4.4b Total internal reflection

THE IB SAYS

Essential idea: Waves interact with media and each other in a number of ways that can be unexpected and useful.

Understandings: Snell’s law, critical angle and total internal reflection

Applications and skills: Solving problems involving Snell’s law, critical angle and total internal reflection

Guidance: Quantitative descriptions of refractive index are limited to light rays passing between two or more transparent media. If more than two media, only parallel interfaces will be considered.

Data booklet:

My vodcasts

This is my main vodcast on this topic

This is a brief, focused, vodcast on defining and demonstrating what is the critical angle?

Dispersion

Snell's law gave us a formula for calculating the angle of refraction at an interface between two different media. However, for the case of light, what we neglected to mention is that the velocity of light in a medium is a function of the wavelength. This means that when white light, which is mixture of different wavelengths and colours, is refracted those colours will begin to separate, taking different paths. For a continuous distribution of light (such as that given off by a hot object, such as the Sun) this will result in a continuous spectrum of light. This process is known as dispersion.

Dispersion can be enhanced by an object whose geometry promotes dispersion both when light enters and exits the material. The classical example of this kind of object is a triangular prism, but other objects, such as cut gems and droplets of water, also readily show dispersion.

Total Internal Reflection and the Critical Angle

According to Snell's Law and our work on refraction, when a ray exits a transparent medium and it's velocity increases (more optically dense to less optically dense medium) it will bend away from the normal. Therefore there must be an angle of incidence for which the refracted angle is equal to or greater than 90º. At this point refraction can no longer occur. Instead all of the light is reflected. Since all of the light is reflected, and it is reflected back into the more optically dense medium, this phenomena in known as total internal reflection.

The angle of incidence at which this occurs (known as the critical angle) is that for which the angle of refraction is 90º, and is a function of the relative velocity of the light in the two media, or alternatively the refractive index of the two media.

if your external medium is a vacuum or air with an effective refractive index of 1,

Rainbows

Rainbows are a good example of both dispersion and total internal reflection. Light from the sun enters raindrops and is initially dispersed, it is then total internally back in the same direction it came from before being further dispersed on exiting the raindrop. The effect with millions of raindrops together is to form a rainbow. Examples of the practical use of TIR include communications through fibre optics and imaging systems such as endoscopy.

Simulation

The excellent PhET website has a great interactive simulation that can be used to carry out experiments.

Resources from textbooks

Oxford Physics: pages 148 - 150

Hamper HL (2014): pages 187 - 189

Relevant questions from Dot Point Physics (4 Oscillations and Waves)

None - oddly doesn't seem to be covered unless I'm looking in the wrong place.

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