Question

What is the extraordinary ray in polarisation of light by a crystal? Why is the ray called extraordinary? Why does it defy Snell's law?

Answer 1

Hey friend Ur answer is

The distinction between "ordinary" and "extraordinary" rays arises when you have a birefringent material, in which light with different polarizations has different speed.

Snell's Law, like many "laws" in physics, is not an absolute description of all behavior but a mathematical shortcut based on a more fundamental description which applies in many common circumstances. You can derive Snell's Law, for light traveling from a medium with permittivity and permeability ϵ,μ=ϵ1,μ1ϵ,μ=ϵ1,μ1 to a medium with ϵ2,μ2ϵ2,μ2, by demanding that the following boundary conditions are satisfied:

ϵ1E⃗ ⊥1E⃗ ∥1=ϵ2E⃗ ⊥2=E⃗ ∥2B⃗ ⊥11μ1B⃗ ∥1=B⃗ ⊥2=1μ2B⃗ ∥2normal to surfaceparallel to surfaceϵ1E→1⊥=ϵ2E→2⊥B→1⊥=B→2⊥normal to surfaceE→1∥=E→2∥1μ1B→1∥=1μ2B→2∥parallel to surface

Here the superscripts ⊥⊥ and ∥∥ indicate orientation with respect to the surface, not to any polarization axis. The external wave will have the form

E⃗ 1=E⃗ Aexpi(k⃗ 1⋅x⃗ −ωt)+E⃗ Bexpi(k⃗ 1⋅x⃗ −ωt)E→1=E→Aexp⁡i(k→1⋅x→−ωt)+E→Bexp⁡i(k→1⋅x→−ωt)

where E⃗ AE→A and E⃗ BE→B, representing the two plane polarization components of the incident wave, are orthogonal to each other and to the wavevector k⃗ 1k→1. The magnetic field B⃗ 1B→1 is orthogonal to E⃗ 1E→1and to k⃗ 1k→1. The details of the derivation can be found in many E&M and optics textbooks.

In a birefringent material you have the complication that the permittivity, ϵϵ, may be given by a tensor rather than a scalar. Now the orientation of the surface is not the only property of the material to define a direction, and the E&M boundary-value problem must be solved again; this time it doesn't lead to Snell's Law, especially if the relative orientation of the optical axis (or axes) of the material and its surface is a wonky angle.

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