# Refraction

## Basic

Fig.1: Refraction of a light ray

Refraction is the change of direction in which light travels as it passes from one substance to another that has a different optical density (as from air into a gemstone).

Optical density is a property that manifests itself in the slowing down of light, i.e. the higher the optical density, the lower the velocity of light. This change in velocity causes light to bend (refract), as can be seen when a spoon is put into a glass of water. Because light travels slower through water than air, the spoon appears to be bent. This bending of the light is referred to as refraction. Refraction is based on Snell's laws of refraction (see below).

In Fig.1, the angle of incidence is indicated with i and the angle of refraction by r. When light travels from air to an optically denser medium (like a gemstone), it will hit the surface at an angle to an imaginary line named the normal (NO). It will then partially enter the stone (other parts will be reflected). Due to the slowing down of light inside the stone, it will bend (refract) towards the normal.

The opposite of this is also true. Light that travels from a gemstone into an optically rarer (or less dense) medium such as air will bend away from the normal. The angle at which light is now refracted out of the stone is the same as the angle of incidence, which means it will continue along the same path as on incidence (when it entered the stone).

A gemstone’s index of refraction depends on wavelength. White light is composed of 7 spectral colors (Red, Orange, Yellow, Green, Blue, Indigo and Violet), each of which travels at different wavelengths and thus at different speeds. Therefore, the refractive index will be different for each of those colors.

In gemology, yellow light is used as the main source for measuring the refractive index of a gemstone. Yellow light was chosen because in the early days of gemology it was easily produced by salt (sodium) in a flame and was an inexpensive means of producing monochromatic light. The wavelength of sodium light lies at 589.6nm, known as the Fraunhofer D-line. When n is used to describe the index of refraction, we use nD to indicate the refractive index when measured with sodium light. This is commonly abbreviated as RI (refractive index).

The instrument of choice to obtain the refractive index of a gemstone is the refractometer.

#### The math behind Snell’s laws of refraction

Refraction follows the laws of Snell, which state that:

• The sine of the angle of incidence (i) and the sine of the angle of refraction (r) are related to each other at a fixed ratio. This ratio is known as the index of refraction. The ratio depends both on the wavelength of the light and on the substances in which this light travels.
$Index\ of\ refraction = \frac{\sin i}{\sin r}$
• The incident ray, the refracted ray and the normal all lie in the same plane.

The index of refraction is abbreviated with the letter n. As the index of refraction also relates to the velocity of light, one could write:

$n = \frac{velocity\ of\ light\ in\ air}{velocity\ of\ light\ in\ medium}$

#### The relationship between wavelength and speed of light

Speed of light and wavelength

Light in air travels at approximately 300,000km/hour, when it enters an "optically denser medium" this light will slow down. The amount at wich it slows is related to the index of refraction of that material.

Assuming the RI of the material = 2, then the light (comming from air) will be slowed down to 150,000km/hour. So half the speed of the light in air.

As there is also a direct relationship between the speed of light and wavelength, the wavelength will decrease aswell. This means that a beam of red light (with a wavelength of about 700nm) will travel at a wavelength of 350nm inside the material with index of refraction = 2.
A ray of light travelling at 350nm is longwave ultra-violet light.

$\mathbf{c} = \mathbf{l}\mathbf{n}$