# Refraction – Definition, Refractive Index, Snell’s Law Refraction is the change in the speed and direction of a wave as it passes into a different medium.

In physics, refraction is the change in speed and direction of a wave as it enters a new medium. Perhaps the most familiar example is the refraction of white light in a prism, bending wavelengths of light different amounts and producing a rainbow. But, refraction also occurs in other types of waves, including sound and water.

### Examples of Refraction

Here are examples of refraction of different types of waves:

• Refraction of light in a prism bends violet light the most and red light the least, producing a rainbow. The separation of light according to wavelength is dispersion.
• Water refracts and disperses light in the atmosphere, making a rainbow.
• Refraction of sound occurs when a sound wave travels from warm air into cold air. The wavelength of the sound wave decreases.
• The lens of the human eye bends light via refraction, forming images on the retina.
• A straight item, like a pencil, looks bent when partially immersed in water because of the refraction of light in water.
• Water waves refract when they move from deeper water to shallow water, or vice versa. Water waves travel faster in deep water and slower in shallow water. A ripple tank illustrates both refraction and diffraction of water waves.
• Consider a marching band as a wave. The members of the band march in step. As they move from concrete onto grass, the band slows. It changes direction depending on which foot hits the grass first. A similar example occurs when one tire of a car edges off the road, slowing it and changing its direction.

### Index of Refraction

The index of refraction (also called the refractive index) is a dimensionless number that compares the speed of light in a vacuum to its speed in a given medium (its phase velocity):

n = c / v

Here, n is the index of refraction, c is the speed of light in a vacuum, and v is the phase velocity. So, the index of refraction in a vacuum is 1. The index of refraction of light in water at 20 °C is 1.333.

The index of refraction comparing wave speed to the speed of light in a vacuum is the absolute index of refraction. In some references, the speed of light in air at standard temperature and pressure replaces the speed of light. In this case, the value is not “absolute”.

### Snell’s Law

Snell’s law describes the refraction of light. For a pair of media, the ratio of the sines of the angle of incidence θ1 and the angle of refraction θ2 equals the ratio of the phase velocities of the two media (v1 / v2) or the indices of refraction ( n2 / n1 ). The index of refraction is

sin θ1 / sin θ2 = v1 / v2 = n2 / n1

A variation is the law of refraction:

n1 sin θ1 = n2 sin θ2

### How Refraction of Light Works

You may wonder why light changes its path and speed when it enters a new medium.

#### Speed

Light is an electromagnetic oscillation that makes matter oscillate, too. In particular, the electrons of atoms vibrate and emit electromagnetic waves in response to light. These waves interact with the light waves, resulting in a slower combined wave (constructive interference). The medium slows light, but if it returns to a vacuum there is no slowing effect so it returns to its original speed.

#### Direction

The reason refraction bends the path of light is because part of the wave strikes the medium earlier than the other part. The side of the wave going slower pivots the entire wave in that direction. A wave bends away from the surface or toward normal as it goes into a slower material. It bends toward the surface or away from normal as it enters a faster material. In essence, the frequency of the wave remains the same, but wavelength changes. Or, as speed decreases, wavelength decreases.

It is worth noting that the color of light does not change as it enters the medium. Yes, wavelength changes, but the frequency (and color) remain the same.

### References

• Born, Max (1999). Principles of Optics (7th ed.). Cambridge University Press. ISBN: 978-0521642224.
• Dill, Lawrence M. (1977). “Refraction and the spitting behavior of the archerfish (Toxotes chatareus)”. Behavioral Ecology and Sociobiology. 2 (2): 169–184. doi:10.1007/BF00361900
• Hecht, Eugene (2002). Optics. Addison-Wesley. ISBN 0-321-18878-0.
• Hogan, C. Michael (1973). “Analysis of highway noise”. Water, Air, & Soil Pollution. 2 (3): 387–392. doi:10.1007/BF00159677