Refractometry

Refractometry is the measurement of indices of refraction. In mineralogy the term refers almost exclusively to the determination of a mineral’s refractive index using the immersion method: a grain mount of the unknown mineral is prepared using oils of known refractive index, and the oil whose index matches the mineral is identified. Two techniques - assessing relief and applying the Becke line method - together allow the petrographer to bracket and then pinpoint the mineral’s index of refraction. Accuracy of about ±0.003 is achievable with white light illumination. ^[1]

The Immersion Method

Commercially available immersion oil sets cover the range of indices found in most common minerals, typically from about 1.4 to 1.8, in increments of 0.002, 0.004, or 0.005. A small number of mineral grains is placed in a drop of oil on a glass slide, covered with a coverslip, and examined under the microscope. If the mineral’s index of refraction does not match the oil, light is refracted at the oil-mineral boundary and the grains appear to stand out from the background. This is called relief. If the indices match exactly, no refraction occurs at the boundary and the grains effectively disappear. By systematically changing the oil until the grains show minimal relief, the mineral’s index is bracketed and then matched. ^[1]

Relief

Relief is the degree to which mineral grains visually stand out from the immersion oil (or epoxy/glass in thin section). When the mineral and oil have different refractive indices, light is refracted at every grain boundary, creating visible edges and apparent depth differences. Three grades are used:

• High relief: the difference in index of refraction between mineral and oil is > 0.12. ^[1]
• Moderate relief: difference is between 0.04 and 0.12. ^[1]
• Low relief: difference is < 0.04. ^[1]

Relief is described as positive when the mineral index is higher than the oil, and negative when it is lower. However, in both cases the mineral will stand out to the same degree if the absolute difference is equal - both positive and negative relief make the grain visible; only the Becke line tells the direction. Anisotropic minerals add a complication: because the slow and fast rays have different indices, the relief of an anisotropic mineral may visibly change as the stage is rotated in plane light, especially if the mineral has moderate to high birefringence. ^[1]

The Becke Line Method

The Becke line is a bright band or rim of light visible at the edge of a mineral grain in grain mount. It is the primary tool for determining whether the mineral’s index is higher or lower than the surrounding oil - that is, whether relief is positive or negative. The Becke line is most easily seen with the medium-power objective, with the image very slightly out of focus and the aperture diaphragm closed somewhat. The diagnostic rule: if the microscope stage is lowered (increasing the distance between sample and objective), the Becke line moves into the material with the higher index of refraction. If the stage is raised, the Becke line moves in the opposite direction. ^[1]

Lens Effect

The first mechanism that creates the Becke line is the lens effect. Most mineral grains in a grain mount are thinner at their edges than in the centre - a natural consequence of irregular fracture. This shape means each grain acts as a crude lens. If the mineral’s index is higher than the oil, the grain acts as a converging lens, focusing light toward the centre of the grain (and above it). If the mineral’s index is lower than the oil, the grain acts as a diverging lens, spreading light into the surrounding oil. In either case, the lens action concentrates light on one side of the grain boundary. ^[1]

Internal Reflection Effect

The second mechanism is the internal reflection effect. Even though most of a grain’s surface is oblique, every grain must have some vertical boundary edges. Moderately convergent light from below strikes these vertical boundaries and may be internally reflected or refracted, depending on the angle of incidence and the relative indices. The geometry of both refraction and internal reflection at these vertical walls concentrates light into a thin band in the material with the higher index of refraction. ^[1]

Both the lens effect and the internal reflection effect independently concentrate light on the same side of the boundary - the side with the higher index. Together they form a cone of light propagating upward from the edge of the grain. If the mineral has the higher index, this cone converges above the mineral; if the oil has the higher index, the cone diverges above the mineral. When the stage is crisply focused on the grain, the Becke line coincides with the grain edge or may vanish. As the stage is lowered, the plane of focus rises to where the cone’s concentration is greatest, making the Becke line appear to shift into the higher-RI material. Raising the stage moves the focus downward, reversing the apparent motion. ^[1]

Dispersion Effects on the Match

A complication in the immersion method arises because the dispersion of immersion oils - the variation of their refractive index with wavelength - is generally greater than the dispersion of most minerals. This means a perfect match of index between oil and mineral can only be achieved for one specific wavelength at a time. The target wavelength for a match is 589 nm (the sodium D line), because published refractive indices for minerals are conventionally reported for this wavelength. If the oil is changed so that the dispersion curves of the oil and mineral intersect in the visible spectrum, the oil will have a higher index than the mineral for wavelengths shorter than the match point, and the mineral will have a higher index for wavelengths longer than the match point. This produces two colored Becke lines - one on each side. ^[1]

