Total Internal Reflection (introduction)
Total internal reflection can be seen in many places in our life. Underwater plants in an aquarium, and their inverted images (top) formed by total internal reflection in the water-air surface. In optical instruments, right-angled prisms are widely used to divert the light rays. As the total internal reflection takes place within them. Mirage is formed in the desert due to TIR. So here we are going to discuss the topic of Total internal reflection and its applications.
TOTAL INTERNAL REFLECTION
When a ray passes from a denser to a rarer medium. The angle of refraction is greater than the angle of incidence as shown in fig.
When we gradually increase the incident angle. At a certain stage, the refracted angle will become . Then the incident angle of that stage is called the CRITICAL ANGLE. From fig
is a critical angle.
If the incident angle is increased further, then the entire light is back into the first medium, i.e reflection occurs. This phenomenon is called TOTAL INTERNAL REFLECTION.
” The phenomenon of reflection of total light when the light traveling in a denser medium strikes the interface separating the denser medium and the rarer medium at an angle greater than the critical angle is called TOTAL INTERNAL REFLECTION”
From fig, using Snell’s law
For total internal reflection incident angle must be greater than critical angle i.e
CONDITIONS OF TIR:-
1. The light should travel from a denser medium to rarer medium
2. The angle of incidence must be greater than the critical angle.
| Substance medium | Refractive index | Critical angle |
|---|---|---|
| Water | 1.33 | 48.75 |
| Crown glass | 1.52 | 41.14 |
| Dense flint glass | 1.62 | 37.31 |
| Diamond | 2.42 | 24.41 |
APPLICATION OF TOTAL INTERNAL REFLECTION
[ total internal reflection examples]
1. TOTALLY REFLECTING PRISM
It is a right-angled isosceles prism that turns the light through or
.
Refractive index of crown glass is 1.5
i.e critical angle of air-glass is
i.e if the incident angle is > for an air-glass interface, the TIR will occur. Such a prism is also used to invert images without changing their size.
2. OPTICAL FIBRES
These are also based on the phenomena of TIR.
Optical fibres is a very long fine quality fibre of glass or quartz (Core) coated with a thin layer of material of lower refractive index (Cladding). Light incident on one end of the fibre at a suitable angle. It undergoes repeated total internal reflection inside the fibre. It finally comes out of the other end, even if the fibre is bent or twisted in any form.
Optical fibres are nowadays used to carry telephone, television, and computer signals from one place to another.
The main requirement in fabricating optical fibers is that there should be very little absorption of light as it travels for ling distance inside them. This has been achieved by purification and special preparation of materials such as quartz. In silica glass fibers, it is possible to transmit more than 95% of the light over a fiber length of 1 km.
3. THE BRILLIANCE OF DIAMOND
It is due to the total internal reflection of light. R.I for a diamond is 2.42, so a critical angle for air interface is , which is very minimum for this interface. So it is a maximum chance to occur TIR when rays enter into a diamond. The diamond is also cut suitably so that light entering the diamond for any face falls at an angle greater than
. It suffers multiple TIR at the various face and remains within the diamond. Hence diamond sparkles.
4. MIRAGE
Mirage in desert/ hot place is caused by total internal reflection.
Due to heating of the earth on a summer day, the R.I of air near the surface of the earth becomes lesser than above it. Light from distant objects reaches the surface of the earth with an angle greater than the critical angle. So that TIR will take place and we the image of an object along with the object, creating an illusion of water near the object.
IMPORTANT QUESTIONS FOR PRACTICE
|
1. What is the critical angle for light going from a medium in which wavelength is 2. (a) In the following fig shows a cross-section of a ‘light pipe’ made of a glass fiber of refractive index 1.68. The outer covering of the pipe is made of material of refractive index 1.44. What is the range of the angles of the incident rays with the axis of the pipe for which total reflections inside the pipe take place? (b) What is the answer if there is no outer covering of the pipe?
3. At what angle should a ray of light be incident on the face of a prism of a refractive angle 4. A liquid of refractive index 1.5 is poured into a cylindrical jar of radius 20 cm up to height 20 cm. A small bulb is lighted at the centre of the bottom of the jar. Find the area of the liquid surface through which the light of the bulb passes into the jar. |
