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Total Internal Reflection is a phenomenon that occurs when the rays of light travel from an optically denser medium to an optically rarer medium. It occurs when the angle of incidence is greater than the critical angle. Total Internal Reflection or TIR is also responsible for the shining of diamonds and forming different optical illusions such as a mirage.
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Key Terms: Lights, Refractive index, Mirror, Lenses, Optical Fibres, Sparkling of Diamonds, Mirage
Total Internal Reflection
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Total Internal reflection can be defined as a phenomenon that occurs when the ray of light travels from a more optically denser to an optically rarer medium.
| Have you ever put a coin in a glass of water and observed it? The coin is not visible from sideways but it is visible when looked at from the top. This happens due to the phenomenon of total internal reflection. |
When light is incident on a medium of lesser refractive index, the ray of light is bent away from the normal, therefore the exit angle of the light is greater than the incident angle. This reflection is commonly known as "internal reflection".
- The exit angle will then approach 90° for a critical incident angle θc, and for incident angles that are greater than the critical angle, there will be total internal reflection.
Total Internal Reflection
- When a light ray enters from a denser to a rarer medium, it bends away from the normal, leading to the angle of refraction is greater than the angle of incidence.
- When the angle of incidence is smaller, both reflection and refraction occur and most of the light gets refracted.
- The whole of the light is reflected back into the dense medium itself leading to the phenomenon of total internal reflection.
- The images formed hence are brighter than the ones formed by lenses or mirrors.
- This is because when light is refracted through a lens or reflected from a mirror, some loss of intensity of light always takes place with it.
- When the angle of refraction is 90 degrees, the corresponding angle of incidence is known as the critical angle (ic).
- When this critical angle is smaller than the angle of incidence, the incident ray of light is reflected back to the medium.
For example - when a light ray is passed from water to air, it gets refracted at the junction where the two mediums meet. As the light moves from a medium that has a higher refractive index to the one having a lower one, the light rays that are refracted bend away from the normal. When i (angle of incidence) > ic (critical angle), total internal reflection occurs.
The video below explains this:
Critical Angle & Total Reflection Detailed Video Explanation:
Total Internal Reflection Formula
Total internal reflection Formula: \(\begin{array}{l}\frac{n_{1}}{n_{2}}=\frac{sin r}{sin i}\end{array}\)
- Where n1 = Refractive index of the first medium
- n2 = Refractive index of second medium
- r = angle of refraction
- i = angle of incidence
And, \(\begin{array}{l}sin \theta =\frac{n_{2}}{n_{1}}\end{array}\)
Where Θ = the critical angle
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Conditions for Total Internal Reflection
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The conditions required for Total Internal Reflection to occur are as follows –
- The light ray moves from a denser to a rarer medium.
- The angle of incidence must be greater than the critical angle.
Applications in nature
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The phenomenon of TIR or Total Internal Reflection is seen across various elements in nature such as –
- Sparkling of Diamonds – Known for their sparkling brilliance, diamonds are an excellent example of the application of Total Internal Reflection. The sparkling of the diamond is due to internal reflection that occurs at various faces of the diamond when light enters it. The diamonds are cut and shaped in such a way that the critical angle for a light ray travelling from the diamond to the air is very small. The critical value of the diamond is 23 degrees. Hence when the light enters the diamond from any face with an angle of incidence less than 24 degrees, the light comes out from it and the diamond appears to be sparking and bright.
- Optical Fibres - The optical fibres are made up of several thousands of very long fibres of quartz or glass. These fibres are coated with a layer of material that has a lower refractive index. Thus the light entering undergoes multiple total internal reflections. Thus signals are transferred speedily with no loss of light on the sides of the fibre.
- Mirage - It is an optical illusion that is observed mainly in deserts or roads on a day with high temperatures. The air that is near to the ground is hotter than the air above so it is rarer. So when light rays travel from the upper air to the lower region, total internal reflection occurs and the water layer appears to be at shorter distances.
