Total Internal Reflection, definition, conditions, application

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Total Internal Reflection

Dear Candidates, General Science is a vital subject for all competitive exams including SSC CGL. RRB NTPC, CDS, UPSC. In physics, “Ray Optics” is one of the important topics, often 2-3 questions asked about this topic. In this topic we provide a detailed notes on “Total Internal Reflection”, “mirage formation in hot desert” and “Application of Total Internal Refection”. 

What is Total Internal Reflection?

• When light travels from an optically denser medium to a rarer medium on the surface of the two mediums, most of the part of the light reflected back into the optically denser medium and the remaining refracted to the rarer medium. This reflection phenomena is called the total internal reflection.

Total internal reflection, explanation

• When a ray of light enters from a denser medium (like Water or Glass) to a rarer medium (like Air), it bends away from the normal.

•  But there are two situations when the incident light formed a unique angle in which the reflected light pass through the surface of both dense and reared medium this phenomena is called Grazing emergence. And the angle is called critical angle.

• Now, if we increase the incident rays of light beyond the critical angel then at a certain angle the refraction of light stops and the incident light totally reflected by the denser medium, this phenomenon is called Total Internal Reflection.

• According to the law of reflection of light, here also the angle of incident light and the angle of reflection will be equal.

<i =<r

• In case of Total Internal Reflection the light reflected without any mirror or other polished surface.

Total internal reflection Diagram

• Consider the following ray diagram of total Internal Reflection _

Here,

AO1 is the incident ray

O1B’ is partially reflected ray and

O1B is partially transmitted ray

Total internal reflection Diagram
Total internal reflection Diagram

Now let’s see what happens if we gradually increase the value of the angle of incidence.

When we gradually increase the angle of incidence, then at a certain angle (ic= ∠AO3N)  the refracted ray (∠O3D) bent so much away from the normal that it passes through the surface at the interface between the two media. This phenomenon is called Grazing effect. As the bending refracted ray graze the interface between the two media.

 

• In the grazing effect phenomenon the angle of refraction is 90 deg. And the angle of incidence ∠AO3N, is called the critical angle (ic) for the given pair of media.

• If the angle of incidence is increased still further (e.g., the ray AO4), refraction is stopped, and the incident ray is totally reflected. This is called total internal reflection.

 

Critical angle of some transparent media with respect to air

Substance medium Critical angle Refractive index
Diamond 24.41 2.42
Dense flint glass 37.31 1.62
Crown glass 41.14 1.52
Water 48.75 1.33

Conditions for Total internal reflection in a nutshell

• There are two conditions for the total internal reflection to take place: They are:

1. The ray of light must travel from a denser medium into a rarer medium.

2. For a particular  pair of media, the angle of incidence in the denser medium must be greater than the critical angle.

Total internal reflection in nature

Mirage

Mirage is an optical illusion in which an observer observed a reflection of any tall object on the ground like a reflection of a tree in the water.

• Suppose, A thirsty traveler in a hot desert looking for some water. After grazing some time he fined some tall tree.

• For the total internal reflection the traveler will see a reflection of that tree on the sand, just as the reflection of a tree in the water. As a result, he may think that there is a source of water. In this way the traveler gets confused.

Technical Definition of Mirage

• Mirage is an optical illusion caused by atmospheric conditions, especially the appearance of a sheet of water in a desert or on a hot road caused by the refraction of light from the sky by heated air.

In where Mirage has generally been Found

• Mirage is especially common in hot deserts.
• It also found on a road during a hot summer day.

• As an example, you might have noticed that while moving in a car during a hot summer day, a distant patch of road, especially on a highway, appears to be wet. However, upon arrival at the scene we do not find any evidence of water.

How Mirage occur in a hot desert

• On hot summer days, the layer of air near the ground (sand) becomes hotter than the layer of air at higher levels.

