Snell’s Law

Snell’s law, in optics, a relationship between the path taken by a ray of light in crossing the boundary or surface of separation between two contacting substances and the refractive index of each. This law was discovered in 1621 by the Dutch astronomer and mathematician Willebrord Snell (also called Snellius). The account of Snell’s law went unpublished until its mention by Chriastiaan Huygeens in his treatiseon light. In the Figure, n1 and n2 represent the indices of refraction for the two media, and α1and α2 are the angles of incidence and refraction that the ray R makes with the normal (perpendicular) line NN at the boundary. Snell’s law asserts that n1/n2 = sin α2/sin α1.

Because the ratio n1/n2 is a constant for any given wavelength of light, the ratio of the two sines is also a constant for any angle. Thus, the path of a light ray is bent toward the normal when the ray enters a substance with an index of refraction higher than the one from which it emerges; and because the path of a ray of light is reversible, the ray is bent away from the normal when entering a substance of lower refractive index.

Sample:

Light travels from air into an optical fiber with an index of refraction of 1.44.  (a)  In which direction does the light bend?  (b)  If the angle of incidence on the end of the fiber is 22^o, what is the angle of refraction inside the fiber?  (c)  Sketch the path of light as it changes media.

Solution:

(a)	Since the light is traveling from a rarer region (lower n) to a denser region (higher n), it will bend toward the normal.
(b)	We will identify air as medium 1 and the fiber as medium 2.  Thus, n1 = 1.00, n2 = 1.44, and θ/font>1 = 22o.  Snell's Law then becomes (1.00) sin 22o = 1.44 sin θ2. sin θ2 = (1.00/1.44) sin 22o = 0.260 θ2 = sin-1 (0.260) = 15o.
(c)	The path of the light is shown in the figure below.

Bibliography

Encyclopedia Britannica. (jul 20,1998). Snell Law. Retrieved from https://www.britannica.com/science/Snells-law