Mineralogy

Geology (B.Sc) · Earth materials · free study notes for exams, placements and interviews

In short

Mineralogy is the study of naturally occurring, inorganic, crystalline solids with a definite chemical composition and ordered atomic structure — their crystallography, physical and optical properties, chemistry, structural classification, occurrence and uses. It is the foundation subject of a B.Sc Geology degree because every rock, ore body, soil and industrial raw material is described in terms of its constituent minerals. It is examined in university practicals (hand-specimen and thin-section identification), in GATE Geology (Section: Mineralogy and Crystallography), UPSC Geologist/Geo-Scientist (GSI, CGWB), and in the entry tests of the Geological Survey of India, Mineral Exploration and Consultancy Ltd (MECL), ONGC, Coal India, Hindustan Zinc, Vedanta, Tata Steel, JSW, UltraTech and cement/refractory companies. On the job it drives ore microscopy, mineral beneficiation decisions, XRD/XRF quality control and resource classification under the UNFC system used by the Indian Bureau of Mines.

Explained

What a mineral is, and how it is defined

Mineral: naturally occurring, normally inorganic, solid, with a definite (or definite range of) chemical composition and an ordered internal atomic arrangement (crystal structure).
Exceptions that are examined: mercury and water (ice) — liquid/solid state issues; opal and volcanic glass — amorphous, so called *mineraloids*; coal, amber, pearl — organic, excluded.
Mineraloid: mineral-like but lacking crystallinity (opal, limonite as a field term).
Rock: an aggregate of one or more minerals. Ore mineral: a mineral from which a metal can be extracted at a profit. Gangue: valueless associated minerals.
Rock-forming minerals (about 30 common ones) make up nearly all crustal rocks; feldspars alone are ~50-60% of the crust, silicates as a group over 90%.

Crystallography: lattices, symmetry and indices

Crystal: a solid bounded by flat faces (*euhedral* if fully developed, *subhedral* partly, *anhedral* none) reflecting internal lattice order.
Space lattice: a 3-D periodic array of points. Unit cell: smallest repeating parallelepiped, defined by a, b, c and α, β, γ. The 14 Bravais lattices arise from 7 systems × lattice centring (P, I, F, C).
Steno's Law (Law of Constancy of Interfacial Angles): for a given mineral the angle between corresponding faces is constant irrespective of crystal size or distortion — measured with a contact or reflecting goniometer.
Law of Rational Indices (Haüy): faces intercept crystallographic axes at simple rational multiples of unit lengths.
Symmetry elements: plane of symmetry (m), axis of symmetry (2-, 3-, 4-, 6-fold; 5-fold and >6-fold are impossible in lattices), centre of symmetry (i), plus roto-inversion axes. Combinations give 32 crystal classes (point groups) and, with translations (screw axes, glide planes), 230 space groups.
Seven crystal systems with their normal-class symmetry:
1. Cubic (isometric): a=b=c, all 90°; highest symmetry 3A⁴, 4A³, 6A², 9P, C — e.g. galena, halite, garnet, pyrite, diamond, magnetite.
2. Tetragonal: a=b≠c, all 90° — zircon, rutile, cassiterite, chalcopyrite.
3. Hexagonal: a=b≠c, γ=120° — beryl, apatite, graphite.
4. Trigonal (rhombohedral, often taken as a division of hexagonal): calcite, quartz, corundum, tourmaline, hematite.
5. Orthorhombic: a≠b≠c, all 90° — barite, olivine, staurolite, topaz, aragonite.
6. Monoclinic: a≠b≠c, α=γ=90°, β≠90° — gypsum, orthoclase, augite, hornblende, micas.
7. Triclinic: all axes and angles unequal — plagioclase, microcline, kyanite.
Miller indices (hkl): reciprocals of fractional axial intercepts, cleared of fractions. A face cutting a at 1, b at 2, c at ∞ → reciprocals 1, ½, 0 → ×2 → (210). Bar over an index means a negative intercept. {hkl} = a form (all symmetry-equivalent faces); [uvw] = a zone/direction.
Forms: closed forms enclose space (cube, octahedron, dodecahedron, dipyramid); open forms do not (prism, pyramid, pinacoid, dome, pedion). Number of faces: cube 6, octahedron 8, rhombic dodecahedron 12, tetrahexahedron 24, hexoctahedron 48 (the holosymmetric cubic form).
Twinning: two or more crystals of the same species joined in a rational, symmetry-related orientation. Types — *contact* (simple, e.g. spinel), *penetration* (e.g. staurolite cross, fluorite), *polysynthetic/multiple lamellar* (albite twinning in plagioclase), *cyclic* (rutile, chrysoberyl). Named laws: Carlsbad, Baveno, Manebach (orthoclase), Albite and Pericline (plagioclase, giving "tartan twinning" in microcline), Dauphiné and Brazil (quartz).
Crystal habit: external shape — tabular, prismatic, acicular, bladed, fibrous, micaceous/foliated, botryoidal, reniform, dendritic, radiating, granular, massive, colloform.

