Difference between revisions of "Double Refraction and Birefringence"
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=== Wave Surfaces === | |||
[[Image:Example.jpg|thumb|300px|]] | |||
There are two useful constructs when considering liquid crystals; wave surfaces and index elipsoids. | |||
A material that an isotropic refractive index has the same index of refraction from all directions. An example is a crystal with a cubic lattice. | |||
The electric field of light is perpendicular to its direction of propagation. A point source emitting light from the center of an isotropic crystal emanates light outward uniformly in all directions. The position of the wave front defines a sphere (wave surface) whose radius is increasing with time | |||
Think about a point source in the center of the material emitting light that forms a wave surface. The wave surface is the tangent to the surface of the wavefront of a wave of light coming from that point. In a isotropic material the wave surface forms a sphere. In a material with a higher index of refraction the wave surface has a smaller radius. | |||
We can also draw another construct with a surface defined by a vector whose magnitude is the refractive index of light travelling in a given direction. In isotropic material this surface would also form a sphere, however since the magnitude of each vector is greater with a higher index of refraction this surface would have a large radius for when there is a higher index of refraction. In the example the first low index material has a larger wave surface than the second material which has a high index. | |||
If we chose another material with a larger susceptibility (more polarizable), its wave surface would expand more slowly because the susceptibility relates to the square of the refractive index. At an arbitrary time (t), the wave surface shows a radius inversely proportional to the index of refraction. | |||
Revision as of 14:38, 24 June 2009
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Wave Surfaces
There are two useful constructs when considering liquid crystals; wave surfaces and index elipsoids.
A material that an isotropic refractive index has the same index of refraction from all directions. An example is a crystal with a cubic lattice. The electric field of light is perpendicular to its direction of propagation. A point source emitting light from the center of an isotropic crystal emanates light outward uniformly in all directions. The position of the wave front defines a sphere (wave surface) whose radius is increasing with time
Think about a point source in the center of the material emitting light that forms a wave surface. The wave surface is the tangent to the surface of the wavefront of a wave of light coming from that point. In a isotropic material the wave surface forms a sphere. In a material with a higher index of refraction the wave surface has a smaller radius.
We can also draw another construct with a surface defined by a vector whose magnitude is the refractive index of light travelling in a given direction. In isotropic material this surface would also form a sphere, however since the magnitude of each vector is greater with a higher index of refraction this surface would have a large radius for when there is a higher index of refraction. In the example the first low index material has a larger wave surface than the second material which has a high index.
If we chose another material with a larger susceptibility (more polarizable), its wave surface would expand more slowly because the susceptibility relates to the square of the refractive index. At an arbitrary time (t), the wave surface shows a radius inversely proportional to the index of refraction.
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