Science Vault - Year 11 HSC Physics

8.2 - The World Communicates

8.2.4 - Refraction

refraction / snell's law / total internal reflection


Often the light will penetrate a surface rather than being reflected from it. As most media have slightly different physical properties they will also exhibit different optical (light properties). The optical density is a term which describes the ease or speed with which light moves through a substance. The higher the optical density the slower light moves through that substance. When light enters a new substance its speed changes and this results in a change in wavelength. The frequency of any wave (light included) will remain the same however when changing media. The new speed causes the light wave to bend or refract. When a (light) wave enters a medium and is able to go faster the wave will refract or bend away from the normal, when the (light) wave enters a medium in which it propagates more slowly it will bend toward normal. There are diagrams below to reinforce this concept.

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Snell's Law

In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction), is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves, passing through a boundary between two different media, such as air and glass. The law says that the ratio of the sines of the angles of incidence and of refraction is a constant that depends on the media. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. Named for one of its discoverers, Willebrord Snellius (Willebrord Snel van Royen), Snell's law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of velocities in the two media, or equivalently to the inverse ratio of the indices of refraction:

The quantities in the above equation are represented in the following diagram.

Refraction of light at the interface between two media of different refractive indices, with n2 > n1. Since the velocity is lower in the second medium (v2 < v1), the angle of refraction θ2 is less than the angle of incidence θ1; that is, the ray in the higher-index medium is closer to the normal.

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Total Internal Reflection

When light moves from a dense to a less dense medium, such as from water to air, Snell's law cannot be used to calculate the refracted angle when the resolved sine value is higher than 1. At this point, light is reflected in the incident medium, known as internal reflection. Before the ray totally internally reflects, the light refracts at the critical angle; it travels directly along the surface between the two refractive media, without a change in phases like in other forms of optical phenomena.

As an example, a ray of light is incident at 50° towards a water–air boundary. If the angle is calculated using Snell's Law, then the resulting sine value will not invert, and thus the refracted angle cannot be calculated by Snell's law, due to the absence of a refracted outgoing ray:

In order to calculate the critical angle, let θ2 = 90° and solve for θcrit:

When θ1 > θcrit, no refracted ray appears, and the incident ray undergoes total internal reflection from the interface medium.

An example of the angles involved within total internal reflection.

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download activity 8.2.4 - refraction

download answers to activity 8.2.4 - refraction

download worksheet 8.2.4 - snell's law

Syllabus and Textbook References

Syllabus References

These references relate to the content covered on this page and can be found in Section 8.2.4 of the syllabus.

4. Many communication technologies use applications of reflection and refraction of electromagnetic waves.


  • explain that refraction is related to the velocities of a wave in different media and outline how this may result in the bending of a wavefront.

  • define refractive index in terms of changes in the velocity of a wave in passing from one medium to another.

  • define Snell’s Law:

  • identify the conditions necessary for total internal reflection with reference to the critical angle • outline how total internal reflection is used in optical fibres.

Students learn to:

  • perform an investigation and gather information to graph the angle of incidence and refraction for light encountering a medium change showing the relationship between these angles.

  • perform a first-hand investigation and gather information to calculate the refractive index of glass or perspex.

Textbook References

Taken from:

Heffernan, D., Parker, A., Pinniger, G. & Harding, J. (2002) Physics Contexts 1, Pearson Education, Melbourne

  • Section 4.2 on pp.170 - 179