Cauchy Optical Dispersion Calculator

Estimate refractive index n($\lambda$) using Cauchy’s equation from $n_d$ and Abbe number $V_d$ (at the d-line, 587.6 nm). Pick a material preset or enter custom values; the tool solves $A$, $B$, $C$ from the Fraunhofer F/d/C lines, plots n vs. wavelength (200 nm to 1000 nm, extendable to 2000 nm). It reports dispersion ($dn/d\lambda$) with a reference table. Note: Cauchy is most accurate over limited transparent bands (typically visible); for broader ranges or near absorption, prefer the Sellmeier model.

Formula

Cauchy's equation provides the refractive index as a function of wavelength:

$$n(\lambda) = A + \frac{B}{\lambda^2} + \frac{C}{\lambda^4}$$

Where:

  • $n(\lambda)$ is the refractive index at wavelength $\lambda$ (in micrometers)
  • $A$, $B$, and $C$ are the Cauchy coefficients
  • When only $n_d$ and $V_d$ (Abbe number) are known, we can solve for the coefficients using:

$$V_d = \frac{n_d - 1}{n_F - n_C}$$

Where $n_F$, $n_d$, and $n_C$ are measured at standard Fraunhofer F (486.1 nm), d (587.6 nm), and C (656.3 nm) lines.

Validity & when to use another model: Cauchy is an empirical fit that works best for transparent dielectrics over a limited spectral band (typically the visible). It becomes less representative near absorption edges (deep UV) and further into the IR, or for strongly dispersive/absorbing materials. For broader accuracy or outside the visible, prefer the Sellmeier equation.

Material Properties
Enter the refractive index nd at 587.6 nm (d-line) and the Abbe number Vd to calculate Cauchy coefficients.
Cauchy Coefficients Calculate to view Cauchy coefficients.
Wavelength Input
Set the wavelength for evaluating n($\lambda$) and dispersion.
Results Enter values to compute.
Refractive Index vs. Wavelength Plot
Reference Table
Calculated refractive index and dispersion values for different wavelengths:
Wavelength Refractive Index Dispersion (dn/dλ)