Total Internal Reflection

Total Internal Reflection

When light travels from an optically denser medium to a rarer medium at the interface, it is partly reflected back into the same medium and partly refracted to the second medium. This reflection is called the internal reflection.

When a ray of light enters from a denser medium to a rarer medium, it bends away from the normal, for example, consider the ray AO₁ B shown in figure. The incident ray AO₁ is partially reflected (O₁C) and partially transmitted (O₁B) or refracted, the angle of refraction (r) being larger than the angle of incidence (i). As the angle of incidence increases, so does the angle of refraction, till for the ray AO₃, the angle of refraction is /2. The refracted ray is bent so much away from the normal that it grazes the surface at the interface between the two media. This is shown by the ray AO₃ D in the figure. If the angle of incidence is increased still further (e.g., the ray AO₄), refraction is not possible, and the incident ray is totally reflected. This is called total internal reflection.

The angle of incidence corresponding to an angle of refraction 90°, say angle of AO₃N, is called the critical angle (i_c ).

Substance Medium	Refractive index	Critical angle
Water	1.33	48.75
Crown glass	1.52	41.14
Dense flint glass	1.62	37.31
Diamond	2.42	24.41

Total internal reflection in nature and its technological applications:

i. Mirage:

· On hot summer days, the air near the ground becomes hotter than the air at higher levels. The refractive index of air increases with its density. Hotter air is less dense, and has smaller refractive index than the cooler air.

· If the air currents are small, that is, the air is still, the optical density at different layers of air increases with height. As a result, light from a tall object such as a tree, passes through a medium whose refractive index decreases towards the ground.

(a) A tree is seen by an observer at its place when the air above the ground is at uniform temperature, (b) When the layers of air close to the ground have varying temperature with hottest layers near the ground, light from a distant tree may undergo total internal reflection, and the apparent image of the tree may create an illusion to the observer that the tree is near a pool of water.

· Thus, a ray of light from such an object successively bends away from the normal and undergoes total internal reflection, if the angle of incidence for the air near the ground exceeds the critical angle. It is shown in the above diagram.

ii. Optical fibres:

· Nowadays optical fibres are extensively used for transmitting audio and video signals through long distances. Optical fibres too make use of the phenomenon of total internal reflection.

· It is fabricated with high quality composite glass/quartz fibres consisting of a core(having higher refractive index than clad) and cladding.

· When a signal in the form of light is directed at one end of the fibre at a suitable angle, it undergoes repeated total internal reflections along the length of the fibre and finally comes out at the other end as shown in the figure. Since light undergoes total internal reflection at each stage, there is no appreciable loss in the intensity of the light signal.