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An unknown mineral shows three distinct pleochroic colours. Explain what observations you need to make in order to decide which crystal system it belongs to.

If it has three pleochroic colours this means that it must have a biaxial indicatrix and must therefore be orthorhombic, monoclinic or triclinic. In order to work out which one of these it is you need to work out the orientation of the indicatrix with respect to the crystallographic axes but I'm not sure how you can do this. You can measure the extinction angle with respect to things like cleavage but if it's an unknown mineral then you don't know how the cleavage is oriented with respect to the axes. How do you determine which direction the crystallographic axes are in using a petrographic microscope?

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    $\begingroup$ Sounds like a homework/exam question? $\endgroup$ – winwaed May 24 '16 at 12:35
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    $\begingroup$ @winwaed It was an exam question from a previous year - hence why I tagged it with 'homework' and described what I have done and where I am stuck. $\endgroup$ – bon May 24 '16 at 13:07
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Theoretical answer:

You need to measure extinction angles. If it is always extinct when aligned to cleavage or crystal faces, then it is orthorhombic. If it sometimes aligns and the colour is consistent, it's monoclinic. Otherwise it's triclinic. You do not need to know how cleavage is oriented with respect to the axes in advance because there very few orthorhombic minerals with oblique cleavage (if any at all).

Practical answer (and a rant):

I have no idea why is this still taught in 2016. The motivation of this thing is to know optical properties so you can derive chemical information from them. These days it's probably cheaper and faster to put the sample in XRD or SEM-EDS to know what it is. Even when three colours exist, it is usually very subtle and you will need a lot of self-convincing to see the third colour on its own and not as a combination of the other two. Then there's the issue of a real mineral actually having a proper crystal shape and cleavage (good luck doing this on a 10 micrometre wide anhedral crystal in a thin section).

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