Mirage and Total Internal Reflection
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Things to Remember
- Total Internal reflection occurs when the ray of light travels from a more optically denser medium to a less optically denser medium.
- When a light ray enters from a denser to a rarer medium, it bends away from the normal, leading to the angle of refraction being greater than the angle of incidence.
- The whole of the light is reflected back into the dense medium itself leading to total internal reflection.
- The light ray moves from a denser to a rarer medium. The angle of incidence must be greater than the critical angle.
- Mirage is an optical illusion that is observed mainly in deserts or roads on a day with high temperatures.
Sample Questions
Ques 1. State the conditions for the phenomenon of the total internal reflection to take place. (Delhi 2010)
Ans. The two important conditions for the total internal reflection to take place are as follows,
- Light should travel from an optically denser medium to an optically rarer medium.
- The angle of incidence in the denser medium should be greater than the critical angle for the two media.
Ques 2. Calculate the speed of light in a medium whose critical angle is 30 degree. (Delhi 2010)
Ans. \(\because n = \frac{1}{sinC} = \frac{1}{sin 30^o}\) ∴ n = 2
⇒ n = \(\frac{c}{v}\) = 2 ⇒ \(\frac{3 * 10^8}{v}\) = 2
Therefore, the speed of light is v = 1.5 x 108 ms-1
Ques 3. Glass has an index of refraction of n = 1.5 while water has n = 1.33. What is the critical angle for light that travels from glass to water?
(a) 41.8°
(b) 62.5°
(c) 33.5°
(d) 41.4° (1 mark)
Ans. The equation used to find out the critical angle in total internal reflection is,
sinθc = \(\frac{n_r}{n_i}\)
Where, the subscripts c is the critical, r is the refraction, i is the incident index of refraction.
Now, by putting the values,
sinθc = \(\frac{1.33}{1.5}\)
θc = sin-1 (\(\frac{1.33}{1.5}\)) = 62.5o
Thus, the critical angle for the light that travels from glass to water is 62.5°.
Ques 4. State True or False and if false, state the reason why?
“For TIR to occur, the critical angle should be greater than the angle of incidence”
(A) True
(B) False (1 mark)
Ans. B) False
TIR occurs only when the angle of incidence is greater than the critical angle.
Ques 5. List down some applications of Total Internal Reflection. (2 marks)
Ans. Some of the applications of TIR are:
- Mirage
- It is due to TIR that air bubbles shine in the water.
- Working of optical fibres
- Porro prisms which are used in binoculars
- Shining of diamonds.
Ques 6. Define the term critical angle for a pair of media. A point source of monochromatic light S is kept at the centre of the bottom of a cylinder of radius 15.0 cm. The cylinder contains water with refractive index 4/3 to a height of 7.0 cm. Draw a ray diagram and calculate the area of the water surface through which the light emerges in air. (Delhi 2013C)
Ans. For an incident ray that is travelling from an optically denser medium to an optically rarer medium, the angle of incidence, for which the angle of refraction is 90°, is known as critical angle.
Alternatively,
μ = \(\frac{1}{sini_c}\)
sin ic = \(\frac{3}{4}\)
cos ic = \(\frac{\sqrt{7}}{4}\)
tan ic = \(\frac{3}{\sqrt{7}}\)
From figure, tan ic = \(\frac{x}{7}\)⇒ \(\frac{3}{\sqrt{7}}\)⇒\(\frac{x}{7}\)⇒x
= 3\(\sqrt{7}\) cm
Area= πx2 = 63π cm2
Ques 7. (a) What are the necessary conditions for the phenomenon of total internal reflection to occur?
(b) Write the relation between the refractive index and the critical angle for a given pair of optical media. (Delhi 2013)
Ans. (a) The necessary conditions for the phenomenon of total internal reflection to occur are,
- Light should travel from an optically denser medium to an optically rarer medium.
