First in the Bowen's reaction series; Olivine is studied in depth at stage 2.
(This means it can be Mg+2or Fe+2 since both these ions have the same charge and relative atomic size. This is called a solid solution)
Olivine is a mafic mineral (it appears in mafic and ultramafic rocks) that's usually green in colour. In thin section it is either colourless or sepia in plain polarised light (PPL) and is birefringent in cross polars (XPL). Olivine has a high relief in PPL and although often cracked, its never cleaved.
Olivine is most common in oceanic crust as Fe and Mg are common in the mantle. Olivine is the first mineral to crystallise in basalts. You would expect an Olivine rich rock to have probably come from a mid ocean ridge or hot spot volcano.
Olivine thin section in PPL
Here is some Olivine in Plan Polarised Light (PPL). You can see it stands out against the other minerals in the sample. The dark outline around the olivine crystals is the relief. You can also see many jagged cracks int he olivine crystals. These are fractures, not twins and not cleavage. In PPL Olivine is a light green colour or sepia tone. The Olivine crystals in the thin section are labelled Ol, NB not all the Olivine crystals are labeled.
Olivine thin section in XPL
Here we see the same picture with the Cross Polarising Filter in. (XPL)
Notice the colours of the Olivine is XPL. The blues and greens are the birefringence. Olivine has a second order birefringence. You can also see the crystal just up and right of the centre has gone extinct in XPL. (Gone black)