The interference colour is not a property of the mineral. It is the retardation — how far the slow ray has fallen behind the fast one — and that is birefringence multiplied by thickness. Read the colour, know the thickness, and the birefringence follows. Get the thickness wrong and every mineral in the slide is misidentified together.
A standard section is 30 µm, and the way to know yours is quartz: at 30 µm quartz shows first-order white to pale yellow, retardation about 0.009 × 30 = 270 nm. If the quartz in your slide is grey, the section is thin; if it reaches first-order red, it is thick. Every other birefringence in the slide scales with that error.
This is computed, not a photograph of somebody's chart: white light through crossed polars, each wavelength extinguished where the retardation is a whole number of its own wavelengths, the survivors added back together. The orders repeat and wash out — beyond the third the colours become the pale pinks and greens everybody stops trying to name, which is why high-birefringence minerals are recognised by their washed-out look rather than a colour.
Between crossed polars a grain goes black four times in a full turn, whenever a vibration direction lines up with a polariser. The angle between extinction and a crystal direction — a cleavage, a twin plane, a face — is diagnostic, and for the plagioclases it is the composition.
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Straight or inclined is a property of the crystal system and the section, so it is only diagnostic when the grain is in a known orientation — an elongate section parallel to the length, most usefully.
A grain stands out because its refractive index differs from what surrounds it. In a standard slide that is the mounting medium, near 1.54 — which is why quartz almost disappears in it and garnet looks like it has been drawn in ink.
Which side the index falls is settled by the Becke line: rack the focus up and the bright line moves into the material of higher index. It costs two seconds and settles what relief alone cannot.
Conoscopic light — the condenser in, a high power lens, the Bertrand lens or the pinhole — turns the field into a picture of directions rather than of the grain. It answers the two questions a plane-polarised view cannot: how many optic axes, and is the mineral positive or negative.
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The sign comes from the accessory plate: insert the gypsum plate into an off-centre figure and watch the quadrants. Blue where the slow direction of the plate lies along the slow direction of the mineral, yellow where they oppose — and in a uniaxial figure blue in the north-east quadrant means positive.
Counting what the slide is made of, with real confidence limits, is in the Lab companion — its point counter takes a photomicrograph and a grid and gives the modal composition with the error that a count of that size actually carries.