectance

thumb|Reflectance of smooth water at 20&nbsp;°C (refractive index 1.333)

Reflection of light occurs at a boundary at which the index of refraction changes. Specular reflection is calculated by the Fresnel equations. Fresnel reflection is directional and therefore does not contribute significantly to albedo which primarily diffuses reflection.

A liquid surface may be wavy. Reflectance may be adjusted to account for waviness.

Grating efficiency

The generalization of reflectance to a diffraction grating, which disperses light by wavelength, is called diffraction efficiency.

Other radiometric coefficients

See also

  • Bidirectional reflectance distribution function
  • Colorimetry
  • Emissivity
  • Lambert's cosine law
  • Transmittance
  • Sun path
  • Light Reflectance Value
  • Albedo
  • Reststrahlen effect
  • Lyddane–Sachs–Teller relation

References

  • Reflectivity of metals .
  • Reflectance Data.