Refractive Index
Light, Sound and Waves

## Refractive index

Glossary Definition for 16-19 #### Description

Refractive index is a material property that describes how the material affects the speed of light travelling through it.

Refractive index is usually represented by the symbol n, or sometimes μ .

The refractive index, n, of a material is defined as

n = cv

where c is the speed of light in a vacuum and v the speed of light in the material. Figure 1: Light passes from a material of refractive index n1 at incidence angle θ1 into a material of refractive index n2 at refraction angle θ2.

#### Discussion

Refractive index determines how much a ray of light changes direction when it travels from one medium into another. This property allows the construction of lenses that can, for example, focus the light to form real images, as in a cinema projector.

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#### Expressed in SI base units

n is dimensionless

#### Mathematical expressions

• n = cv

where c is the speed of light in a vacuum and v is the speed of light in the material.
• Snell's law states that, at the boundary between two materials of refractive indexes n1 and n2

n1sinθ1 = n2sinθ2

where θ1 and θ2 are the incident and refracted angles to the normal (see figure 1).

• Speed

#### In context

In general, n depends on the frequency of the light. In the visible range, a typical glass might have a 2% difference between the refractive index of glass for red light with n = 1.513 , and for violet light, with n = 1.532 .

Since it is always the case that vc, it is always the case that |n| ≥ 1 Although n = 1  only applies in a vacuum, nair = 1.0003 at sea-level atmospheric pressure, so nair is generally taken to be 1. In some special materials, n may be negative.

When spectacles were first invented (in the 13th century) they were lenses made from glass with n ~ 1.6. In the 20th century, polymer lenses were introduced that had n ~1.3. These lenses needed to be very highly curved and much thicker than glass ones to achieve the necessary deviation of the light rays. Advances in technology have led to polymers with values of n up to 1.757 so that much thinner lenses can now be used.