- The angle of incidence in the denser medium should be greater than the critical angle for the two media.
(b) The relation between the refractive index and critical angle for a given pair of optical media are,
As per Snell’s law,
\(\frac{sin i_c}{sin90^o} = n_{21} = \frac{n_1}{n_2}\)
∴ sin ic = \(\frac{n_1}{n_2}\)
Ques 8. A fish in a water tank sees the world as if it is at the vertex of the cone such that the circular base of the cone coincides with the surface of the water. Given the depth of water being ‘h’ where the fish is located and the critical angle for water-air interface being ic. find out by drawing a suitable ray diagram the relationship between the radius of the cone and the height h. (Delhi 2012C)
Ans.
From the figure above, if C is critical angle, then
tan C = r/h
⇒ r = h x tanC
⇒ r = h x \(\frac{sinC}{cosC}\)
⇒ e = h x \(\frac{sinC}{\sqrt{1 - sin^2 C}}\)[as sin2a + cos2a = 1]
We know that,
sin C = \(\frac{1}{\mu}\)
r = \(\frac{h}{\sqrt{\mu^2 - 1}}\)
Ques 9. Explain briefly how the phenomenon of total internal reflection is used in fibre optics? (Delhi 2011)
Ans. Applying the total internal reflection, fibre optics involves the transmission of light down fibres of plastic or glass. Meaning, the optical fibre uses the optical principle of total internal reflection in order to capture the light transmitted in an optical fibre and confine the light to the core of the fibre. An optical fibre consists of a light-carrying core in the centre, which is surrounded by cladding that behaves to trap light in the core. Cladding prevents the light from being transmitted between fibres in a bundle. The glass fibre is covered by a plastic buffer coating that protects it from the environment and allows smooth handling for splicing or termination.
The index of refraction of glass or any optical material is the measure of the speed of light in the material and the changes in the index of refraction causes light to bend. As shown in the figure below,
The refraction will cause the light to be reflected from the surface beyond a certain angle. And the optical fibre uses this reflection to trap fibre in the core of the fibre by choosing core as well as cladding materials with the proper index of refraction that will cause all the light to be reflected if the angle of the light is below a certain angle.
Ques 10. (a) For a ray of light travelling from a denser medium of refractive index n1 to a rarer medium of the same n2, prove that, n2/n1 = sin ic, where ic is the critical angle of incidence for the media.
(b) How is the above principle used for transmission of video signals using optical fibres? Explain with the help of a diagram. (Delhi 2008)
Ans. (a) As per the Snell’s law,
(a) Snell’s law is \(\frac{sin i}{sin r} = \frac{n^2}{n_1}\) ...(1)
Critical angle refers to the angle of incidence in denser medium for which the angle of refraction in the rarer medium is 90 degree.
i = ic and r = 90 degree
∴ From (1)
\(\frac{sin i_c}{sin 90^o} = \frac{n^2}{n_1}\) ⇒ \(\frac{n^2}{n_1}\) = sin ic
(b)
An optical fibre is the device that is based on total internal reflection with the help of which a light signal may be transmitted from one place to another with a negligible loss of energy. It is a very long and thin pipe of quartz (n = 1.7) with a thickness of nearly ≈ 10-4 m coated all around with a material of refractive index 1.5. A large number of these fibres held together form a light pipe which are used for communication of light signals. When a light ray is incident on one end at a small angle of incidence, it suffers refraction from air to quartz and strikes the air coating interface at an angle which is more than an critical angle and so suffers total internal reflection. This strikes the opposite face at an angle greater than the critical angle and so again suffers total internal reflection. Therefore, the ray inside the fibre suffers a multiple TIR and finally strikes the other end at an angle less than critical angle for quartz air interface and emerges in air.
The light signal is transmitted by this device without any appreciable loss of energy as there is no loss of energy in total internal reflection.
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