Snell's Law

Refractive Index

We have seen previously seen that when a ray of light passes between media of different densities, Refraction can occur.

In the above diagram, we can see that as the light passes from the less dense air into the more dense glass, the ray of light is refracted towards the normal.

If the angle of incidence is varied and the corresponding angles of refraction measured, the following graph can be obtained:-

As this graph shows that the angle of incidence is directly proportional to the angle of refraction (for a given Wavelength of light) we can state that:-

Where:-

n = Refractive Index (ratio, therefore no units)

sin θ1 = Angle in less dense medium

sin θ2 = Angle in more dense medium

The value of Refractive Index is set by the material and has ranges from a value of n = 1 to a value of ~4 for everyday materials. The greater the refractive index, the larger the refraction. The refractive index of a material varies with the Wavelength of the light. The longer the Wavelength of light, the smaller the value of refractive index. This means that red light experiences less refraction than violet light. This is the cause of the dispersion on light by a triangular prism.

Snell's Law and the Wave Equation

We know from National 5 that when light passes from a less dense medium into a more dense medium, the following occurs:-

1. Frequency remains unchanged

2. Wavelength is decreased

3. Wave speed is decreased


By combining this information with Snell's Law, the following can be obtained:-