Biotite is a series or subgroup of micas that typically contain Fe in the formula. Zinnwaldite is a species of mineral that is sometimes classified as a member of the biotite group. It will be easier to distinguish zinnwaldite from muscovite optically than any of the biotite series members. The pleochroism of zinnwaldite will be darker, potentially brown, green, or blueish in comparison to muscovite. The 2V angle for muscovite can also be slightly greater, 35-45 degrees in comparison to zinnwaldite which is approximately 30. The real difficulty will be optically distinguishing zinnwaldite from other metallic bearing micas, like phlogopite and annite. 2V angles can differ slightly between them as well, but the other optical properties of these species are incredibly similar. Are you trying to distinguish between micas in a natural sample?
Yes, I have thin sections of a granite, and they show two micas, one presents a dark pleochroism and the other one doesn't. The last one has higher birefringence, so that made me think it wasn't muscovite. I'll try to measure the 2V angle. Thanks!
If you still have the original sample from which the section was made then zinnwaldite will normally be a pale green colour unlike either muscovite (yellow to pale beige to white) or the biotite family (generally brown or dark brown).
Good suspicion, but are you sure the birefringence is higher than that of biotite ? - the latter has already a higher order white birefringence (masked by pleochroism) in normal thin sections. If colours are brighter, the birefringence is actually lower - but from what you write I think you know that. Indeed muscovite normally has a larger 2V than both biotite and zinnwaldite, and zinnwaldite also has a higher relief than the other two. Additionally, zinnwaldite has a poorer cleavage with "brittle mica" separations, but I wouldn't rely only on microscopy in this case.. The colour in hand sample is not very reliable either.