1.6: Refraction by a Prism
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Figure I.11 shows an isosceles prism of angle
I have drawn just one ray of a single color. For white light, the colors will be dispersed, the violet light being deviated by the prism more than the red light. We’ll choose a wavelength such that the refractive index of the prism is
Apply Snell’s law at each of the two refracting surfaces:
and eliminate
Equations
The angle of minimum deviation
Of particular interest are prisms with

Solar Halo
When hexagonal ice crystals are present in the atmosphere, sunlight is scattered in all directions, according to the angles of incidence on the various ice crystals (which may or may not be oriented randomly). However, the rate of change of the deviation with angle of incidence is least near minimum deviation; consequently much more light is deviated by 21°.8 than through other angles. Consequently we see a halo of radius about 22° around the Sun.
Seen sideways on, a hexagonal crystal is rectangular, and consequently refraction is as if through a 90° prism (Figure I.14):
Again, the rate of change of deviation with angle of incidence is least near minimum deviation, and consequently we may see another halo, of radius about 46°. For both haloes, the violet is deviated more than the red, and therefore both haloes are tinged violet on the outside and red on the inside.
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