Snell's Law

The Picture (at least part of the Picture) was Provided by Jonathan Knowles

If you have ever half-submerged a straight stick into water, you have probably noticed that the stick appears bent at the point it enters the water. This optical effect is due to refraction. As light passes from one transparent medium to another, it changes speed, and bends. How much this happens depends on the refractive index of the mediums and the angle between the light ray and the line perpendicular (normal) to the surface separating the two mediums (medium/medium interface).  Each medium has a different refractive index.  The angle between the light ray and the normal as it leaves a medium is called the angle of incidence. The angle between the light ray and the normal as it enters a medium is called the angle of refraction.

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Picture by One-School

Snell's Law

Snell's law gives the relationship between angles of incidence and refraction for a wave impinging on an interface between two media with different indices of refraction. The law follows from the boundary condition that a wave be continuous across a boundary, which requires that the phase of the wave be constant on any given plane, resulting in

where  and  are the angles from the normal of the incident and refracted waves, respectively.

Definition and Picture provided by Science World

The index of refraction is defined by

where c is the speed of light and  is the phase velocity. It gives the amount of refraction which takes place for light passing from one medium to another.

Consider the phase velocity to be the apparent velocity of light in the medium.  This "change" in velocity of light (which would appear to violate Einsteins 2nd postulate) is a result of light being absorbed and re-transmitted.

Definition provided by Science World

Vacuum                1.00000

Air at STP          1.00029

Ice                            1.31

Water at 20 C            1.33

Acetone                    1.36

Ethyl alcohol             1.36

Sugar solution(30%)   1.38

Fluorite                   1.433

Fused quartz             1.46

Glycerine                1.473

Sugar solution (80%)  1.49

Typical crown glass   1.52

Crown glasses   1.52-1.62

Spectacle crown           1.523

Sodium chloride             1.54

Polystyrene            1.55-1.59

Carbon disulfide              1.63

Flint glasses           1.57-1.75

Heavy flint glass             1.65

Extra dense flint          1.7200

Methylene iodide            1.74

Sapphire                        1.77

Rare earth flint          1.7-1.84

Lanthanum flint       1.82-1.98

Arsenic trisulfide glass    2.04

Diamond                      2.417

Table Provided by Hyperphysics

Example

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 degree, what is the angle of refraction inside the fiber?

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 θ1 = 22o.  Snell's Law then becomes

(1.00) sin 22 = 1.44 sin θ2.

sin θ2 = (1.00/1.44) sin 22 = 0.260

θ2 = sin-1 (0.260) = 15 degree.

Example Problem Provided by Rensselar Polytechnic Institute