In many optic experiments, it's always mentioned to cutting the crystal perpendicular to the optic axis, but why? cuz nothing change at all!
I'm going to add a picture for clarity:
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2 Answers
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I will just expand on UVphoton's answer. I think that OPs confusion is on the actual cutting and not the physical properties.
Maybe it's not clear, but before you have a cube, you have a crystal that certainly does not resemble a cube and it will have a certain orientation. For you to have a cube where the optical axis is perpendicular to the face of the cube, you need to cut it that way!
(Imagine the crystal looking like a stereotypical crystal and the optical axis being in a weird direction. For example an hexagonal prism with a pointy tip. The optical axis maybe will be a direction that is 20° from one of the rectangular faces that make the hexagonal prism. Hence you need to cut the crystal in the right way to have that axis perpendicular to the face of your optic.)
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If the materials are crystals the index of refraction is described as an index of refraction ellipsoid. Take a look at uniaxial and biaxial crystals and birefringence. By cutting perpendicular to the optical axis you defining the surface of your optical component in a way that you know what the refractive index properties are.
Depending on the orientation of the material and the polarization of the light the phase delay of the light will be different. This is useful and allows you to make phase plates, 1/4 wave plates and 1/2 wave plates for example with a 1/4 wave plate you can convert between linear and circular polarized light. Sometime people will talk about a fast and slow axis, rather than the optical axis.
