I'm trying to write some code to find the refractive index in glass given a wavelength. Glass manufacturers use a equation called Sellmeier which given some fitted co-efficients for each type of glass will give you the refractive index.
Sellmeier: $$ n^2(\lambda) - 1 = \frac{B_1 \cdot \lambda^2}{(\lambda^2 - C_1)} + \frac{B_2 \cdot \lambda^2}{(\lambda^2 - C_2)} + \frac{B_3 \cdot \lambda^2}{(\lambda^2 - C_3)} $$
I wish to find the refractive index at wavelength 587.6nm of a glass called N-BK7 which has the Sellmeier coefficients of:
- B1 = 1.03961212
- B2 = 0.231792344
- B3 = 1.01046945
- C1 = 0.00600069867
- C2 = 0.0200179144
- C3 = 103.560653
Now here is where I must be going wrong (not much of a heavy math user). I must be getting the transposition wrong somehow because my solution comes to the wrong expected value. $$ n(587.6) = \sqrt{1 + \frac{1.03961212 \cdot 587.6^2}{(587.6^2 - 0.00600069867)} + \frac{0.231792344 \cdot 587.6^2}{(587.6^2 - 0.0200179144)} + \frac{1.01046945 \cdot 587.6^2}{(587.6^2 - 103.560653)}} $$ Gives: 1.81168 Expected: 1.51680
[in wolfram](https://www.wolframalpha.com/input/?i=sqrt(1+%2B+(1.03961212*587.6%5E2)+%2F+(587.6%5E2+-+0.00600069867)+%2B+(0.231792344*587.6%5E2)+%2F+(587.6%5E2+-+0.0200179144)+%2B+(1.01046945+*+587.6%5E2)+%2F+(587.6%5E2+-+103.560653))
What am I doing wrong?
Since the Sellmeier coefficients are usually quoted in square microns (not square nanometers) I think you have a units error.
Try using the wavelength as $0.5876$ microns, which gives an answer of $1.517$ by my slide-rule calculation.