Interference Colors

Interference colors are the colors visible when an anisotropic mineral is placed between crossed polarizers. They arise because retardation between the slow and fast rays selectively cancels some wavelengths of white light while transmitting others, and the eye perceives the surviving combination of wavelengths as a specific color. Interference colors are one of the most diagnostic and widely used properties in optical mineralogy.

Monochromatic Interference

It is simplest to first consider what happens with a single wavelength of light (monochromatic illumination). When the slow ray lags the fast ray by exactly an integer number of wavelengths (Δ = iλ), the two wave components resolved into the upper polarizer’s vibration direction are equal in magnitude but opposite in direction - they cancel completely, and no light passes. The mineral grain appears dark. When the retardation equals i + ½ wavelengths (Δ = (i + ½)λ), the resolved components point in the same direction and constructively interfere, producing maximum brightness. ^[1]

Note that this behavior - in-phase cancels, out-of-phase constructively interferes - appears counterintuitive compared to ordinary wave interference. The reversal occurs because the two rays vibrate at right angles to each other after passing through the mineral. When they are resolved into the single vibration direction of the upper polarizer, the geometry of that resolution inverts the usual relationship.

Polychromatic Illumination and the Michel-Lévy Chart

With white light, all wavelengths are present simultaneously. Each wavelength is split into slow and fast rays. For a given mineral thickness, the retardation is approximately the same for all wavelengths. At that retardation, some wavelengths arrive at the upper polarizer in phase (and are canceled) while others arrive out of phase (and are transmitted). The combination of transmitted wavelengths produces what is perceived as an interference color. ^[1]

The quartz wedge - a wedge-shaped piece of quartz mounted in an accessory holder - is placed between crossed polarizers to display the complete sequence of interference colors. At the thin edge, retardation is zero and all wavelengths cancel; the color is black. As thickness increases, the sequence progresses: gray, white, yellow, red, then a repeating cycle of blue, green, yellow, red, each repetition becoming progressively paler. This sequence, displayed as a chart, is the Michel-Lévy chart. ^[1]

Interference Orders

The sequence of interference colors is divided into orders, with each order spanning 550 nm of retardation. First- and second-order colors are the most vivid and saturated. Higher-order colors become progressively more washed out. Above the fourth order, all interference colors degenerate into a pale, creamy white that is nearly indistinguishable between orders. ^[1]

The chart displays retardations from 0 to 1800 nm along its bottom edge.

Quantitative Examples: Quartz at Three Thicknesses

Quartz has a maximum birefringence of 0.009. Three worked examples illustrate how retardation controls perceived color: ^[1]

• Thickness 0.0278 mm → retardation ~250 nm: Over 80% of every wavelength is transmitted, producing a first-order white color with a yellow tinge, because small amounts of the violet and red ends of the spectrum are canceled. ^[1]
• Thickness 0.056 mm → retardation ~500 nm: The 500 nm wavelength (green) is entirely canceled, along with most blue and green light, leaving a color perceived as red with a purplish cast (first-order red). ^[1]
• Thickness 0.278 mm → retardation ~2500 nm: Wavelengths at 417, 500, and 625 nm are canceled; wavelengths near 455, 555, and 714 nm pass with maximum intensity. The result is a creamy white - an upper-order color where contributions from all parts of the spectrum are roughly balanced. ^[1]

Using the Michel-Lévy Chart

The primary purpose of the chart is to read retardation from an observed interference color. Find the color on the chart, then read the retardation value from the bottom edge. A mineral displaying second-order green, for example, has a retardation of about 700 nm between its slow and fast rays. ^[1]

To distinguish which order a color belongs to when similar colors occur in multiple orders, examine the thin edge of the grain: because grain thickness goes to zero at the edge, so does retardation. Counting interference colors from the edge inward locates the order. The boundary between orders is marked by a distinctive dark band where the red and blue colors of adjacent orders overlap. ^[1]

Determining Thin-Section Thickness

If a mineral of known maximum birefringence is present, its interference color in thin section can be used to calculate section thickness via Δ = d · δ rearranged as d = Δ / δ. Quartz is ideal for this because its maximum birefringence is a consistent 0.009. The procedure is: find the quartz grains showing the highest interference color (farthest right on the chart - these are the grains cut perpendicular to the c axis, which display true maximum birefringence); read the retardation from the chart; divide by 0.009 to get thickness. A first-order white with a hint of yellow color corresponds to a retardation of 270 nm, giving d = 270 / 0.009 = 30,000 nm = 0.03 mm, which is the standard thin-section thickness. ^[1]

Anomalous Interference Colors

Some minerals display interference colors that do not appear on the standard chart. These anomalous interference colors arise when the dispersion of refractive indices differs substantially between the slow and fast rays. The result is that different wavelengths experience different amounts of retardation, so the complement of wavelengths reaching the eye is unusual, and the eye perceives a color that does not fit the standard sequence. Mineral color can also shift interference colors - a mineral with a strong green body color will lend a green cast to its interference colors. ^[1]

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