Today, i am going to talk about Refraction at a Uniaxial Crystal Surface
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The Keywords that used in this presentation are:
-Uniaxial Crystal 
-Optic axis
-Ordinary ray or o-ray
-And Extraordinary ray or e-ray

Briefly:
-Uniaxial Crystal is a crystal that has one optic axis.

-And the optic axis is the propagation direction when the two values 
of n in Fresnel's equation are equal, that is, n1 equals n2.

-Now...Natural light after entering into uniaxial crystal 
is divided into ordinary ray and extraordinary ray.
o-ray is correspond to index n_o which is equal n_z
and e-ray is correspond to index n_e which is equal to n_x and n_y.

Now.. I am going to talk about what happens when this two rays enter a uniaxial crystal.
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O-Ray Refraction:
The propagation of o-ray in the uniaxial crystal obeys Snell’s law.
So.. Simply, the equation is in this form...
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Next, E-Ray Refraction:

For the e-ray, the refractive index n_e in the uniaxial crystal is expressed as...
as we see, n_e is a function of theta alone, not on phi.
where theta prime is the angle between e-ray wave vector and 
optical axis as demonstrated in this figure. In this figure theta_kp is used instead of 
theta prime... 
Anyway, n_e is a constant at theta=0

The e-ray obeys the extensive Snell’s law, that is:
.... تكملة من السلايد

Now... The influencing factors of e-ray wave vector are:
incident angle, index outside the crystal, ordinary index, 
extraordinary index and the optical axis of uniaxial crystal.

Now... From this figure, we notice that the incident light is divided into two
rays when entering the crystal.. so maybe someone ask, why this separation?
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Why this separation?
Simply, because it is a crystal.

Basically, crystal is an anisotropic material, so it is possible for the light 
to experience different indices of refraction depending on the alignment 
of the electric field or polarization.

Therefore, when light enters a uniaxial crystal, it has two different 
indices of refraction. 
And if we have two different indices then we have two different angles of refraction.
And ofcourse, two different velocities, and two different wavelengths in the crystal. 

For example:
-If n_e is less than n_o (in this case we have what we call negative crystal) 
then theta_e in this case is larger than theta_o.
-And if n_e is larger than n_o (or positive crystal) 
then theta_e is less than theta_o.
According ofcourse to Snell's Law.

This is why we have to separate them.
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And... The End.. Thank you
The refereces i used in this presentation are... these
So...Thank you.











The e-ray obeys the extension Snell’s law because the refractive index of e-ray is
changed with the angle of wave vector and optical axis. The propagation of e-ray in the uniaxial crystal
is relevant to not only the refractive index of isotropic media, the refractive index of uniaxial crystal
but also optical axis