Physical properties and how they are tested

Colour: diagnostic in idiochromatic minerals (malachite green, magnetite black); unreliable in allochromatic ones (quartz, fluorite, beryl, tourmaline).
Streak: colour of the powder on an unglazed porcelain plate — hematite gives red-brown streak even when steel-grey; more reliable than colour.
Lustre: metallic, sub-metallic, and non-metallic types — vitreous (quartz), resinous (sphalerite), pearly (talc), silky (asbestos), adamantine (diamond), earthy/dull (kaolinite).
Hardness — Mohs scale (relative, 1-10): talc 1, gypsum 2, calcite 3, fluorite 4, apatite 5, orthoclase 6, quartz 7, topaz 8, corundum 9, diamond 10. Field aids: fingernail ≈2.5, copper coin ≈3.5, knife/glass ≈5.5, steel file ≈6.5. The scale is ordinal, not linear — diamond is many times harder than corundum in absolute (Vickers/Knoop) terms.
Cleavage: breakage along planes of weak bonding — cubic (galena, halite), octahedral (fluorite, diamond), rhombohedral (calcite), basal/perfect in one direction (mica, graphite), prismatic two directions at ~87°/93° (pyroxene) and ~56°/124° (amphibole — the single most-tested contrast). Parting is along twin or deformation planes; fracture is irregular — even, uneven, hackly (native copper), conchoidal (quartz, glass), splintery.
Specific gravity: quartz 2.65, calcite 2.71, feldspars 2.55-2.76, micas ~2.8-3.0, olivine 3.2-4.4, barite 4.5, pyrite 5.0, galena 7.5, gold 15-19.3. Measured by Walker's steelyard balance, pycnometer, or heavy liquids (bromoform SG 2.89, methylene iodide 3.32) used for mineral separation.
Other properties: tenacity (brittle, malleable, sectile — gypsum; flexible — talc; elastic — mica), magnetism (magnetite strongly, pyrrhotite weakly), double refraction visible in Iceland spar calcite, fluorescence (fluorite, scheelite), effervescence with cold dilute HCl (calcite, and only on powder for dolomite), taste (halite), play of colours (labradorite), chatoyancy, asterism, piezoelectricity and pyroelectricity (quartz, tourmaline), radioactivity (uraninite, monazite).

