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Calcite deviation between r-ray and o-ray
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Jan29-12, 01:53 PM
One explanation of the deviation of o-ray and e-ray is done using Huygen's wave fronts which for the o-ray is a circle and for the e-ray is and ellipse. The ellipse is given by the two refraction induces of 1.658 and 1.486 (http://physics.info/refraction/)
are "a" (major axis) and "b" (minor axis) respectively.
I have read in several places that the maximum deviation of the o-ray and e-ray is about 6 degrees.
However when I do the calculation for the angular difference for the same tangent using Huygen's wave fronts (a circle and ellipse) I only get a maximum angular deviation of about 3 degrees.
Can anyone explain the difference, which obviously includes some possible error of mine?
As, for example, in the following equations, the square root only gives positive values the equations require the addition of "-" to put the results in the correct quadrant.
The ellipses I used had the angle from the major axis which I put along the y-axix; given the tangent angle Ang the tangent line equation is
y = Ang*x + sqrt(Ang^2*b^2+a^2)
The x coordinate of the point on the ellipse is
x = - [ sqrt( (b^4*a^2) / ( tan(Ang)^-2 a^4 + b^2*a^2 ) ) ]
where the "-" comes in because the positive slopes are to the left of zero.
One then uses the radian arcsin of "(-x/b)" to get the angle to that tangent point (TangentAngle =arcsin(-x/b)*180/\pi).
Subtracting the starting (circle tangent) Ang-TangentAngle gives you the deviation.
The maximum deviation is at ~46.568 where the asymmetry is due to the "stretching" along the "a" direction.
Any experimental measurement of the maximum deviation angle will be appreciated.
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