# What is the entirety of Cauchy's equation?

In my textbook it says that Cauchy's equation is $$\mu(\lambda)=A+\frac{B}{\lambda^{2}}+\frac{C}{\lambda^{4}}+ \cdots$$

But what comes after $$\frac{C}{\lambda^{4}}$$? There is literally nothing given in my book as to what comes after $$\frac{C}{\lambda^{4}}$$. I even searched the entire Internet and no where did I find what comes after $$\frac{C}{\lambda^{4}}$$. Please tell me. I am so confused.

The equation is an empirical relationship, there is no derivation. The equation could continue with inverse powers of $$\lambda^6$$, $$\lambda^8$$ etc., however often only the $$A$$ and $$B$$ terms are necessary to obtain a good approximation for wavelengths in the visible part of the spectrum. The Sellmeier equation, developed after Cauchy's equation, can provide a better approximation at longer wavelengths than visible.
• So, should the equation be $μ(λ) = Α+\frac{B}{λ^{2}}+\frac{C}{λ^{4}}+ \frac{D}{λ^{6}} +\frac{E}{λ^{8}} + \frac{F}{λ^{12}}+\frac{G}{λ^{14}}+......$? Are the powers of $λ$ multiples of $2$? May 2, 2021 at 3:12
• You missed out 10 but yes, the equation has even powers of $\lambda$.
• Oh sorry, I missed $10$. One more question. Are $A, B, C, D, E, ....$etc. all constants? If they are constants, on what the factors do their values depend upon? May 2, 2021 at 11:34
• Do the values of $A, B, C, .....$ depend on the medium characteristics? May 2, 2021 at 13:27