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Total Internal Reflection

Consider an object at O in a denser medium.A ray of lightincident normally to XY goes undeviated along AB. As theangle of incidence increases, the angle of refraction alsoincreases.

On increasing the angle of incidence for a particular valuesay i = C, the angle of refraction is found to be 90

o.

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

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Light should travel from a denser to rarer medium

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

According to Snell's law

When i = c, r = 90o

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Applications of Total Internal Reflection

Mirage is an optical illusion, which occurs usually in desertson hot summer days. On such a day, temperature of air nearthe earth is maximum and hence is rarer or lighter. Theupper layers of air, which are relatively cool, are denser. Aray of light from the top of a tree travels from denser to rarerand bend away from the normal. At a particular layer, if theangle of incidence is greater than 'c', total internal reflection

occurs. To far away observer, this ray i.e., AE appears to becoming from I i.e., mirror image of O. Thus inverted image oftree creates an optical illusion of reflection from a pond ofwater.

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Right angled isosceles prism can turn light through90o

or 180o. This is based on total internal reflection.

Since m for glass-air is 1.5, the value of 'C' is 42o. In

such a prism, the angle of incidence in the densermedium 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

oand c (the critical angle) is

24.4o for diamond-air interface. The faces of the diamond areso cut that a ray of light entering the diamond fall at anglegreater than 24.4

o. This results in multiple, total internal

reflections at various angles and remains within the diamond.Hence diamond sparkles.


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Optical Fibers: Optical fibres consist of a very fine

quality of glass or quartz fibres. They are coated withthin layer of material of lower refractive index than thatof the fiber. The thickness of the strand is 10

-4. The

optical fiber works on the principle of total internalreflection.

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The word total means that reflection in the abovecase occurs with no loss of intensity. Thisphenomena enables doctors to inspect many internalbody sites.

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

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

Fiber optics finds its use in the medical field too.Endoscopes use fiber optics technique. A patient canswallow a tube containing a fine glass fiber through

which a doctor can examine the internal stomachparts and hence unnecessary surgeries can beavoided. 'Fiber optics' is used to destroy tumors. If afiber optic cable is passed into the organ laser lightcan be directed along it. The laser is directed at thetumor cells and kills them.

The red plastic reflector on the back of a bicycle uses

total internal reflection

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RefractionThe electromagnetic waves exhibit a number ofphenomenon. They undergo reflection, refraction,diffraction etc. In this section let us see what happenswhen a ray of light traveling from one medium toanother medium of different density.

It is a matter of common experience that a swimming

pool appears to have less depth than its actual depth.Similarly a straight stick partly immersed in waterappears to be bent at the surface of water. Theabove observations suggest that light changes itspath as it passes from one medium to another. Thischange in the path of light is due to the fact that thevelocity of light varies as it travels from one mediumto another.

Apparent Star Position due to Atmospheric Refraction

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The twinkling of stars is due to atmospheric refractionof starlight. Since the atmosphere bends starlighttowards the normal the apparent position of the staris slightly different from its actual position. Hence thestar appears slightly higher than its actual position.

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Atmospheric Refraction at Sunrise and Sunset

We have observed that the sun is visible at the horizon about 2 minutesbefore the actual sunrise, and about 2 minutes after the actual sunset.This is also because of atmospheric refraction. In this section we willlearn more about refraction.

What is Refraction?

The deviation in the path of light when it passes from one medium toanother medium of different density is called Refraction.

Wave Refraction

We see a boat on a see moving up and down along with the wavesand at the same time maintaining a horizontal movement. Imagine aparticle makes this kind of motion without water. We will beinvariably reminded of the motion of a boat along with the waves inthe sea. For the same reason, a horizontal motion with an up anddown oscillation is called a wave motion. Wave refraction is aphenomenon that takes when a wave passes through one mediumto another medium.

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Refraction of Light

All electromagnetic transmissions including light are wavemotions only. Since the wave length and the amplitudesare infinitely small, we indicate such wave motions asstraight lines in our study. Since light rays also indicate awave motion, concept involved in refraction of light and in

wave refraction are exactly the same.

We will define a ratio of velocity of a light ray in vacuum to thevelocity of the light ray in a given medium as a constant n. Thisconstant n is called as the refractive index of the medium or theindex of refraction of the medium.

n

=cv

This concept will be of great use later when we discuss the law ofrefraction. That is, the rule which is followed by the refraction of awave.

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Law of Refraction

As mentioned earlier, a light ray travels in different velocities indifferent mediums. In the process the direction of ray changeswhen it enters the second medium.As per Snells law, the sin of

the angle made by the ray with the normal to the surface ofinterface between the mediums is directly proportional to thevelocity in that medium. This law can be mathematicallyexplained with the following diagram.We know that the phenomenon of refraction is taking place because the speed oflight changes when it is travelling from one optical medium to another.

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Thus we can define refractive index in terms of the speed of lightin the two media.

As per Snells law,sinisinr= vIvR

Where,vI- The velocity of the incident lightvR - The velocity of the refracted lighti - The angle of incidencer - The angle of refraction

Now bringing the concept of refractive index of the media by therelationv = cn,

sinisinr= n2n1

That is, the ratio of sine of the angle of incidence and the sine ofthe angle of refraction of a ray when it crosses a medium is theratio of the refractive index of the second medium to that of thefirst medium. This is the mathematical form of law of refractionand known asSnells Law of Refraction after the scientistWillebrod Snellius who first formulated it.
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The refractive index of glass with respect to air is given bythe relation.

Airnglass = SpeedoflightinairSpeedoflightinglass = cvIn general, if a ray of light is passing from medium 1 tomedium 2, then

1n2 = Speedoflightinmedium 1Speedoflightinmedium 2

If the medium 1 is air or vacuum, the refractive index ofmedium 2 is referred to as the Absolute Refractive Index.

The Refractive Index of a medium depends on thefollowing factors:

The nature of the medium The color or wavelength of the incident light

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Look at the above diagram. A ray IO crosses frommedium 1 (Air) to medium 2 (Glass) at point O. Normallythe ray undergoes refraction at O. It bends away fromthe normal as OR

1if the medium 2 is lighter than 1 or

bends towards the normal as OR if the medium 2 isheavier than 1. In rare cases, if the medium has anegative permittivity and negative permeability, the raygets bent as ORn, on the opposite side of normal. In a

way it looks like as if the ray is reflected back, but to thesecond medium. This type of refraction is calledNegative Refraction.

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What Cause of Refraction?

What Causes Refraction of Light? A wave travels at different velocitiesin different mediums. But the frequency of the motion is not altered. Sincethe phase velocity is frequency times the wave length, a change in phasevelocity means a change in wave length. The change in velocity alsoresults change in direction of the wave propagation which we defined asthe wave refraction or refraction of a light ray.

Reflection and Refraction

When a light ray passes from one medium to another medium, the lightray may be totally absorbed by the boundary if it is an opaque surface. Insuch a case, no light is seen on the other medium. In some cases thelight ray may be sent back, following a rule, to the same medium if theboundary has the ability to do so. This phenomenon of light ray beingsent back is calledReflectionof light ray and the ability of theboundary is called as reflective property of the medium . However, inmost cases, the boundary is transparent and the light ray is able to enter

the second medium. However, the path of the light ray will no longer bethe same. Depending on many factors, it may bend towards the normal tothe surface, away from the normal to the surface or, in exceptional cases,the ray be even be reflected back. In any case the phenomenon of any of

such things happening is called the Refraction of the light ray. Therefraction of light ray also follows a certain rule.

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