Chemical mineralogy and classification

Isomorphism: minerals of similar structure with mutually substituting ions, forming solid solution series — olivine (Mg₂SiO₄ forsterite–Fe₂SiO₄ fayalite), plagioclase (NaAlSi₃O₈ albite–CaAl₂Si₂O₈ anorthite, a coupled substitution NaSi ⇌ CaAl).
Polymorphism: one composition, several structures — SiO₂ (quartz, tridymite, cristobalite, coesite, stishovite), CaCO₃ (calcite–aragonite), C (graphite–diamond), Al₂SiO₅ (kyanite–andalusite–sillimanite, the classic metamorphic triple point). Pseudomorphism: a mineral retaining the form of another (limonite after pyrite).
Goldschmidt's rules of substitution: ions substitute freely if radii differ by <15% and charge is the same or balanced by coupled substitution; higher-charge/smaller ions are preferentially captured.
Dana/Berzelian chemical classification (the exam-standard order): native elements; sulphides (and sulphosalts); oxides and hydroxides; halides; carbonates; nitrates and borates; sulphates; phosphates (and arsenates, vanadates); tungstates/molybdates; silicates.
Silicate structures — built on the SiO₄⁴⁻ tetrahedron, classified by the degree of polymerisation (Si:O ratio): | Class | Linkage | Si:O | Example | |---|---|---|---| | Nesosilicate (ortho) | Isolated tetrahedra | 1:4 | Olivine, garnet, zircon, topaz | | Sorosilicate | Paired, one shared O | 2:7 | Epidote, hemimorphite | | Cyclosilicate (ring) | 3-, 4-, 6-membered rings | 1:3 | Beryl, tourmaline, cordierite | | Inosilicate (single chain) | Two O shared | 1:3 | Pyroxenes (augite, diopside, enstatite) | | Inosilicate (double chain) | 2-3 O shared | 4:11 | Amphiboles (hornblende, tremolite) | | Phyllosilicate (sheet) | Three O shared | 2:5 | Micas, chlorite, talc, clays, serpentine | | Tectosilicate (framework) | All four shared | 1:2 | Quartz, feldspars, feldspathoids, zeolites |
Structural control on properties: isolated tetrahedra → high SG, no good cleavage (olivine); chains → two prismatic cleavages; sheets → one perfect basal cleavage, low hardness; frameworks → hard, low SG, no cleavage.
Bowen's reaction series (order of crystallisation from magma): discontinuous (mafic) branch olivine → pyroxene → amphibole → biotite; continuous (felsic) branch Ca-plagioclase → Na-plagioclase; converging to K-feldspar → muscovite → quartz. Early-formed minerals are least stable at the surface, so quartz dominates sands (Goldich weathering series is the reverse order).

Optical mineralogy and instrumental identification

Polarising (petrological) microscope: light source, polariser (lower nicol), rotating stage, objectives, Bertrand lens, analyser (upper nicol), accessory slot for the gypsum (1λ), mica (¼λ) and quartz wedge plates. Thin sections are ground to a standard 30 µm (0.03 mm) thickness, because interference colours are calibrated to it.
Plane-polarised light (analyser out): observe colour, pleochroism (change of colour on rotating the stage — biotite, hornblende, tourmaline), relief and refractive index by the Becke line method (the line moves towards the higher-RI medium on raising the tube), cleavage, form, and isotropism.
Crossed polars (analyser in): isotropic minerals (cubic and glass) stay dark in all positions; anisotropic minerals show four extinction positions per 360° rotation.
- Birefringence δ = n_max − n_min; interference colour depends on δ × thickness, read off the Michel-Lévy chart. Quartz δ≈0.009 (first-order grey-white), calcite δ≈0.172 (extreme, pale high-order).
- Extinction: straight/parallel (orthopyroxene, apatite), symmetrical (calcite), inclined at a measurable angle (augite ~36-45°, hornblende ~12-34°), and mica-like "bird's-eye" mottling.
- Twinning is seen under crossed polars: albite lamellae in plagioclase, tartan in microcline, simple Carlsbad in orthoclase.
Conoscopic (convergent) light with Bertrand lens: interference figures distinguish uniaxial (tetragonal, hexagonal, trigonal — one optic axis; a cross that stays unbroken on rotation) from biaxial (orthorhombic, monoclinic, triclinic — two optic axes; a cross that splits into hyperbolae). Sign (+/−) from accessory plate behaviour; 2V is the optic axial angle.
Indicatrix: sphere for isotropic; prolate (uniaxial +) or oblate (uniaxial −) ellipsoid of revolution; triaxial ellipsoid with nα<nβ<nγ for biaxial.
Modern analytical methods: XRD for crystal structure and phase identification (Bragg's law), XRF/ICP for chemistry, EPMA/SEM-EDS for mineral chemistry at the micron scale, DTA/TGA for clays, Mössbauer and Raman for Fe-site and structural work. GSI, IBM, AMD and NGRI laboratories plus NABL-accredited private labs (ISO/IEC 17025) do this routinely; IBM Mineral Processing Laboratories report mineralogy for mining plan approvals under the Mineral Conservation and Development Rules, 2017.

