Total Internal Reflection

 Total Internal Reflection

  When a ray of light goes from denser to rarer medium it bends away from the normal and as the angle of incidence in denser medium increases, the angle of refraction in rare medium also increases and a certain angle, angle of refraction becomes 90, this angle of incidence is called critical angle.

 

When angle of incidence exceeds the critical angle then  light ray comes back in to the same medium after reflection from interface. This phenomenon is called Total Internal Reflection . 

Condition for Total Internal Reflection

•       Light should travel from a denser medium to a rarer medium.

•       Angle of incidence in denser medium should be greater than the critical angle for the pair of media in contact.

Relation between Refractive Index and Critical Angle (c )

Optical Path 

It is defined as distance travelled by light in vacuum in the same time in which it travels a given path length in medium.

For two media in contact

    

Field of vision of fish (or swimmer)

A fish (swimmer) inside the water can see the whole world through a cone with radius of base r = h tan C 

APPLICATIONS  OF TOTAL INTERNAL REFLECTION

The brilliance of Diamond

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 from

                                            =1/sin c is 24.4˚

The diamond is cut suitably so that light entering the diamond from any face fall at angle greater than 24.4˚. Therefore it suffers multiple total internal reflection at various faces and remain within the diamond and does not come out. Hence the diamond sparkles.

MIRAGE

It is an optical illusion which occurs usually in desert on hot summer days. The objects such as a tree appears to be inverted as if the tree is on the bank of pond water.

On a hot summer days, 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 of the tree goes from denser to rarer medium bending successively 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 it appears as if an inverted image of the tree is seen and the sand looks like a pool of water.

Totally reflecting glass prism

These are right angled 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 prism , angle of incidence is made 45˚ , which is greater than critical angle of the  glass air interface . Hence the light suffers total internal reflection.

Optical fibers

•     It consist of thousands of very long fine quality fibers of glass or quartz . The diameter of each fiber is of the order of 1/10000 cm with refractive index of material of the order of 1.5.

•       The fibers are created with a thin layer of material of lower refractive index of the order of 1.48.

•   Light incident on one end of the fiber at a small angle enters the fiber after reflection inside other end ,even if the fiber is bend or twisted in any form and there is almost no loss of light through the sides of the fiber.

•       Application of optical fibers:-

1. Optical fibers are used in transmission and reception of electrical signals by converting them first into light signals.
2. A bundle of optical fibers is called light pipe. This pipe can transmit an image .Hence it is used in medical and optical examination of even  the inaccessible parts of human body , as in endoscopy.
3. Optical fiber are used in telephone and other transmitting cables. Each fiber can carry upto 2000 telephone message without much loss of intensity.