• Cold air is much thicker than hot air. As the air temperature gradually decreases from low levels to high levels, it forms a few layers of denser and rarer medium and the optical density at different layers of air increases with height.

• Now, when a light from a tall object such as a tree, passes through the denser (upper level) to rarer (lower level or just below the upper level) medium the ray of light successively bends away from the normal and undergoes total internal reflection, if the angle of incidence of the air near the ground exceeds the critical angle.

 Mirage in a hot desert
Mirage in a hot desert

Total Internal Reflection in Diamond

♦ Have you ever wondered why a diamond is brighter than a piece of glass of the same shape?

• The brilliance of a diamond is mainly due to the total internal Reflection of light inside them.

• The critical angle for the diamond-air interface (≅ 24.4°) is very small, whereas the critical angle for the glass-air interface is 42°, therefore once light enters a diamond, it is very likely to undergo total internal reflection in it.

Lets understand this with some diagram

• Now we have known that, for total internal reflection the incident rays of light should form an angle which is greater than the critical angle. In the case of glass the critical angle is 420, it means all the light rays which formed and angle up to 420 refracted to the rarer medium (here Air) and it bend away from normal.

• But all the incident rays of light, which formed an angle greater than the critical angel totally reflected in the same (denser) medium.

• Now, if we incident 90 rays of light (one ray of light per 1 degree), then 42 rays of light will refract the rare medium and bend away from the normal, as because all the 42 rays of light passes through critical angle, on the other hand all the 48 rays of light (90-42) go through the total internal reflection, as it is passes through beyond the critical angel.

• Similarly, In case of Diamond only 24 rays (critical angle id =240) of light pass through critical angle, and 66 rays of light totally reflected by the surface of both the medium.

• From the diagram, we clearly see that in diamond the amount of light totally reflected is greater than the total reflected light in the glass. This is why a diamond is brighter than a piece of glass of the same shape.

Total Internal Reflection in Diamond
Total Internal Reflection in Diamond

 Total Internal Reflection in Prism

• Prisms designed to bend light by 90° or by 180° make use of total internal reflection. Such a prism is also used to invert images without changing their size .

• In the first two cases, the critical angle ic for the material of the prism must be less than 45°. We see from Table 9.1 that this is true for both crown glass and dense flint glass.

Total Internal Reflection in Prism
Total Internal Reflection in Prism

 Application of Total Internal Reflection

• In modern times, total internal reflection has many important applications such as_

Optical fibers
♦ Data Transmission:
• Optical fibers are extensively used for transmitting and receiving electrical signals which are converted to light by suitable transducers.

Total Internal Reflection in Optical fibres
Total Internal Reflection in Optical fibers

◘ Visual examination of internal organs:
• Optical fibers can also be used as a ‘light pipe’ to facilitate visual examination of internal organs like esophagus, stomach and intestines.

◘ Decorative lamp:
• A bundle of fine plastic fibers with their free ends fixed over an electric lamp and the other end forming a fountain like structure.

• When the lamp is switched on, the light travels from the bottom of each fiber and appears at the tip of its free end as a dot of light.

Decorative lamp
Decorative lamp

 Diagnostic tools like endoscopy
• To see the inside of the human body, such as the stomach and the duodenum.

  Sparkling Brilliance of Diamonds
• Total Internal Reflection phenomena used in polishing of diamonds, to create a sparkling Brilliance effect in diamond.

In optical instrument like Periscope, Binoculars
• Total Internal Reflection phenomena used in Periscope and Binoculars to bend light at 900 and 1800.

Cat’s eye reflectors
• Cat’s eye reflectors reflect the light rays from the headlamps of a car back to the driver. This makes the road visible at night.

 Single-lens Reflex Camera (SLR)
• In Single-lens Reflex Camera a pentaprism is used to reflect the light several times to correct the inversions caused by the lens, and align the image with the viewfinder.


You can also see:

List of Optical Instruments  

An Image formed by Plane Mirror


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