Adjusting the relation between the imaginary part of the dielectric constant and the wavelength

In the literature, an equation has two forms, although they are widespread, they are wrong. The first form that correlates the dielectric constant imaginary part, epsilon(2), with the third order of wavelength, lambda(3), as epsilon(2) = epsilon(infinity)(omega(p))(3)lambda(3)/ (8 pi(2)c(3)tau). Unfortunately, the dimensions of the left-hand side and the right-hand side are not the same. Where the LHS (epsilon(2)) has no dimensions and the RHS epsilon(infinity)(omega(p))(3)lambda(3)/(8 pi(2)c(3)tau) has s(-1) units. The second form has been written as epsilon(2) = (1/4 pi(3)epsilon(0)) (e(2)/c(3)) (n/m*) (1/tau)lambda(3) although it is dimensionally correct, something went wrong when it was deduced which made it give twice the value of epsilon(2). Therefore, the use of these relationships must be discontinued. The correct forms of these relationships have been derived as epsilon(2) = (omega(p))(2)lambda(3)/(8 pi(3)c(3)tau) and epsilon(2) = (1/8 pi(3)epsilon(0)) (e(2)/c(3)) (n/ m*) (1/tau)lambda(3) which agree with the textbooks and literature.

Automated summary

This passage discusses two forms of equations that are commonly used but incorrect. The correct forms have been derived and validated, aligning with the information found in textbooks and literature.