3
$\begingroup$

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.

$\endgroup$

1 Answer 1

3
$\begingroup$

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.

$\endgroup$
7
  • $\begingroup$ 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 $2$? $\endgroup$ May 2, 2021 at 3:12
  • $\begingroup$ You missed out 10 but yes, the equation has even powers of $\lambda$. $\endgroup$
    – Nick
    May 2, 2021 at 8:26
  • $\begingroup$ 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? $\endgroup$ May 2, 2021 at 11:34
  • $\begingroup$ They're all empirical constants. You do an experiment to measure some data, then calculate values of A, B etc that give the best fit to the data. $\endgroup$
    – Nick
    May 2, 2021 at 12:21
  • $\begingroup$ Do the values of $A, B, C, .....$ depend on the medium characteristics? $\endgroup$ May 2, 2021 at 13:27

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.