Total Internal Reflection Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. Which of the following is a necessary condition for total internal reflection?

1. The angle of incidence in the rarer medium must be greater than the critical angle for the two media
2. The angle of reflection in the denser medium must be greater than the critical angle for the two media
3. The angle of incidence in the denser medium must be greater than the critical angle for the two media
4. The angle of incidence in the denser medium must be lesser than the critical angle for the two media

Ans. The correct answer is c. The angle of incidence in the denser medium must be greater than the critical angle for the two media

Explanation: The necessary conditions for total internal reflection:

• Light travels from an optically denser to an optically rarer medium
• The angle of incidence in the denser medium is larger than the critical angle for the two media.

Ques. Why is the sequence of colors in the secondary rainbow reverse of that in the primary rainbow?

1. Dispersion
2. Reflection of light
3. Two internal reflections
4. Refraction of light

Ans. The correct answer is c. Two internal reflections

Explanation: The sequence of colors in the secondary rainbow is the reverse of the primary rainbow because a secondary rainbow is produced by two internal reflections of light in water droplets, whereas a primary rainbow is formed by just one total internal reflection.

Ques. What causes haloes (rings) around the sun or the moon?

1. Total internal reflection
2. Dispersion
3. Reflection of light
4. Refraction of light

Ans. The correct answer is c. Reflection of light

Explanation: Haloes, or rings, are seen when the sun or moon is seen through a thin veil of high clouds. These are generated as a result of light reflection by icy crystals in the atmosphere.

Ques. Which of the following waves can undergo total internal reflection?

1. Sound waves
2. Water waves
3. Light waves
4. All of the above

Ans. The correct answer is d. All of the above

Explanation: All of the mentioned waves i.e. sound waves, light waves, and water waves can undergo total internal reflection.

Ques. The brilliance of a diamond is due to

1. Total internal reflection
2. Reflection
3. Diffraction
4. Refraction

Ans. The correct answer is a. Total internal reflection

Explanation: The total internal reflection of light within the diamond is the main cause of its brilliance.

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Short Answers Questions [2 Marks Questions]

Ques. Define total internal reflection.

Ans. Total internal reflection is the phenomenon in which waves arriving at the interface from one medium to another are entirely reflected back into the first medium rather than refracted into the second medium.

Ques. Define critical angle. What is the formula to find the critical angle?

Ans. The critical angle is the angle of incidence for which the angle of refraction becomes 90 degrees. It is the angle of incidence above which total internal reflection takes place.

The formula of critical angle is given by

sin C = µ₁/µ₂

Where

• µ₁ is the refractive index of the rarer medium
• µ₂ is the refraction index of the denser medium.

Ques. What are the conditions for the occurrence of total internal reflection?

Ans. The conditions for the occurrence of total internal reflection are

• The light must travel from denser to rarer medium.
• The angle of incidence must be greater than the critical angle for the given pair of media.

Ques. What is the reason for the shiny air bubble in the water?

Ans. The critical angle for the water-air interface is 48°45’. When light propagates from water (denser medium) is incident on the surface of the air bubble (rarer medium) at an angle greater than 48°45’, the total internal reflection takes place. Hence, the air bubble in water shines brilliantly.

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Long Answers Questions [3 Marks Questions]

Ques. What is the advantage of total internal reflection over reflection?

Ans. The advantages of total internal reflection over reflection are given below

• During the phenomenon of total internal reflection, 100% of the energy is reflected back, while in reflection some amount of energy is absorbed.
• Because some part of the light is absorbed and refracted, no object can produce a 100% reflection.
• Because of this characteristic, the phenomenon of total internal reflection finds extensive practical use in the creation of periscopes, binoculars, and particular types of cameras.

Ques. If the refractive indices for water and glass are 4/3 and 5/3 respectively and the light tends to go from glass to water, then what is the value of the critical angle?

Ans. Given

• Refractive index of water, µ_w = 4/3
• Refractive index of glass, µ_g = 5/3

According to Snell’s law, 

µ_g sin C = µ_w

Where C is the critical angle.

