Measure Of Birefringence


Measure Of Birefringence

The birefringence of a material is characterized by the birefringence magnitude or measure of birefringence, which is he difference in the indices of refraction.

$\Delta n = n_{e} – n_{o}$, where
ne is the refractive indices for light travelling in the parallel direction to the optic axis,
no is the refractive indices for light travelling in the perpendicular direction to the optic axis.

$n_{e} = \frac{c}{V_{e}}$, where
c is the speed of light in vacuum
Ve is the velocity of the e-ray (component that propagates parallel to the optic axis).

$n_{o} = \frac{c}{V_{o}}$, where
c is the speed of light in vacuum,
Vo is the velocity of the o-ray (component that propagates perpendicular to the optic axis).

 

Phase Difference Between Component Rays

The optical path for a wave travelling a distance d in a crystal is given as nd, so that the optical path difference for the two components mentioned above will be d(ne – no) = dΔn.

Hence, the phase difference between the two components is: $\delta = 2 \pi \frac{d \Delta n}{\lambda}$, where
λ is the wavelength of the wave in vacuum,
d is the distance travelled in the crystal.

 

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