When the dispersion curves cross within the visible range, the short-wavelength Becke line moves into the oil as the stage is lowered, while the long-wavelength Becke line moves into the mineral. The color of each Becke line depends on the wavelength at which the curves cross, and the patterns are systematic enough to indicate whether the mineral’s index is higher or lower than the oil’s, and by roughly how much. The relationships are summarized in the table below, which covers the full range from a clear mismatch in one direction to a clear mismatch in the other, with the match at 589 nm sitting in the middle. ^[1]

| Condition | Observation (stage lowered) | Interpretation | | --------------------------------------------------------------- | ------------------------------------------------------------ | -------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | n_oil higher for all wavelengths | White line into oil | n_D(oil) >> n_D(mineral) | ^[1] | | n_oil = n_mineral for orange/red light | Red line into mineral; bluish-white line into oil | n_D(oil) > n_D(mineral) | ^[1] | | n_oil = n_mineral for yellow light (589 nm) | Yellowish-orange line into mineral; pale blue line into oil | n_D(oil) = n_D(mineral) | ^[1] | | n_oil = n_mineral for blue light | Yellowish-white line into mineral; blue-violet line into oil | n_D(oil) < n_D(mineral) | ^[1] | | n_oil lower for all wavelengths | White line into mineral | n_D(oil) << n_D(mineral) | ^[1] |

Practical Procedure: The Bracketing Technique

Systematic bracketing is the recommended approach to determining an unknown mineral’s index of refraction in grain mount. Working randomly through available oils wastes time; working from both ends of the range simultaneously homes in on the match with the minimum number of mounts. With practice, a match can be obtained with as few as four or five grain mounts. ^[1]

The procedure begins by preparing a grain mount with an oil in the middle of the available range. Relief and the Becke line immediately tell whether the mineral’s index is higher or lower than that oil, which eliminates half the remaining range at once. Each subsequent mount uses an oil that splits the remaining range, progressively narrowing the bracket. If high relief persists after two mounts, it may be worth jumping to an oil at the extreme end of the range to confirm that the mineral’s index actually falls within the span of available oils. ^[1]

Refractometry in Thin Section

Precise index measurement is not practical in thin section because the mineral cannot be compared against a calibrated oil - the cement has a fixed index that may or may not match any particular mineral. However, useful estimates can be made. The cement used in most thin sections has an index of refraction of about 1.540, though the exact value depends on the manufacturer. Relief in thin section gives an approximate indication of how different a mineral’s index is from the cement, and Becke lines at mineral-cement or mineral-mineral boundaries can confirm which side is higher and which is lower. These observations do not yield precise numerical values, but they are often sufficient to narrow the possibilities considerably and confirm a tentative identification. ^[1]

Measuring Indices of Uniaxial Minerals

For a complete identification of a uniaxial mineral, both nω and nε must be measured. From these values the birefringence is calculated as δ = |nω − nε|. The key constraint is that each index can only be measured on a grain oriented so that all light passes exclusively as that ray type - a mixed grain that carries both ordinary and extraordinary rays simultaneously yields only an intermediate value n′ε, not the true nε. This is why grain orientation must be selected deliberately before making the comparison with the oil. ^[1]

Measuring nω: Select a grain whose optic axis is vertical - it will display the lowest-order interference color and stay uniformly dark as the stage rotates. A confirmation interference figure with the melatope near centre confirms the orientation. Alternatively, any grain can be used: at one of its extinction positions, the ordinary ray vibration direction lies parallel to the lower polarizer. Use an accessory plate to identify which ray direction is slow and which is fast, then rotate the appropriate direction (slow for negative minerals, fast for positive) parallel to the lower polarizer so that all light passes as ordinary ray. Once oriented, compare the grain with the oil using relief and the Becke line and change oils until a match is obtained. ^[1]

Measuring nε: Accurate measurement requires a grain with the optic axis horizontal. Scan between crossed polarizers for the grain displaying the highest interference colour - that grain has its optic axis approximately parallel to the stage. Confirm with a flash (optic normal) interference figure. The ε ray is the slow ray in optically positive minerals and the fast ray in optically negative minerals. From an extinction position, rotate the stage 45° clockwise, insert an accessory plate to identify slow and fast rays, then rotate back (clockwise or counterclockwise as needed) to place the ε ray direction parallel to the lower polarizer. The grain now passes only extraordinary rays, and nε can be compared with the oil and matched by the bracketing technique. ^[1]

Measuring Indices of Biaxial Minerals

Three indices - nα, nβ, and nγ - must be measured for biaxial minerals. Each requires a different grain orientation. Measuring nβ requires a grain with the optic axis vertical (lowest interference colour, confirmed by an optic axis interference figure). With the upper polarizer removed, the grain is compared against the oil using relief and the Becke line. Measuring nα and nγ both require a grain with the optic normal vertical (highest interference colour, optic normal flash figure). For nα, the fast ray vibration direction is rotated parallel to the lower polarizer so all light passes with index nα; for nγ, the slow ray vibration direction is used instead. ^[1]

Because nα and nγ both come from the same grain orientation (optic normal vertical), they can be measured on the same grain mount by rotating the vibration direction 90°. A useful efficiency: once nβ is known, knowledge of the birefringence and 2V gives a good estimate of how far nα and nγ lie from nβ, so oils for those measurements can be selected from the start without blindly bracketing from the full range. ^[1]

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