From the above equation, we get

Critical angle, C = sin^-1 (µ_w/µ_g)

On substituting the values, we get

C = sin^-1 [(4/3)/(5/3)]

⇒ C = sin^-1 (4/5) = sin^-1 (0.8000)

⇒ C = 53°8’

Ques. What are the advantages of a totally reflecting prism over a plane mirror?

Ans. The following are the advantages of a totally reflecting prism over a plane mirror

• In the case of a totally reflecting prism, the entire incident light energy is reflected. Hence there is no loss in the intensity of the reflected light. As a result of this, the image formed is bright. In a plane mirror, some incident light energy is absorbed by the reflecting surface. Therefore entire light energy is not reflected by the plane mirror. Hence there is some loss in the intensity of reflected light. As a result of this, the image formed is not so bright.

• In the case of a totally reflecting prism, only one bright image of an object is formed, while in the case of a plane mirror, a number of faint images in addition to a main image are formed.

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Very Long Answers Questions [5 Marks Questions]

Ques. Light travels in two media A and B with speeds 1.8 x 10⁸ m/s and 2.4 x 10⁸ m/s respectively. What is the critical angle between them?

Ans. Given

• Speed of the light in medium A, v_A = 1.8 x 10⁸ m/s
• Speed of light in medium B, v_B = 2.4 x 10⁸ m/s

Light travels slower in denser medium. Hence medium A is denser and medium B is rarer.

Here light travels from medium A to medium B.

Let C be the critical angle between them, then

sin C = 1/Bµ_A

Where Bµ_A is the refractive index of medium A with respect to medium B.

We can also write the above relation as

sin C = Aµ_B

Where Aµ_B represents the refractive of medium B with respect to medium A.

But, Aµ_B = (speed of light in medium A)/(speed of light in medium B) = v_A/v_B

⇒ sin C = v_A/v_B

On substituting the values, we get

sin C = (1.8 x 10⁸)/(2.4 x 10⁸)

⇒ sin C = 3/4

⇒ C = sin^-1 (3/4)

Ques. What are the applications of total internal reflection?

Ans. The following are the applications of total internal reflection

• Sparkling of Diamonds: Diamonds are known due to their amazing brilliance and shining appearance. The diamond's brilliance is caused by the phenomena of total internal reflection. Diamonds are cut and fashioned so that the critical angle for a light beam travelling from the diamond to the air is relatively small. The critical angle of the diamond is 23 degrees. As a result, when light enters the diamond from any face with an angle of incidence less than 24 degrees, light comes out of it, giving the diamond a sparkly and shining appearance.
• Optical Fibres: Optical fibres are made of high-quality composite glass fibre and consist of a core and cladding. The refractive index of the cladding material is lower than the refractive index of the core material. When a light beam moves at an angle from one end of an optical fibre to the other, it experiences repeated total internal reflections. This reflection occurs throughout the fibre, and the light then emerges from the opposite end. This concept is used to send and receive electrical signals.
• Mirage: It is an optical illusion that is most commonly seen on hot days in deserts or on roadways. The air near the ground is hotter than the air above, it is rarer. As a result, as light rays travel from the top air to the lower region, total internal reflection occurs, making the water layer appear to be at shorter distances.

Ques. Explain the formation of a mirage.

Ans. Mirage is an optical phenomenon that causes the appearance of a water layer over short distances on long straight roads. 

• Mirage is most common on sunny days when the earth is hot and the air is cool.
• This is produced by atmospheric refraction between different layers of air, giving us a watery appearance.
• When light rays pass through the atmosphere at different speeds through hot and cold air.
• As we all know, for a mirage to develop, the ground must be extremely hot and the surrounding air must be quite cold.
• The layer above the earth warms, and light rays are refracted (bent) as they go through the cold air layer into the hot air layer.
• The heated layer near the ground bends these light rays into a 'U' form, creating a water layer.

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