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Hello ,the math doesnt take it into account.The math uses in the calculation isotropic material.

we have n1 and n2 and thats it.

Where did i go wrong?

Thanks.

crystalline materials may have different indices of refraction associated with different crystallographic directions. A common situation with mineral crystals is that there are two distinct indices of refraction, and they are called birefringent materials. If the y- and z- directions are equivalent in terms of the crystalline forces.