Total Internal Reflection
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 90o.

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

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 90o.

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

Diamonds

From glass to air the critical angle is about 42o 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 24.4o 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.

 

Uses of Total Internal Reflection

Fibre Optic Cables (see separate page on this - it is a very important use with many applications)

  • Telecommunications

Two types of optical fibre are used in telecommunications:

  • Step-index fibre - The core is made from on type of glass while the outer cladding has a lower refractive index.
  • Graded-index fibre - The refractive index of the material gradually decreases outwards from the centre of the fibre.

Before optical fibres had been developed, telecommunications used copper cables. Because of copper's resistance (changing some of the energy into heat), signals were reduced and had to be re-amplified every few kilometres. Compared to copper cables, optical fibres are far more efficient, less bulky and heavey and much cheaper (they are made from sand!).

  • Local Area Networks
  • Cable TV
  • CCTV
  • Astronomy

If light from several stars or galaxies needs to be studied simultaneously (for example to analyse red-shift or spectra). Optical fibres are then bundled together and placed at the focus of a telescope in a block. Each optical fibre receives light from parts of the image of the sky, fibres then lead the light to an instrument where it can be studied by translating the ligt into an electrical signal and feeding the collected data into a computer.

  • Optical Fibre Sensors
  • The endoscope or fibroscope

    An endoscope is any instrument used to look inside the body. Thousands of optical fibres are bundled together in an endoscope which is inserted into a human body so that the doctor can 'see' inside. Light can be directed down the fibres even if they are bent, allowing the surgeon to illuminate the area under observation (an incoherent bundle is used to do this!). S/he can then view this from a television camera linked to a monitor by coherent fibres.
    Usually consisting of a fiber-optic tube attached to a viewing device, endoscopes can be used to explore and biopsy such areas as the colon and the bronchi of the lungs. By employing miniature television cameras and tiny surgical implements thy allow not only exploration but also endoscopic surgery. Through small incisions; such surgery is much less traumatic to the patient than traditional open surgery. Recovery times are shorter, and less anaesthetic is required (sometimes none!).

    Examples of surgical uses:

    • Laparoscopic surgery, in which the endoscope is inserted through a small incision in the abdomen or chest, is used to correct abnormalities of the ovaries and as an alternative to traditional gall bladder and chest surgery.
    • Arthroscopic surgery is endoscopic surgery performed on joints such as the knee or shoulder.

     

    Endoscopes are widely used both in medical and vetenary practices. The physics principle on which they are based is total internal reflection within a fibre optic bundle of fibres.

 

Prismatic Optical Instruments

Some optical instruments, such as periscopes and binoculars use prisms instead of mirrors to reflect light around corners. This is because mirrors do not reflect light as totally as prisms do (mirrors only reflect about 95% of that reflected by prisms under TIR conditions). Also refraction distortion can result in using a glass fronted mirror. Therefore the image is crisper and brighter. In prismatic binoculars, total internal reflection in prisms is used to extend the path length between objective and eyepiece, effectively `folding' the optical path. This makes them compact and easy to carry.

Bicycle Reflector

If you position two mirrors at a right angle to each other, all of the incoming light will bounce twice and then retrace approximately the same path on its way out. (Try it out, and you'll discover thatt the image that you see in the mirror-pair is NOT laterally inverted as it would be in a single mirror!). If you put THREE mirrors together and look into the corner of them, you'll see an upside-down, unreversed image of your face. And no matter how you twist the mirrors or move your head, the image of your face will stay in the same spot. This device is called a CORNER-CUBE REFLECTOR. It returns incoming light back to its source.

Bicycle reflectors are composed of hundreds of tiny Corner-Cube Reflectors formed into the plastic - a 'Corner-Cube Array'.

When you look deeply into a white bicycle reflector close up you will notice that it looks black. The black colour is actually the upside-down image of your eye's dark pupil! If the reflector facets were lots bigger, you'd see an image of your eye within each one. Gaze at the reflector while slowly moving the edge of a white piece of paper across your eye, and just before it blocks your vision, you'll see small white bits appear in the facets of the bicycle reflector.

If you take one apart, you'll find that the faceted back of the plastic is NOT a metal-coated mirror. In fact, if it was metallized, it would only reflect about 80% of the light; same as normal mirrors. Without the metal, it reflects 100% of the light (if it is made of transparent plastic!) by using Total Internal Reflection instead. The reflectors, however, are manufactured in different colours of plastic material so that they only reflect a portion of the light in the desired colour (e.g. 'red' on the back of a bike). The coloured plastic works like a filter - (if you cycle see here).