In the Maxwell Garnett approximation, the effective medium consists of a matrix medium with  and inclusions with . Maxwell Garnett was the son of physicist William Garnett, and was named after Garnett's friend, James Clerk Maxwell. He proposed his formula to explain colored pictures that are observed in glasses doped with metal nanoparticles. His formula has a form
where  is effective relative complex permittivity of the mixture,  is relative complex permittivity of the background medium containing small spherical inclusions of relative permittivity  with volume fraction of . This formula is based on the equality
where  is the absolute permittivity of free space and  is electric dipole moment of a single inclusion induced by the external electric field . However this equality is good only for homogeneous medium and . Moreover, the formula (1) ignores the interaction between single inclusions. Because of these circumstances, formula (1) gives too narrow and too high resonant curve for plasmon excitations in metal nanoparticles of the mixture.