Generalized Lorentz-Lorenz law

The dimension of the problem can be reduced by using the properties of determinants and the final result is 

In the low frequency limit, the size of the particle is considered to be very small compared to the incident wavelength. It is then sufficient to take only the lowest-order coefficients in the fields expansions, and in this limit, the elements of the T matrix can be obtained in closed form for simple shapes. For spherical particles, we have 

As a result, the long-wavelength equation for the effective wave number takes the form 

For an ensemble of spheres of radius R and small fractional concentrations c, 

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