How is Abbe's Number Calculated Using Fraunhofer's Lines?

[Donchay]

I don't understand how the formula works;

v_D= n_D-1 / n_F-n_C

given n_D,n_F and n_C are the Fraunhofer's line with wavelength of 589.3, 486.13, and 656.27 respectively in nm.

Now my trouble starts here. Since the wavelengths are already given , V_D is always a constant. How does the relationship between wavelength and refractive index goes here? Say if I want to measure a random value of refractive index/wavelength of a glass, how do I put the refractive index of my glass into the above equation?

 

[DrDu]

Abbe's number is indeed a constant, which is characteristic for each glass. It tells you whether a glass has a high or a low dispersion.
To answer your questions it would be helpful to know what you really are trying to do with the refractive indices.

 

[Donchay]

DrDu

I'm working on a university project to find the the optical property of a kind of glass. One of the property I'm doing research on is the dispersion of the glass, and therefore I will be looking into it's Abbe number. I have done the test on refractive index and obtain some data experimentally.

How should I use the refractive index i obtain experimentally to calculate Abbe's number of my kind of glass, since I don't know where to fit in my refractive index into that formula?

I was thinking about to start using the Cauchy dispersion formula, which you have seen on my previous post. By finding the constants A, B and C, I can then plug in the wavelength of the Fraunhofer values and obtain the refractive index of the Fraunhofer values. Can it work? Or is this the way it should work?

Thank you.

 

[DrDu]

Yes, this sounds very reasonable.