Refraction of light

When we place a pencil in a beaker containing water, we observe that the pencil appears to be bent at the point where it just enters water. Again, when we put a coin in the bottom of an empty cup and position our head so that the coin is just off sight, we can bring it into our view without moving head or the cup, by just pouring water in the cup.

The above two observations lead us to conclude that the ray of light bends at the boundaries of air and water medium. The phenomenon of bending of light as it passes from one medium to another is known as the refraction of light.

Refraction is the change in direction of a wave due to a change in its medium. It is essentially a surface phenomenon.

The phenomenon is mainly in governance to the law of conservation of energy and momentum. Due to change of medium, the phase velocity of the wave is changed but its frequency remains constant. Refraction of light is the most commonly observed phenomenon, but any type of wave can refract when it interacts with a medium, for example when sound waves pass from one medium into another or when water waves move into water of a different depth. Refraction is described by Snell’s law, which states that for a given pair of media and a wave with a single frequency, the ratio of the sines of the angle of incidence θ1 and angle of refraction θ2 is equivalent to the ratio of phase velocities (v1 / v2) in the two media, or equivalently, to the opposite ratio of the indices of refraction (n2 / n1):

An easy way to remember Snell’s law is that

The refractive index of the medium with respect to air (or vacuum) is called the absolute refractive index of the material. The refractive index for light going from first medium to second is equal to the reciprocal of the refractive index for light going from second to first medium.

The refractive index of glass with respect to water is equal to the ratio of refractive index of glass and refractive index of water with respect to air.

Similarly, the refractive index of water with respect to glass is:

The refractive index of the medium gives the light bending ability of that medium. Glass has higher refractive index than air. So more bending of light rays take place in glass. Glass is said to be optically denser medium and air is an optically rarer medium. The following table shows the refractive index of some common materials with respect to air or vacuum:

Measuring Refractive Index

The simplest way to measure the refractive index of a liquid is to measure its apparent depth and its real depth. We can place a scale inside a glass beaker containing liquid. Take another scale and hold it outside of the beaker by stand. View the scale from the top and adjust the outside scale until the bottom ends of both scales appear to be at the same level. Measure the heights h1 and h2 of the level of water surface on both scales. h1 and h2 are the real and apparent depth respectively. The refractive index of the liquid with respect to air.