Economic and systematic mineralogy in the Indian setting

Metallic ore minerals: haematite Fe₂O₃ and magnetite Fe₃O₄ (Odisha, Jharkhand, Chhattisgarh, Karnataka); bauxite (gibbsite/boehmite — Odisha, Gujarat, Jharkhand); chromite FeCr₂O₄ (Sukinda, Odisha — most of India's output); galena PbS + sphalerite ZnS (Rampura Agucha and Zawar, Rajasthan — Hindustan Zinc); chalcopyrite CuFeS₂ (Malanjkhand MP, Khetri Rajasthan, Singhbhum Jharkhand); pyrolusite MnO₂/psilomelane (Balaghat, Keonjhar); ilmenite, rutile, monazite, zircon and garnet in the beach placers of Kerala, Tamil Nadu and Odisha (IREL); cassiterite SnO₂ (Bastar); gold in native form (Kolar, Hutti — Karnataka); uraninite/pitchblende (Jaduguda, Tummalapalle).
Industrial minerals: limestone (calcite) for cement, mica (Koderma, Nellore), barite (Mangampet, Andhra Pradesh — among the world's largest deposits), gypsum, kaolinite, quartz and feldspar for ceramics and glass, wollastonite, magnesite (Salem), dolomite, graphite (Odisha), sillimanite/kyanite refractories, apatite/rock phosphate (Jhamarkotra), diamond (Panna, MP).
Regulatory and classification practice: mineral resources are reported in India under the United Nations Framework Classification (UNFC) per the Minerals (Evidence of Mineral Contents) Rules, 2015 and IBM guidelines, with much private reporting also following the JORC-style codes; the governing statute is the Mines and Minerals (Development and Regulation) Act, 1957, as amended (notably 2015 for auction-based allocation, 2021, and 2023 which opened deep-seated and critical minerals including lithium to private exploration). Atomic minerals (uranium, thorium-bearing monazite, beryl) are controlled under the SHANTI Act, 2025 (in force from December 2025, which repealed the Atomic Energy Act, 1962) and handled by AMD/IREL. Mine safety is now administered under the Occupational Safety, Health and Working Conditions Code, 2020 — one of the four Labour Codes in force from 21 November 2025 — which repealed the Mines Act, 1952; DGMS enforces it, with the Coal Mines Regulations, 2017 and Metalliferous Mines Regulations, 1961 continuing under the Code's savings clause (s.143(3)). Exact threshold values in these rules are revised periodically — confirm against the current IBM/Ministry of Mines notification.

Key points

Mineral - naturally occurring, inorganic, solid, definite composition, ordered atomic structure; rocks are mineral aggregates.
Steno's Law - interfacial angles of a given mineral species are constant regardless of crystal size or habit.
32 crystal classes, 230 space groups, 14 Bravais lattices, 7 crystal systems - the full symmetry hierarchy.
Miller indices - reciprocals of axial intercepts cleared of fractions; (hkl) a face, {hkl} a form, [uvw] a direction.
Cubic system has the maximum symmetry (9 planes, 13 axes, a centre in the holosymmetric class); 5-fold rotation axes are impossible in crystals.
Streak beats colour - hematite is grey to black but always streaks red-brown.
Mohs scale is ordinal - the gap between 9 and 10 is far larger than between 1 and 2.
Pyroxene vs amphibole cleavage - ~87°/93° versus ~56°/124°; the single most reliable thin-section discriminator.
Silicate classification follows polymerisation - neso 1:4, soro 2:7, cyclo 1:3, single-chain ino 1:3, double-chain ino 4:11, phyllo 2:5, tecto 1:2.
Isomorphism - same structure, substituting ions (olivine, plagioclase); polymorphism - same composition, different structures (quartz polymorphs, Al₂SiO₅ trio).
Goldschmidt's rule - substitution is easy when ionic radii differ by less than about 15% with charge balance maintained.
Bowen's reaction series - olivine first, quartz last; weathering stability is the reverse (Goldich).
Thin sections are 30 µm - interference colours on the Michel-Lévy chart assume this thickness.
Isotropic minerals (cubic, glass) remain dark under crossed polars; anisotropic minerals extinguish four times in a full stage rotation.
Uniaxial vs biaxial - trigonal/tetragonal/hexagonal are uniaxial; orthorhombic/monoclinic/triclinic are biaxial, characterised by 2V.
Birefringence δ = n_max − n_min - quartz ~0.009 (low), calcite ~0.172 (extreme).
Twin laws to name - Carlsbad/Baveno/Manebach (orthoclase), Albite/Pericline (plagioclase, tartan in microcline), Dauphiné/Brazil (quartz).
Indian resource reporting uses UNFC under MMDR Act, 1957 (as amended 2015/2021/2023), administered through IBM.

