Cauchy Equation
Definition
The empirical equation n(λ) = A + B/λ² + C/λ⁴ that describes the wavelength dependence (dispersion) of a material's refractive index; used to correct RI measurements to the standard sodium D line (589 nm) wavelength.
- Form
- n(lambda) = A + B/lambda squared + C/lambda to the fourth
- Describes
- Wavelength dependence (dispersion) of refractive index
- Use
- Correcting RI to the sodium D line, 589 nm
- Field
- Trace evidence, glass and fibre refractive index analysis
Common questions
Why does refractive index need correcting to a standard wavelength at all?+
A material's refractive index varies with the wavelength of light used to measure it, so two labs measuring the same glass fragment under different illumination would get different raw values unless both convert their results to the same reference wavelength for comparison.
How is the Cauchy equation used in practice with instruments like GRIM or a hot stage?+
An examiner measures refractive index at several known wavelengths or temperatures and fits the Cauchy relationship to that data, which lets the instrument interpolate or extrapolate the index value at the standard sodium D line for consistent comparison against reference collections.
Related terms
- ASTM E1967
- The ASTM International standard for forensic glass RI measurement; specifies three acceptable methods (automated, semi-automated, manual), minimum precision of ±0.0001 RI units,...
- Bayesian Likelihood Ratio
- A statistical framework for expressing the evidential value of a comparison: the ratio of the probability of the observed RI similarity given...
- Becke Line
- The bright optical halo at the edge of a solid fragment immersed in a liquid, visible under the microscope; moves toward the...
- Dispersion
- The variation of refractive index with wavelength; all glasses and immersion oils show dispersion, which is why RI must be specified at...
- ENFSI ENG3-2013
- The ENFSI Glass Expert Working Group guideline for glass comparison casework; specifies the examination sequence, within-source variation requirements, statistical comparison framework, and...
- GRIM-3
- Glass Refractive Index Measurement, third-generation instrument by Foster + Freeman (UK); an automated phase-contrast hot-stage system that identifies the RI match point...
- Immersion Method
- The forensic technique of matching a glass fragment's RI to that of a reference oil by adjusting temperature; the fragment becomes invisible...
- Locke 1985 Protocol
- The calibrated immersion-oil series and operational procedure for forensic glass RI measurement described by Locke and Underhill (1985); specifies the oil series,...
- Mettler FP-90
- A general-purpose laboratory hot stage widely used in forensic glass RI measurement to provide ±0.1 °C temperature control for the manual Becke-line...
- Phase-Contrast Microscopy
- An optical technique that converts phase differences (RI differences at an interface) into intensity differences visible in the image; exploited by the...
- Refractive Index (RI)
- A physical property of glass measuring how much light bends as it passes through. RI is the primary discriminating characteristic used in...