Total Internal Reflection
When a ray of light enters from a denser medium to a rarer medium, it bends away from the normal. Therefore, the angle of refraction is greater than the angle of incidence. The angle of incidence corresponding to an angle of refraction 90º is called the critical angle (ic) for the given pair of media.
For small angles of incidence, there occurs both reflection and refraction. Most of the light is refracted. The whole of the light is reflected back into the dense medium itself. This phenomenon is called total internal reflection (TIR).
Images formed by TIR are much brighter than those formed by the mirrors (or lenses). Some loss of intensity always takes place, when light is reflected from a mirror (or refracted through a lens).
For the case of critical angle, we have
where μd is the refractive index of the denser medium w.r.t. the rarer medium. The lesser the value of μ, the greater is the critical angle θC.
For a given pair of media, since μ depends on the wavelength of light the critical angle also depends on the wavelength. The greater will be the critical angle.
Total internal reflection in nature and its technological applications
- Mirage and Looming: Mirage is an optical illusion observed in deserts and roads on a hot day. When the air near the ground is hotter (and hence rare) than the air above, there occurs a continuous decrease of refractive index of air towards the ground. A ray of light from a point O of a tree is, therefore, refracted more and more away from the normal. Ultimately it gets totally reflected to reach the eye E. To the observer it appears to come from I, which is the image of O. This image gives the impression of reflection from a pond of water.
Similarly, in cold countries (near Polar Regions), the refractive index decreases with height. Due to TIR (fig. B), the image of a but appears hanging in the air. This is called looming.
- Diamond: Diamonds are known for their spectacular brilliance. Their brilliance is mainly due to the total internal reflection of light inside them. The critical angle for diamond-air interface (≅ 24.4°) is very small, therefore once light enters a diamond; it is very likely to undergo total internal reflection inside it. Diamonds found in nature rarely exhibit the brilliance for which they are known. It is the technical skill of a diamond cutter which makes diamonds to sparkle so brilliantly.
- Air bubbles in water shine due to TIR.
- The working of an optical fibre is due to multiple TIR inside it.
- Porro prisms used in periscopes or binoculars bend the ray due to TIR. Some examples are shown in the figure.
- Optical fibres: Optical fibres consist of several thousands of very long fine quality fibres of glass or quartz. The fibres are coated with a thin layer of material of lower refractive index. Light incident on one end of the fibre at a small angle passes inside and undergoes repeated total internal reflections inside the fibre. There is almost no loss of light on the sides of the fibre.