Formulas and examples

Miller indices: (h k l) = reciprocals of intercepts (p, q, r) in axial units, multiplied by their LCM to clear fractions. Intercept ∞ → index 0.
Bragg's Law (XRD): nλ = 2d sinθ — n = order of reflection (integer), λ = X-ray wavelength (Å; Cu-Kα = 1.5418 Å), d = interplanar spacing (Å), θ = half the diffraction angle 2θ (degrees).
Cubic d-spacing: d(hkl) = a / √(h² + k² + l²) — a = unit cell edge (Å).
Specific gravity: G = W_air / (W_air − W_water) — weights in the same unit (g); dimensionless.
Walker's steelyard: G = (a × W) / (b × (W − W₁)) form varies; more simply G = W/(W − W₁) with W₁ the apparent weight in water.
Birefringence: δ = n_ε − n_ω (uniaxial) or n_γ − n_α (biaxial); retardation Δ = t × δ, with t in nm (30,000 nm for a standard section) and Δ in nm giving the interference colour.
Density from cell content: ρ = (Z × M) / (N_A × V) — Z = formula units per unit cell, M = formula mass (g/mol), N_A = 6.022 × 10²³ /mol, V = unit cell volume (cm³).
Snell's law / RI: n = sin i / sin r = c/v; relief in thin section is judged against Canada balsam, n ≈ 1.537.
Molecular (weight) percentage of a metal: % metal = (atomic mass × number of atoms / formula mass) × 100.

Example 1 — Miller indices. A crystal face intercepts the a-axis at 2 units, the b-axis at 3 units and is parallel to the c-axis.

Reciprocals: 1/2, 1/3, 1/∞ = 0.
LCM of denominators 2 and 3 = 6 → 6 × (1/2, 1/3, 0) = 3, 2, 0.
Indices = (320), an open prism-type face parallel to c.

Example 2 — Metal content of an ore mineral. Calculate the Fe grade of pure haematite, Fe₂O₃ (Fe = 55.85, O = 16.00).

Formula mass = 2 × 55.85 + 3 × 16.00 = 111.70 + 48.00 = 159.70.
% Fe = 111.70 / 159.70 × 100 = 69.94% — the theoretical maximum, which is why Indian "high-grade" haematite ore at 62-65% Fe is reported as having ~90% of the mineral plus silica-alumina gangue.
For magnetite Fe₃O₄: formula mass = 3 × 55.85 + 4 × 16.00 = 167.55 + 64.00 = 231.55; % Fe = 167.55/231.55 × 100 = 72.36%.

Example 3 — Bragg's law and cubic cell edge. A halite powder sample gives a first-order (n = 1) reflection from the (200) planes at 2θ = 31.70° with Cu-Kα radiation (λ = 1.5418 Å).

θ = 15.85°; sin θ = 0.2732.
d = nλ / (2 sin θ) = 1.5418 / (2 × 0.2732) = 1.5418 / 0.5464 = 2.821 Å.
For (200) in a cubic cell, √(h²+k²+l²) = √4 = 2, so a = d × 2 = 5.642 Å — the accepted cell edge of halite (~5.64 Å).

