TOTAL INTERNAL REFLECTION (TIR) OF LIGHT :
Question: What is total internal reflection and critical angle? State the conditions under which total internal reflection of light occurs. Find the relation between critical angle and refractive index of a medium.
When a ray of light from point O in the denser medium falls at Q point on the interface separating denser and rarer medium, it is refracted along QQ'. As the angle of incidence increases say at point S, the refracted ray bends towards the interface (say along SS').
At a particular angle of incidence ($\theta_c$), the refracted ray TU travels along the surface of the interface and the angle of refraction is 90$^\circ$ (i.e. r = 90$^\circ$). The angle of incidence corresponding to which angle of refraction becomes 90$^\circ$ is called critical angle ($\theta_c$).
When the angle of incidence becomes greater than the critical angle, there is no refraction of light and whole of the incident light is reflected back to the denser medium. This phenomenon is known as Total internal reflection.
Definition: The phenomenon by virtue of which a ray of light travelling from a denser medium to a rarer medium is sent back to the same denser medium provided it strikes the interface of the denser and the rarer media at an angle more than the critical angle is called total internal reflection of light.
Conditions for Occurrence of Total Internal Reflection:
(i) The ray of light must travel from denser to rarer medium.
(ii) The angle of incidence must be more than the critical angle for the given pair of media.
Relation between refractive index of the medium and the critical angle:
When a ray of light goes from denser medium (2) to the rarer medium (1), then according to Snell's Law:
${}_{2}n_1 = \frac{\sin i}{\sin r}$
When angle of incidence, i, is equal to the critical angle $\theta_c$, then angle of refraction r = 90$^\circ$.
${}_{2}n_{1} = \frac{\sin \theta_c}{\sin 90^\circ}$
${}_{2}n_{1} = \sin \theta_c$
${}_{2}n_{1} = \frac{1}{{}_{1}n_{2}}$
${}_{1}n_2 = \frac{1}{ \sin \theta_c}$
$\sin \theta_c = \frac{1}{{}_{1}n_2}$
Application:
A right angled isosceles prism is called totally reflecting prism.
When the ray of light falls on a face of a right angled prism at an angle greater than 41.8$^\circ$, it will suffer total internal reflection.
The refractive index of glass is 1.5. The critical angle for glass-air interface is given by,
$\sin \theta_c = \frac{1}{1.5}$
$ \theta_c = \sin^{-1}(0.6667) = 41.8^\circ$
(a) Totally reflecting prism used to deviate the rays of light through 90$^\circ$.
This type of prism is used in the periscope.
(b) Totally reflecting prism used to deviate the rays of light through $180^\circ$.
The directions of incident rays and emergent rays are opposite to each other. Hence, the prism deviates the rays of light through $180^\circ$. The right angled isosceles prism which deviates the rays of light through $180^\circ$ is called porro-prism.
(c) Totally reflecting prism used to invert the image of an object without any change in size.
These rays emerge out of the prism undeviated and form an inverted image A'B' of the same size as that of the object AB. These prisms are called erecting prisms. They are used in binoculars.
(d) Optical Fibre.
Optical fibre is an extremely thin (radius of few microns) and long strand of very fine quality glass or quartz coated with a thin layer of material of refractive index less than the refractive index of the strand. The thin fibre of optical fibre is called core. The coating or surrounding layer of optical fibre is known as cladding. The refractive index of the core of a typical optical fibre is 1.458 and that of cladding is 1.440. The optical fibre is enclosed in a plastic jacket to protect it from any damage. The sleeve containing a bundle of optical fibres is called light pipe.
Principle: Optical fibre works on the principle of total internal reflection of light.
Working: When light falls at one end of the optical fibre, it gets refracted into the fibre. The refracted ray of light falls on the interface separating fibre and coating at an angle which is greater than the critical angle. The total internal reflection takes place time and again. The light travels the entire length of the fibre and arrives at the other end of the fibre without any loss in its intensity even if the fibre is rounded or curved.
Uses of optical fibres:
(1) Optical fibres are used to transmit light without any loss in its intensity over distances of several kilometre.
(2) Optical fibres are used in the manufacture of medical instruments called endoscopes used by the doctor to visually examine the stomach and intestines etc. of a patient.
(3) They are used in tele-communications for transmitting audio and video signals to long distances. The electrical signals are converted to light by special devices called transducers.