Solve for

Reference mineral

Δn range: 0.009–0.009; applied value: 0.009 (tabulated maximum).

Source: Nesse (2012); Raith et al. (2012)

Birefringence

Difference between the slow and fast refractive indices

dimensionless

00.2

Section thickness

Path length travelled by light through the sample

µm

150

Maximum normal colour reference for a mineral oriented at maximum Δn, with its vibration directions at 45° to the crossed polars and under D65 illumination. The sRGB values do not equal a calibrated microscope observation.

CIE1931_2DEG_D65_SRGB_V1

Results

Maximum normal reference colour

Order I

Γ = 270 nm

#f9fff3

First-order white

Birefringence

0.009 Δn

Thickness

30 µm

Δn class

Low

The reported colour is the maximum normal reference colour for the applied Δn value, not a mineral identification.

Michel-Lévy chart

Colour by retardation, birefringence lines and result marker

Move the pointer or use the arrow keys to inspect without changing the inputs.D65 · CIE 1931 2° · sRGB

Fundamentals & Explanation

What the colour represents

Between crossed polars, an anisotropic mineral splits light into two components that travel at different speeds. When they recombine at the analyser, their phase difference produces the interference colour: it is neither the mineral's body colour nor its absorption colour.

The concept of refractive index is developed in Snell's law and Fresnel equations. That basic case considers one index per medium; in an anisotropic crystal, propagation direction and polarisation determine different indices.

That phase difference is expressed as optical retardation Γ and depends on effective birefringence Δn and traversed thickness d:

Γ [nm] = 1000 · Δn · d [µm]

Each chart diagonal keeps the ratio Γ/d constant and therefore represents one value of Δn.

Three ways to use it

Predict: with known Δn and d, calculate Γ and locate its normal reference colour.
Estimate birefringence: with Γ—or an approximate observed colour—and known d, follow the diagonal to read Δn.
Estimate thickness: with known Γ and Δn, read d on the vertical axis.

The horizontal axis shows Γ and the vertical axis d; vertical divisions separate 550 nm orders. By convention, 550 nm corresponds to the end of first order, 1100 nm to the end of second order, and so on.

Example: quartz in a 30 µm section

Using Δn = 0.009, Γ = 1000 × 0.009 × 30 = 270 nm. The result lies within first order and corresponds to its normal reference colour. A real grain can show lower retardation when the section does not expose maximum birefringence.

What it cannot establish

A colour cannot identify a mineral on its own: different combinations of Δn and d produce the same Γ. An anisotropic crystal can also appear black at extinction; that does not imply Δn = 0. The chart must be combined with relief, habit, cleavage, twinning and other petrographic properties.

Before comparing colours

Rotate the stage and seek the strongest colour, about 45° from extinction.
Confirm thickness: 30 µm is common, but not universal.
Consider absorption, pleochroism, uneven thickness and anomalous colours.

The mineral reference values correspond to tabulated maximum birefringence, not every possible grain orientation.

Colour representation criterion

The colour representation adopts the CIE 1931 2° observer, D65 illuminant and sRGB colour space, with T(λ,Γ) = sin²(πΓ/λ). Colours are obtained by interpolating a table calculated in linear RGB.

The sRGB values provide a reproducible reference and may differ from observations made with a particular microscope lamp, camera, eyepiece or calibration.

High orders

Above about 1500 nm colours become paler, narrower and more ambiguous. The numeric order remains defined, but estimating Γ from a colour name alone becomes unreliable.

References

Sørensen, B. E. (2013). A revised Michel-Lévy interference colour chart. European Journal of Mineralogy, 25, 5–10. DOI: 10.1127/0935-1221/2013/0025-2252.
Raith, M. M., Raase, P. & Reinhardt, J. (2012). Guide to Thin Section Microscopy. Mineralogical Society of America.
Nesse, W. D. (2012). Introduction to Optical Mineralogy, 4th ed. Oxford University Press.
CIE datasets: CIE 1931 2° (10.25039/CIE.DS.xvudnb9b) and D65 (10.25039/CIE.DS.hjfjmt59).

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Michel-Lévy birefringence chart

Solve for

Results

Michel-Lévy chart

Fundamentals & Explanation

What the colour represents

Three ways to use it

Example: quartz in a 30 µm section

What it cannot establish

Before comparing colours

Colour representation criterion

High orders

References

What the colour represents

Three ways to use it

Example: quartz in a 30 µm section

What it cannot establish

Before comparing colours

Colour representation criterion

High orders

References