Total internal reflection (T.I.R)

 

TOTAL INTERNAL REFLECTION:

We know that when light enters from denser medium to rarer medium it bends away to the normal.(i<r)

What happens when angle of incidence goes on increasing?.

Observe the diagram below.

So as we increase angle of incidence the refracted ray continue to bend further away from normal and at one particular angle of incidence it grazes through the interface. This angle is known as critical angle.

CRITICAL ANGLE: The angle of incidence for which refracted ray grazes through the interface when light is sent from denser to rarer medium is called critical angle.

At critical angle,   i=c  and  r=90⁰

Let C be the critical angle. Then r becomes 90⁰

we get, µ1/µ2 = sin 90/ sin c (applying Snell’s law)

 =>  µ₁/µ₂ = 1/sin c .

We get sin c = µ₂/ µ₁ .We know that µ₁/µ₂ i.e., µ₁₂ is called refractive

index of denser medium with respect to rarer medium

sin c = 1/µ₁₂

 

What happens when angle of incidence is further increased more than critical angle? (i>c)

In this case the refracted ray never enters into rarer medium but it gets reflected back into the denser medium. This phenomenon is known as Total Internal Reflection, in short T.I.R

T.I.R:

When the angle of the incidence is greater than critical angle, the light

ray gets reflected into the denser medium at the interface i.e., light never

enters the rarer medium. This phenomenon is called total internal reflection.

 

APPLICATIONS OF T.I.R IN DAILY LIFE:

       1)   FORMATION OF MIRAGE:

Mirage is an optical illusion where it appears that water has collected on the

road at a distant place but when we get there, we don’t find any water.

Do you know the reason why it appears so?

The formation of a mirage is the best example where refractive index of a

medium varies throughout the medium. During a hot summer day, air just

above the road surface is very hot and the air at higher altitudes is cool. It

means that the temperature decreases with height. 

As a result density of air increases with height. We know that refractive index of air increases with density. Thus the refractive index of air increases with height. So, the cooler air at the top has greater refractive index than hotter air just above the road. Light travels faster through the thinner hot air than through the denser cool air above it. When the light from a tall object such as tree or from the sky passes through a medium just above the road, whose refractive index decreases towards ground, it suffers, refraction and takes a curved path because of total internal reflection.

 This refracted light reaches the observer in a direction shown in Figure This appears to the observer as if the ray is reflected from the ground.

Hence we feel the illusion of water being present on road  which is the virtual image of the sky (mirage) and an inverted image of tree on the road.

 2)   BRILLIANCE OF DIAMOND:

 

Total internal reflection is the main reason for brilliance of diamonds. The critical angle of a diamond is very low (24.4^o). So if a light ray enters a diamond it is very likely to undergo continuous total internal reflections before coming out, which makes the diamond shine.

 3)   Optical fibres:

 

Total internal reflection is the basic principle behind working of optical fibre. An optical fibre is very thin fibre made of glass (or) plastic having radius about a micrometer (10-6 m). A bunch of such thin fibres form a light pipe.

The above Figure shows the principle of light

transmission by an optical fibre.

 

 The above Figure sketches a optical fibre cable. Because of the small

radius of the fibre, light going into it makes a nearly glancing incidence on the wall. The angle of incidence is greater than the critical angle and hence total internal reflection takes place. The light is thus transmitted along the fibre.

All organs of the human body are not accessible to the naked eye of

the doctor, for example intestines. The doctor inserts an optical fiber pipe

into the stomach through the mouth. Light is sent down through one set of

fibres in the pipe. This illuminates the inside of the stomach. The light

from the inside travels back through another set of fibres in the pipe and

the viewer gets the image at the outer end (generally fed to the computer

screen).

The other important application of fibre optics is to transmit communication signals through light pipes. For example, about 2000 telephone signals, appropriately mixed with light waves, may be simultaneously transmitted through a typical optical fibre. The clarity of the signals transmitted in this way is much better than other conventional methods.

 

 

     4)    LOOMING:

 

Looming is an optical illusion which increases the apparently elevation of a object and sometimes allows an observer to see objects that are located below the horizon.

It is common in polar regions (low temperatures), Due to the cold water (and ice), the air around it is cold and dense. As we go upwards into the atmosphere, the temperature gradually increased hence air is rarer.

Light rays from ship present below the horizon go up from denser to rarer air mediums and are totally internally reflected downwards by the air layers. These rays are received by an observer on shore who is able to see a virtual image of the ship in the sky.

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