Topics in Particle and Dispersion Science

Lambert's law

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Lambert's law of attenuation of light emitted by a unidirectional source (light beam), here assumed to be oriented along the z-axis, is expressed as follows:

F(z) = F(0) e-cz

(1)

where z [length] is the distance in the medium and c [length^-1] is the attenuation coefficient. Given that optical transmission, T(z), is a ratio F(z) / F(0), this equation can be expressed as follows:

T(z) = e -cz

(2)

The Lambert law is a limiting case of the steady-state radiative transfer equation (RTE) for a medium with no sources of radiation (other than the incident beam) in which the path function of the RTE vanishes. This latter condition implies a single-scattering medium (see Single and multiple scattering). In the present context, the path function is the radiance gained per unit distance, z, by scattering of the radiance field at z into direction +z. The Lambert law can also be considered a specific case of the Gershun law (Gershun 1939, see also Preisendorfer RW 1961) for the attenuation of irradiance (Stavn 1981).

Swanson et al (1999) have recently examined the limits of transmission measurements and concluded that the Lambert law applies, by the virtue of suitably reducing the acceptance angle of the transmissometer (see RTE and transmission measurements), to dispersions with the optical thickness of up to about 10. See also comments on the applicability range of the Beer law.

The Lambert law, named after J. H. Lambert (1728-1777) who published it in 1760, is also referred to as Bouguer law (P. Bouguer, 1698-1758), who apparently discovered it first (1729).

See also Radiative transfer equation and Lambert's law

CITATION: Jonasz M. 2006. Lambert's law (www.tpdsci.com/Tpc/LmbLw.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 18-Jan-2006 Modified: 26-Jun-2009 Peer-reviewed: 19-Feb-2007

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