Birefringence

Place a clear https://en.wikipedia.org/wiki/Calcite[calcite] specimen on a transparency bearing printed words on an overhead projector. The projected readout is two copies of the lettering. Put a rotatable linear <polarizer> after the specimen: suitable orientations suppress one copy or the other. These are the actual apparatus and observations in the University of Iowa demonstration.<Polarization - Calcite & Iceland Spar by University of Iowa, Department of Physics and Astronomy>[Demonstration 6H35.15, Equipment and Procedure: crystals, polarizers, printed overhead transparency, two sets of words and selective extinction; final note on natural defects]{ref}

For a useful control, remove the specimen while keeping the transparency, projector and screen fixed: the doubling should disappear. Replace it, hold it stationary and rotate only the <polarizer>; complementary brightness changes distinguish two <linear polarizations> from an accidental duplicate transparency. These are suggested controls, rather than additional reported measurements. Ideally the two copies obey complementary <Malus's law> curves, $I_o(\alpha)=I_{o,\max}\cos^2\alpha$ and $I_e(\alpha)=I_{e,\max}\sin^2\alpha$, with <angle> $\alpha$ measured from the exiting <ordinary wave>'s <linear polarization>. Unequal maxima do not invalidate the test. Finite <polarizer> extinction, poor focus and specimen defects limit visibility; image separation alone does not determine either <refractive index> without the specimen geometry.

\Image[/birefringent-polarization-ray-splitting.png]
{title=Separated <ordinary wave> and <extraordinary wave> paths carry different <linear polarizations>}
{description=An ideal parallel slab with a tilted <optic axis> illustrates <birefringent walk-off> at normal incidence. Both internal <wavevectors> are normal to the faces, but the <extraordinary wave>'s <Poynting vector> is tilted. The rays emerge parallel with a lateral displacement. The paired letters symbolize two image channels, not an optical prescription for the projector. The <polarizer> inset shows how an exiting channel is selected.}


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 Incoming links: Calcite double-image experiment