Value of the constant in 'variation of refractive index'

Donchay

In optics, given the below formula

n_λ= A + B/λ² + C/λ⁴ +......

where A, B and C are constants.

From the above relationship we can deduce that as the wavelength λ increases, the variation of refractive index n_λ decreases.

How do we measure the constant value of A,B and C at the first place?

DrDu

You measure the refractive index at several wavelengths and then you fit the formula to the values obtained.

Donchay

Thank You DrDu.
While the above formula is for Optical Dispersion, then is it the same dispersion for the Abbe Number:

V_d=(n_D-1)/n_F-n_C

where n_F-n_C is the dispersion according to this link http://glassproperties.com/abbe_number/

but somehow on other link I read that n_F-n_C is called Principal Dispersion. I try to search on more about Principal Dispersion but there is almost none explanation about it.

DrDu

n_F is the index of refraction for blue light while n_C is for red light (see the table with the line frequencies).
One assumes that for glass the dispersion is approximately linear over the optical frequency range.

Donchay

I understand about the line frequencies. Just that is it n(lambda)=n_F - n_C ?

DrDu

I would try something like ## n(\lambda)=n_C+(n_F-n_C)\frac{1/\lambda_C^2-1/\lambda^2}{1/\lambda_C^2-1/\lambda_F^2} ##.