Isotropic and Anisotropic Minerals under the CPL arrangement

In the CPL arrangement of the petrological microscope, Isotropic minerals do not show any colour while anisotropic minerals show interference colours.
Isotropic minerals have high symmetry and therefore as shown in the diagram below does not alter the plane of vibartions of light that comes from the polarizer. When this light reaches the analyzer, it cannot pass through because the plane of polarization of the analyzer is perpendicular to that of the polarizer. Therefore no light moves through to the eyepiece resulting in the mineral becoming dark.

Anisotropic minerals have low symmetry and therefore alters the plane of vibration of light that passes through it. Therefore when this "altered" light reaches the analyzer, the light that has the same vibration direction as the analyzer passes through to the eyepiece. Therefore colours are seen in this case.