Critical angle in Total internal reflection


he critical angle is the angle of incidence above which total internal reflection occurs. The angle of incidence is measured with respect to the normal at the refractive boundary. The critical angle θc is given by:
where n2 is the refractive index of the less optically dense medium, and n1 is the refractive index of the more optically dense medium.
If the incident ray is precisely at the critical angle, the refracted ray is tangent to the boundary at the point of incidence. If for example, visible light were traveling from a glass (i.e. Lucite with an index of refraction of 1.50) into air (with an index of refraction of 1.00). The calculation would give the critical angle for light from Lucite into air, which is
.
Light incident on the border with an angle less than 41.8° would be partially transmitted, while light incident on the border at larger angles with respect to normal would be totally internally reflected.
The critical angle for diamond in air is about 24.4°, which means that light is much more likely to be internally reflected within a diamond. Diamonds for jewelry are cut to take advantage of this; in particular the brilliant cut is designed to achieve high total reflection of light entering the diamond, and high dispersion of the reflected light (known to jewelers as fire).
If the fraction: is greater than 1, then arcsine is not defined--meaning that total internal reflection does not occur even at very shallow or grazing incident angles.
So the critical angle is only defined for .

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