Example 4 — Specific gravity and density check. A galena specimen weighs 48.6 g in air and 42.1 g suspended in water.

G = 48.6 / (48.6 − 42.1) = 48.6 / 6.5 = 7.48 — consistent with galena (7.4-7.6), and enough to separate it from sphalerite (3.9-4.1) in heavy-liquid or gravity concentration.
Cross-check from structure: galena is cubic, PbS, Z = 4, M = 207.2 + 32.06 = 239.26 g/mol, a = 5.936 Å → V = (5.936 × 10⁻⁸)³ = 2.0916 × 10⁻²² cm³.
ρ = (4 × 239.26) / (6.022 × 10²³ × 2.0916 × 10⁻²²) = 957.04 / 125.96 = 7.60 g/cm³ — matches the measured value within experimental error.

Example 5 — Retardation and interference colour. A mineral grain in a standard 30 µm thin section shows a maximum birefringence of 0.021.

Δ = t × δ = 30,000 nm × 0.021 = 630 nm.
On the Michel-Lévy chart the first order ends at about 550 nm, so 630 nm falls just inside the second order — the blue to blue-green range typical of augite.
If the section were left too thick at 45 µm, Δ = 45,000 × 0.021 = 945 nm (upper second-order orange-red), which is how a badly prepared section leads to misidentification.

Property	Pyroxene (augite)	Amphibole (hornblende)	Mica (biotite)
Structure	Single chain	Double chain	Sheet
Cleavage	2 at ~87°/93°	2 at ~56°/124°	1 perfect basal
Cross-section	Nearly square/octagonal	Diamond/lozenge	Flakes, elongate laths
Extinction angle	~36-45°	~12-34°	~0-3°, bird's-eye mottling
Colour in PPL	Pale green-brown, weak pleochroism	Green-brown, strong pleochroism	Brown, very strong pleochroism
Habit	Stubby prisms	Elongate prisms, needles	Micaceous, elastic

System	Axes and angles	Uniaxial/Biaxial	Typical minerals
Cubic	a=b=c; 90°	Isotropic	Galena, garnet, halite, fluorite
Tetragonal	a=b≠c; 90°	Uniaxial	Zircon, rutile, cassiterite
Hexagonal/Trigonal	a=b≠c; γ=120°	Uniaxial	Quartz, calcite, beryl, corundum
Orthorhombic	a≠b≠c; 90°	Biaxial	Olivine, barite, topaz
Monoclinic	β≠90°	Biaxial	Gypsum, orthoclase, augite, hornblende
Triclinic	all unequal	Biaxial	Plagioclase, microcline, kyanite

Where it is used

Mineral exploration and resource estimation: GSI, MECL, AMD, state DGMs and private explorers log core, identify ore and alteration minerals, and classify resources under UNFC for mining plans approved by IBM.
Mining and beneficiation: liberation size, grindability and recovery depend on mineralogy — chromite gravity concentration at Sukinda, lead-zinc flotation at Rampura Agucha, iron-ore washing in Odisha-Jharkhand, heavy-mineral beach-sand separation by IREL in Kerala and Tamil Nadu.
Cement, refractory, ceramic and glass industries: UltraTech, ACC-Ambuja, Dalmia and Shree Cement run XRD/XRF on limestone and clinker phases (alite, belite, aluminate, ferrite); refractory grades depend on sillimanite, kyanite and magnesite mineralogy.
Petroleum and groundwater geology: clay mineralogy (smectite swelling, illite, kaolinite) controls reservoir quality and drilling-mud behaviour at ONGC and OIL; mineral dissolution controls fluoride and arsenic in CGWB groundwater studies.
Civil and construction materials: alkali-silica reactivity of strained quartz and chert in concrete aggregate, and petrographic examination of aggregates and dimension stone (granite and marble exports from Rajasthan and Andhra Pradesh).
Gemmology, museums and academia: gem identification and certification (GJEPC-linked labs, Jaipur and Surat), plus teaching and research posts at GSI training institutes, IITs, IISc and central universities.

