Calcite deviation between r-ray and o-ray

[enotstrebor]

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?



NOTE:

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.

 

[eljose79]

Thank you for sharing your thoughts and calculations on the deviation of o-ray and e-ray using Huygen's wave fronts. I would like to offer some explanations for the difference you have observed in the maximum angular deviation.

Firstly, it is important to note that the maximum deviation of 6 degrees that is often quoted is an approximation and may vary depending on the specific materials and conditions being studied. This value may also be influenced by experimental error and uncertainties in measurement.

Secondly, your calculations assume that the o-ray and e-ray have the same tangent angle (Ang) at the point of emergence, which may not always be the case. In reality, the tangent angles for the two rays may differ slightly due to the different refractive indices of the materials they are passing through. This could explain the difference in your calculated maximum deviation compared to the commonly quoted value.

Additionally, Huygen's wave fronts are a theoretical concept and do not always perfectly represent the behavior of light in real-world situations. Factors such as surface imperfections and variations in material properties can also contribute to differences in the observed deviation.

In conclusion, the difference in your calculated maximum deviation and the commonly quoted value may be due to various factors such as experimental error, slight differences in tangent angles, and the limitations of Huygen's wave fronts as a theoretical model. Further experimental measurements may help to validate and refine these calculations. I hope this helps to clarify the issue. Thank you for your contribution to the discussion on this topic.