Total Internal Refraction
To understand the phenomenon of total internal refraction, suppose an interface XY separates a rarer medium (a) i.e. air from a denser medium (b) say water,
O is an object in the denser medium. A ray of light starting from O and incident normally along OA on XYpasses straight along AB. Another ray incident along OA1 derivates away from normal and is refracted alongA1B1. Clearly, angle of refraction is greater than the angle of incidence and it increases with increase in the angle of incidence. For particular value of i = C, the critical angle, the incident ray OA2 is refracted at <r = 90° and goes grazingly along the interface along the interface, along A2B2. When i > C as for the incident ray OA3, the ray goes along A3B3, as if it is reflected from interface XY. This phenomenon is called total internal reflection.
We may define total internal reflection as the phenomenon of reflection of light into a denser medium from an interface of this denser medium and a rarer medium.
Two essential conditions for total internal reflection are:
(i) Light should travel for a denser medium to a rarer medium.
(ii) Angle of incidence in denser medium should be greater than the critical angle for the pair of media in contact.
We may define critical angle for a pair of media in contact as the angle of incidence in the denser medium corresponding to which angle of refraction in the medium is 90°. It is represented by C and its value depends on the nature of media in contact.
Hence we conclude that when a ray of light travelling from an optically rarer medium is incident at an angle greater the ray critical angle for the pair of media in contact, the ray is totally reflected back into denser medium.
Relation between refractive index and critical angle
When i = C, r = 90°
Applying Snell’s law at A2,
µb sin C = µa sin 90° = µa × 1
µb/µa = 1/sinC
As µ depends on wavelength, therefore critical angle for the same pair of media in contact will be different for different colors. Table under shows of µ and C of some media are for = 5900 A°.
Refractive index µ and critical angle V for some media:
||µ of medium w.r.t. air
||Critical angle C
|Dense flint glass
Some application of total internal reflection
1. The brilliance of diamond is due to total internal reflection of light. µ for diamond is 2.42, so that critical angle for diamond air interface as calculated is 24.4°. The diamond is cut suitably so that light entering the diamond from any face falls at an angle greater than 24.4°; suffers multiple total internal reflections at the various faces, and remains within the diamond. Hence the diamond sparkles.
2. Mirage is an optical illusion which occurs usually in deserts on hot summer days. The object such as a tree appears to be inverted, as if the tree is on the bank of a pond of water.
On a hot summer day, temperature of air near the surface of earth is maximum. The upper layers of air have gradually decreasing temperature. Therefore, density and refractive index of air goes on increasing slightly with height above the surface of earth. A ray of light from the top O of a tree goes from denser to rarer medium bending away from normal. At a particular layer, when angle of incidence becomes greater than the critical angle, total internal reflection occurs, and the totally reflected ray reaches the observer along AE, appearing to come from I, the mirror image of O. thus inverted image of tree creates the impression of reflection from a pond of water.
3. Totally reflecting glass prisms totally reflecting glass prisms are right angled isosceles prisms which turn the light through 90° or 180°. They are based on the phenomenon of total internal reflection of light. µ for glass is 1.5 so that critical angle for glass-air interface is 42°. In totally reflecting glass prisms, angle of incidence is made 45° (>C). Hence light suffers total internal reflection as shown in fig.
A’B’ is image of AB seen through the prism PQR after total internal reflection of light. In fig. turning is through90° on account of one total reflection on face QR. In fig. turning is through 180° on account of two internal reflections on faces PQ and PR of the prism.
4. Optical fibres these are based on the phenomenon of total internal reflection.
Optical fibres consist of several thousands of very fine quality fibres of glass or quartz. The diameter of each fibre is of the order of 10-4 cm with refractive index of material being of the order of 1.5. The fibres are coated with a thin layer of material of lower refractive index of the order of 1.48.
Light incident on one end of the fibre at a small angle passes inside and undergoes repeated total internal reflections inside the fibre. It finally comes out of the other end, if the fibre is bent or twisted in any form and there is almost no loss of light through the sides of the fibre.
The only condition is that angle of incidence of light must be greater than the critical angle for the fibre material w.r.t. its coating.
Applications of optical fibres
1. A bundle of optical fibres is called light pipe, this price can transmit an image. Since the pipe can transmit an image. Since the pipe is flexible, it can be twisted in any optical examination of even the inaccessible parts of an equipment of human body, e.g. in endoscopy.
2. Optical fibres are used in transmission and reception of electrical signals by converting them first into light signals.
3. Optical fibres are used in telephone and other transmitting cables. Each can carry upto 2000 telephone messages without much loss of intensity.
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