When a wave hits a boundary with a medium that it can travel faster in (e.g. light going from glass into air) it will be refracted through a larger angle than its angle of incidence.

The bigger the angle of incidence gets the bigger the angle of refraction will get.

This has a limit though! The angle of refraction cannot get bigger than 90^o.

A special name is given to the angle of incidence that produces an angle of refraction of 90^o.

It is called the critical angle.

If the angle of incidence gets any bigger refraction is not possible and all the light is then reflected.

Total Internal Reflection causes 100% reflection.

In no other situation in nature does this occur, so it is unique and very useful as it is 100% efficient at transfering the light energy.

Click on the graphic for a larger version

If you observe carefully when you carry out an experiment into refraction you will notice that light is not just refracted but that some of it is reflected as well. The larger the angle of incidence the more of the light is reflected and less of it passes into the other medium. You therefore get weak reflection and good transmission into the other medium (refraction) with a small angle of incidence and stronger reflection and less transmission as the angle of incidence gets bigger.

When it reaches the critical angle you get NO transmission of the light into the other medium, it is all reflected.

That is why it is called TOTAL internal reflection, and that is why you must always include that word TOTAL when it applies.

 

Total internal reflection occurs when:

a ray of light is incident upon a boundary with an optically rarer medium (one that makes it speed up) and

the angle of incidence is greater than the critical angle. >

(You must mention BOTH points when asked to explain the conditions under which TIR will be observed).

The critical angle is the angle of incidence that produces an angle of refraction of 90^o.

Click here for total internal reflection within a 45^o prism.

Diamonds

From glass to air the critical angle is about 42^o but it varies from one medium to another. The material that gives the smallest critical angle is diamond. That is why they sparkle so much! Rays of light can easily be made to 'bounce around inside them' by careful cutting of the stone and the refraction at the surfaces splits the light into a spectrum of colours!

Relatively speaking, the critical angle 24.4^o for the diamond-air boundary is extremely small. This property of the diamond-air boundary plays an important role in the brilliance of a diamond gemstone. Having a small critical angle, light has the tendency to become "trapped" inside of a diamond once it enters. Most rays approach the diamond at angles of incidence greater than the critical angle (as it is so small) so a light ray will typically undergo TIR several times before finally refracting out of the diamond. This gives diamond a tendency to sparkle. The effect can be enhanced by the cutting of a diamond gemstone with a 'strategically' planned shape. The diagram to the left depicts the total internal reflection within a diamond gemstone with a 'strategic' and a 'non-strategic' cut.

'Cut' Glass or Lead Crystal

Cut glass is made of a glass that contains heavy elements such as lead. This gives it a smaller critical angle between the glass and air as the glass is denser and makes it sparkle more when it is cut into facets. It is sought after for tableware, decorative glassware and in chandeliers.

Click here for Uses of Total Internal Reflection