Interview questions

Q: What are the five essential requirements for a substance to be called a mineral? A: It must be naturally occurring, normally inorganic, solid, of definite or restricted chemical composition, and have an ordered internal atomic structure.
Q: Why is opal not a true mineral? A: It is amorphous — it lacks a periodic crystal structure — so it is classed as a mineraloid even though it is natural, solid and inorganic.
Q: How do you distinguish pyroxene from amphibole in a thin section? A: By cleavage angles — pyroxene shows two cleavages at about 87°/93° and a squarish cross-section, amphibole about 56°/124° with a diamond-shaped section; amphibole is also more strongly pleochroic with a lower extinction angle.
Q: Why can a crystal not have a five-fold axis of symmetry? A: Five-fold units cannot be repeated by lattice translation to fill space without gaps; only 1-, 2-, 3-, 4- and 6-fold axes are compatible with a periodic lattice.
Q: State and explain the Law of Constancy of Interfacial Angles. A: Steno's Law — for a given mineral species the angle between two corresponding faces is constant whatever the crystal's size or distortion, because it is fixed by the internal lattice geometry.
Q: What is the difference between isomorphism and polymorphism? A: Isomorphism is the same structure with substituting ions giving a composition range (plagioclase); polymorphism is the same composition crystallising in different structures (calcite and aragonite).
Q: Why are thin sections ground to exactly 30 micrometres? A: Interference colour depends on the product of birefringence and thickness, and the Michel-Lévy chart used for identification is calibrated for 30 µm; a thicker or thinner section shifts colours and causes wrong identification.
Q: How would you tell quartz from calcite under crossed polars? A: Calcite shows extreme birefringence (δ ≈ 0.172) with pale high-order "twinkling" colours and rhombohedral cleavage; quartz shows low first-order grey-white colours (δ ≈ 0.009), no cleavage and is uniaxial positive.
Q: Which mineral property is more diagnostic — colour or streak, and why? A: Streak, because colour in allochromatic minerals changes with trace impurities and defects, while the powder colour is reproducible, as with hematite's red-brown streak.
Q: How are Miller indices derived for a face cutting a at 1, b at ∞ and c at 1/2? A: Reciprocals are 1, 0, 2, already whole numbers, so the face is (102).
Q: What does Bowen's reaction series tell a geologist about weathering? A: The order is essentially reversed as stability at the surface — olivine and Ca-plagioclase, which crystallise first, weather fastest, while quartz, which crystallises last, survives to dominate sands (the Goldich series).
Q: How is mineralogy used in deciding a beneficiation route? A: Modal mineralogy, grain size and the nature of locking between ore and gangue determine the grind size and whether gravity, magnetic, flotation or leaching recovery is viable — determined by ore microscopy, XRD and EPMA before plant design.
Q: Under which framework are Indian mineral resources reported, and under which Act? A: Under the UNFC, with reporting requirements set out in the rules made under the MMDR Act, 1957 (as amended) and administered through the Indian Bureau of Mines.

Common mistakes

Treating the Mohs scale as linear or quantitative, and quoting it as an absolute hardness value.
Writing Miller indices as intercepts rather than their reciprocals, or failing to clear fractions to the smallest whole numbers.
Confusing cleavage with fracture and with parting, and reporting "one cleavage" for a mineral whose single trace is just the plane of view.
Mixing up the pyroxene and amphibole cleavage angles, or quoting extinction angles without saying they are measured on a specific crystallographic section.
Calling trigonal minerals biaxial — all trigonal, tetragonal and hexagonal minerals are uniaxial; only orthorhombic, monoclinic and triclinic are biaxial.
Reading interference colours without checking section thickness, or using the maximum colour from a randomly oriented grain instead of the grain showing maximum birefringence.
Reporting an ore's metal grade as the mineral's theoretical metal percentage, ignoring gangue and moisture.
Identifying minerals by colour alone (quartz, fluorite, tourmaline and beryl occur in almost every colour), and skipping the streak, hardness and SG checks.