In a vacuum, light travels at a velocity of c = 2.998 × 108m/sec; in more dense media, the velocity of light is lower. The index of refraction of a material, n, is defined as the ratio of the velocity of light in a vacuum to the velocity in the material, v:

n = c/v

For most calculations, the index of refraction of air can be taken as 1.0; typical indices of glasses range from 1.4 to 1.9.

## Snell’s Law

When light is incident on an interface between two materials, it can be reflected or refracted, as shown in figure below. Both situations are described quantitatively by Snell’s Law:

n1 sin θ 1 = nθ 2 where: n1 = index of medium 1 (incident medium)
n2 = index of medium 2
θ 1 = angle of the incident ray with respect to the surface normal
θ 2 = angle of the outgoing ray with respect to the surface normal

## Reflection

In the case of reflection, both rays remain on the same side of the interface. This can be represented by setting n2 = – n1 in Snell’s Law, giving θ2 = – θ1. While reflection generally is associated with metallic surfaces such as mirrors, it also occurs at interfaces with transparent materials. With near-normal incidence on an uncoated glass interface, approximately 4% of the intensity of the incident light is reflected. The remainder refracts at the boundary and is transmitted.

## Refraction

In the case of refraction, Snell’s Law states that the outgoing (refracted) ray travels in a different direction from the incident ray. For n2 > n1, the ray bends toward the surface normal. When light is incident from a medium into a less dense medium, n2 < n1, and the angle of refraction exceeds the angle of incidence, the ray bends away from the surface normal. In this case, a critical angle of incidence (θ C) occurs when θ1 = θC = sin-1 (n2/n1), which corresponds to θ2 = 90°. For θ1 > θC, no beam is transmitted; this is the condition of total internal reflection.