Refraction is defined as the bending of a light wave when it passes from one medium to another at the surface separating the two media. It basically occurs due to the speed of light being different in different media of different densities.
Refraction of light waves is governed by the two Laws of Refraction:
- The incident ray, refracted ray and the normal at the point of incidence lie in the same plane.
- The sine of the angle of incidence bears a constant ratio with the sine of the angle of refraction for a given pair of media. This law is also known as the Snell's law, named after Willebrord Snell.
The process of refraction can be explained with the help of Huygens' construction:
Let us assume a surface separating two different media of different densities, medium 1 and medium 2, in which the speed of light is c1 and c2 respectively (refer to diagram).
A light beam travelling in medium 1, with velocity=c1 strikes the surface and enters medium 2. One of the light rays of the incident beam has a wavefront AB perpendicular to the direction of propagation. This wavefront, at time=0 reaches the point A, which lies on the surface separating the two media. This point, according to Huygens' principle becomes a secondary source of light and emits a secondary wavelet at time=0, into medium 2, with a velocity of c2. At time t, this secondary wavelet is in the form of a hemispherical surface of radius=c2t. At this time, its wavefront reaches a point C, which is on the surface separating the two media.
A tangent CD is now drawn from the point C to the secondary wavelet emitted by A. A point P is now considered on the surface which lies between A and C, such that AP/AC = x. Let there be two perpendiculars from P, PQ and PR, onto AB and AC.
PR/AD = PC/AC = ( (AC - AP)/AC ) = ( AC(1 - x) )/AC = 1-x
PR = (1 - x)AD = (1 - x)c2t
Since QP/BC = AP/AC = x,
QP = xBC = xc1t
Therefore the time taken by the wavefront of the incident beam to reach the point P is t1, where
t1 = QP/c1 = xc1t/c1 = xt
As from Huygens principle, this point P emits another secondary wavelet at this time into medium 2, whose radius at time t is given by
a = c2( t - t1 ) = c2( t - xt) = c2t(1 - x)
Now, PR is the radius of the secondary wavelet emitted by P, whose wavefront at time=t is same as that of the one emitted by A, i.e. CD. Also, the angle between the incident ray and the normal, which is the angle of incidence, i, is equal to angle BAC. Similarly, the angle between the reflected ray and the normal, which is the angle of reflection, r, is equal to angle DCA.
The sine ratios for the two angles are:
sin i = BC/AC, sin r = AD/AC
sin i / sin r = BC/AD = c1t/c2t = c1/c2 = constant
It is also clear from geometry that the incident ray, refracted ray and the normal at the point of incidence lie on the same plane. Hence, the two laws of refraction are proved.
The ratio sin i / sin r gives the refractive index for a a given pair of media. As seen from above:
Refractive Index = sin i / sin r = speed of light in medium 1 / speed of light in medium 2
If medium 1 is vacuum, the ratio c1/c2 is defined as the absolute refractive index of medium 2, and is denoted by 'μ' (mew).
When light travels from a rarer medium to a denser one, it bends towards the normal. When it travels from a denser medium to a rarer one, it bends away from the normal. This bending of light has many implications, one of which is quite prominent in nature - mirage.
A mirage occurs in very hot conditions, when a layer of warm air, next to the ground is trapped by the relatively cooler air above. Light is succesively bent by these different layers of different densities towards the horizontal line of vision and eventually is made to travel upwards by total internal reflection at one of these layers. When these light rays reach the human eye, the human brain perceives them as coming from the image of the object, beneath it, thus giving the wrong impression of a pool of water at some distance. This phenomenon is most prominent on long roads on very hot days and in hot deserts. Another type of mirage, called looming, occurs in extemely cold conditions, when a layer of relatively warm air, lies over another of cool air. The light rays travelling from the cold to the warm layer are bent away from the normal, and finally reflected downwards, to give an impression of an image looming above the real object.
The refraction of light can be used for various purposes. Water-filled spheres, known an lacemakers' condensors, were used in the early nineteenth century by lacemakers to help them see their work. Light passing through these condensors was bent in such a way, so that the rays meet in a small area and light up only a small area of the cloth to enable the lacemaker to focus on it. Another use of refraction is in Schlieren Photography, which uses the fact that air at different temperatures bends light by different amounts. The refractive index of a particular substance which occurs in a huge quantity such as a water reservoir can also be used to measure its real depth by measuring the apparent depth. Since light coming from a denser medium such as glass or water is bent away from the normal, the depth at which an object inside that medium appears to be less than its real depth.
As the angle of incidence for a light ray travelling in a denser medium incident on the surface separating it from a rarer medium increases, the angle of refraction also increases. There comes a certain angle of incidence for which the corresponding angle of refraction is 90, which is known as the critical angle. If the incident angle is more than this the entire light is reflected back into the same medium. This phenomenon is known as Total Internal Reflection. From SLR cameras and simple periscopes to optical fibres and endoscopes, this phenomenon has been used in many fields today. Total reflecting prisms are even more efficient than than mirrors.