# How do I find the constants in Cauchys equation for index of refraction for different wavelengths?

Im trying to find the indexes of refraction for my Dispersion of a Glass Prism lab. Specifically I need to use Cauchy's equation to find the index of refraction for different wavelengths.

$$n=a+\dfrac{b}{\lambda^2}$$

This is what the step says: Convert the wavelengths to μm. Make a table containing the quantities wavelength, wavelength-2, and index of refraction.

I made a graph but Im still not clear on what values a and b would be

This is my data so far

• make $x = 1\lamda^2$ and your graph will be a straight line. You know how to fit a straight line and get a and b, right?
– user83548
Commented May 23, 2016 at 23:51
• en.wikipedia.org/wiki/Cauchy%27s_equation : your $\:a \longrightarrow B\:$ and $\:b \longrightarrow C\:$, choose material. Commented May 23, 2016 at 23:52
• @brucesmitherson , Yes I am able to get the straight line y=mx+b, would m=a? Thanks
– kal
Commented May 24, 2016 at 0:03
• no, m=b, and your b=a
– user83548
Commented May 24, 2016 at 0:04
• ok that helps a lot! I appreciate it @brucesmitherson
– kal
Commented May 24, 2016 at 0:40

Some minor points: First, the units of $\lambda^2$ will be $(\mu m)^2$. Second it seems you are asking for $a, b$ so that you can determine $n$?
In fact, what is more often done is to plot $n$ versus $1/\lambda^2$ to determine $a, b$. At the moment you can't do anything (unless you follow Frobenius and look up $a, b$, however this means you know the material, but it may be a composite material or not listed or depend on a host of other issues), the suggestion is "Make a table containing the quantities wavelength, 1/(wavelength)$^2$, and index of refraction."
So, you need to construct a table with two columns: In the first column you have your measured values of refractive index and in the second column you have the corresponding values of $1/\lambda^2$.