Geology & Earth ScienceMineralogyUniversity
AQAAPOntarioNSWCBSEGCE O-LevelMoECAPS

Gladstone-Dale Relation Calculator

Relates the refractive index of a mineral to its chemical composition and density.

Use the free calculatorCheck the variablesOpen the advanced solver
Open Advanced Calculator
This is the free calculator preview. Advanced walkthroughs stay in the app.
Result
Ready
Refractive Index

Formula first

Overview

The Gladstone-Dale relation defines a linear correlation between a mineral's average refractive index and its density through a compositionally dependent constant. It is primarily used in mineralogy to cross-verify the accuracy of measured physical properties against the chemical analysis of a mineral specimen.

Symbols

Variables

n = Refractive Index, K = Specific Refractive Energy, = Density

Refractive Index
Variable
Specific Refractive Energy
cm³/g
Density
g/cm³

Apply it well

When To Use

When to use: Apply this relation when evaluating the internal consistency of mineralogical data for new or rare species. It is particularly useful when checking if a reported density and refractive index align with the theoretical values derived from the mineral's chemical formula.

Why it matters: This equation is the foundation for the Mandarino compatibility index, which is the standard check for errors in mineral descriptions. Identifying discrepancies between calculated and physical values helps scientists spot measurement errors or the presence of impurities.

Avoid these traps

Common Mistakes

  • Neglecting to calculate the bulk K value from the mineral's specific chemical weight percentages.
  • Using incorrect units for density.
  • Applying the relation to minerals where the Gladstone-Dale constants for specific components are not well-established.

One free problem

Practice Problem

A mineral specimen has a specific refractive constant (K) of 0.190 and a density (rho) of 3.50 g/cm³. Calculate the mean refractive index (n) of this mineral.

Specific Refractive Energy0.19 cm³/g
Density3.5 g/cm³

Solve for:

Hint: Rearrange the formula to solve for n: n = 1 + (K × rho).

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Nesse, W. D. (2017). Introduction to Mineralogy (4th ed.). Oxford University Press.
  2. Klein, C., & Dutrow, B. (2007). Manual of Mineralogy (after James D. Dana) (23rd ed.). John Wiley & Sons.
  3. Wikipedia: Gladstone-Dale relation
  4. Nesse, William D. Introduction to Mineralogy. Oxford University Press.
  5. Klein, Cornelis, and Barbara Dutrow. The 23rd Edition of the Manual of Mineral Science. John Wiley & Sons.
  6. Wikipedia: Refractive index
  7. IUPAC Gold Book: Refractive index
  8. Mandarino, J. A. (1976). The Gladstone-Dale relation and compatibility index. The Canadian Mineralogist, 14(2), 169-170.