Total Internal Reflection and its Application

Total Internal Reflection

Consider an object at O in a denser medium.

A ray of light incident normally to XY goes undeviated along AB. As the angle of incidence increases, the angle of refraction also increases.

On increasing the angle of incidence for a particular value say i = C, the angle of refraction is found to be 90^o.

When i > C, the ray goes along A₄B₄ i.e., the ray is reflected into the denser medium itself. This phenomenon is called total internal reflection.

Sub Topics

Conditions for Total Internal Reflection
Relation between Refractive Index and Critical Angle
Note:
Applications of Total Internal Reflection

Conditions for Total Internal Reflection

Light should travel from a denser to rarer medium

i > C in denser medium for a pair of media in contact

Relation between Refractive Index and Critical Angle

According to Snell's law

When i = c, r = 90^o

$relation between refractive index critical angle$

Note:

m depends on wavelength and therefore 'c' for a same pair of media in contact will be different for different colors.

Applications of Total Internal Reflection

Mirage is an optical illusion, which occurs usually in deserts on hot summer days. On such a day, temperature of air near the earth is maximum and hence is rarer or lighter. The upper layers of air, which are relatively cool, are denser. A ray of light from the top of a tree travels from denser to rarer and bend away from the normal. At a particular layer, if the angle of incidence is greater than 'c', total internal reflection occurs. To far away observer, this ray i.e., AE appears to be coming from I i.e., mirror image of O. Thus inverted image of tree creates an optical illusion of reflection from a pond of water.

Right angled isosceles prism can turn light through 90^o or 180^o. This is based on total internal reflection. Since m for glass-air is 1.5, the value of 'C' is 42^o. In such a prism, the angle of incidence in the denser medium is 45^o(>C) and hence light suffers total internal reflection.

The brilliance of diamond is due to total internal reflection. Now m for diamond is 2.42^o and c (the critical angle) is 24.4^o for diamond-air interface. The faces of the diamond are so cut that a ray of light entering the diamond fall at angle greater than 24.4^o. This results in multiple, total internal reflections at various angles and remains within the diamond. Hence diamond sparkles.

Optical Fibers: Optical fibres consist of a very fine quality of glass or quartz fibres. They are coated with thin layer of material of lower refractive index than that of the fiber. The thickness of the strand is 10^-⁴. The optical fiber works on the principle of total internal reflection.

The word total means that reflection in the above case occurs with no loss of intensity. This phenomena enables doctors to inspect many internal body sites.

A Bundle of fibres transmit an image that can be inspected visually outside the body.

Optic fibers are as thick as a human hair. If a beam of light is send down a thin glass rod, total internal reflection traps the light inside the rod. This technique is called 'fiber optics'.

Fiber optics finds its use in the medical field too. Endoscopes use fiber optics technique. A patient can swallow a tube containing a fine glass fiber through which a doctor can examine the internal stomach parts and hence unnecessary surgeries can be avoided. 'Fiber optics' is used to destroy tumors. If a fiber optic cable is passed into the organ laser light can be directed along it. The laser is directed at the tumor cells and kills them.

The red plastic reflector on the back of a bicycle uses total internal reflection.