The law of refraction relates the angle of incidence (angle between the incident ray and the normal) to the angle of refraction (angle between the refracted ray and the normal). This law, credited to Willebrord Snell, states that the ratio of the sine of the angle of incidence, i, to the sine of the angle of refraction, r, is equal to the ratio of the speed of light in the original medium, v i , to the speed of light in the refracting medium, v r , or sin i /sin r = v i / v r . Snell's law is often stated in terms of the indexes of refraction of the two media rather than the speeds of light in the media. The index of refraction, n, of a transparent medium is a direct measure of its optical density and is equal to the ratio of the speed of light in a vacuum, c, to the speed of light in the medium: n = c/v.
Indexes of refraction are always equal to or greater than 1; for air, n = 1.00029; for water, n = 1.33. Using indexes of refraction, Snell's law takes the form sin i /sin r = n r / n i , or n i sin i = n r sin r. If the original medium is denser than the refracting medium ( n i greater than n r ), sin r will be greater than sin i. Thus, there will be some acute angle less than 90° for the incident ray corresponding to an angle of refraction of 90°. This angle of incidence is known as the critical angle. For angles of incidence greater than the critical angle, refraction cannot take place and the incident ray is instead reflected back into the original medium according to the law of reflection (angle of reflection equals angle of incidence). This phenomenon is known as total internal reflection.
The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.