Refraction

Refraction, bending of waves that occurs when a wavefront passes obliquely from one medium to another. The phenomenon is most familiar with light waves. When light passes from a less dense medium (for example, air) to a denser one (for example, glass), it is refracted towards the normal (an imaginary line perpendicular to the surface). This occurs because the light waves are slowed down by the denser medium, causing them to change direction. On passing from a denser medium into a less dense one, the light is refracted away from the normal.

There are two laws of refraction:

• The incident ray, the refracted ray, and the normal all lie in the same plane.
• For light rays passing from one transparent medium to another, the sine of the angle of incidence, i, and the sine of the angle of refraction, r, bear a constant ratio to one another. This is most simply stated mathematically: sin i/sin r = a constant. This constant is usually given the symbol, n, and is called the refractive index of the material. The higher the refractive index, the greater will be the extent of the refraction. This law is known as Snell’s law.

The laws of refraction can be used to understand how light waves behave when passing through more than two media with parallel boundaries. If the refractive index of the first and last medium is the same (they are both air, for example), but different to that of the intermediate medium (for example, glass), light will be refracted towards the normal on entering the glass, and on leaving will be refracted back away from the normal to exactly the same extent. The effect of this is that the emergent ray is parallel to the incident ray, but is “laterally displaced” from it.

When light waves pass from air through glass in the form of a 60° prism, the laws of refraction explain why the light now behaves somewhat differently than through a mere glass block. At first, as with a solid block of glass, the ray entering the prism is refracted towards the normal, and the emerging ray is refracted away from the normal. However, because of the angle between these two faces of the prism, the ray is turned through a considerable angle. In practice, the different colours (different wavelengths) of light present in white light are refracted to different extents, and using a prism with this arrangement is a convenient method for producing a spectrum.

One everyday effect of refraction is that objects seen under water appear to be at a shallower depth than they really are. The observer sees an underwater object in a higher position, because the eye cannot tell that the light has been refracted on its path from the object.

Total internal reflection is another phenomenon that can be explained by refraction. Because light travelling from a denser to a less dense medium is refracted away from the normal, some rays striking the boundary between the two media at a large angle of incidence cannot pass through it, but are totally internally reflected. Typically, when a ray of light emerges from a denser to a rarer medium, the ray is deflected away from the normal, but in practice there is always a weak reflected ray present also. If the angle of incidence increases, the refracted ray moves closer to the boundary between the two media because the angle of refraction has also increased. The refracted ray also becomes weaker, while the reflected ray within the glass becomes stronger. If a situation is reached when the angle of refraction is 90°, there is only a residual refracted ray grazing along the boundary between the two media, and most of the light is internally reflected. The angle of incidence for an angle of refraction of 90° is called the critical angle. When the angle of incidence is greater than the critical angle, the ray is totally internally reflected, as it is clearly impossible for any light to escape from inside the glass. The critical angle for a ray of light emerging from glass into air is approximately 42°.

Total internal reflection has many commercial uses. A 90° prism, with light totally internally reflected off one face, can be used in prismatic binoculars. This is also the principle on which optical fibres work, since the light pulses passing along such a fibre have a high angle of incidence on the walls of the fibre, and so are unable to escape from it (see Fibre Optics). The high refractive index of diamond gives it a very low critical angle (24°). This means that light is reflected internally many times before it can escape from a well-cut diamond, and can then come out in any direction. This is why diamonds sparkle.