Total Internal Reflection and Critical Angle - Class XII

Comprehensive quiz covering critical angle calculations, total internal reflection conditions, and refractive index relationships - fundamental principles for understanding optical fiber technology

45 Questions Published

Questions

Question 1 Multiple Choice (Single Answer)

Critical angle of glass is $\theta _1$ and that of water is $\theta _2$. The critical angle for water and glass surface would be $(\mu _g=3/2, \mu _w=4/3)$

  1. less than $\theta _2$
  2. between $\theta _1$ and $\theta _2$
  3. greater than $\theta _2$
  4. less than $\theta _1$
Question 2 Multiple Choice (Single Answer)

A ray of light travelling in a transparent medium of refractive index $\mu$, falls on a surface separating the medium from air at an angle of incidence of $45^o$ . For which of the following value of $\mu$ the ray can undergo total internal reflection ?

  1. $\mu = 1.33$
  2. $\mu = 1.40$
  3. $\mu = 1.50$
  4. $\mu = 1.25$
Question 3 Multiple Choice (Single Answer)

A ray of light travelling in a transparent medium of refractive index $\mu $, falls on a surface separating the medium from air at an angle of incidence of $45^o$. For which of the following value of $\mu $ the ray can undergo total internal reflection?

  1. $\mu =1.33$
  2. $\mu =1.40$
  3. $\mu =1.50$
  4. $\mu =1.25$
Question 4 Multiple Choice (Single Answer)

Critical angle for light going from medium (i) to (ii) is $\theta $. The speed of light in medium (i) is v, then the speed of light in medium (ii) is

  1. $v\left( 1-\cos { \theta } \right) $
  2. $\dfrac { v }{ \sin { \theta } } $
  3. $\dfrac { v }{ \cos { \theta } } $
  4. $\dfrac { v }{ \left( 1-\sin { \theta } \right) } $
Question 5 Multiple Choice (Single Answer)

What will be the critical angle of water if $ _a\mu _w=\frac{4}{3}$

  1. $\displaystyle { 42 }^{ \circ }$
  2. $\displaystyle { 49 }^{ \circ }$
  3. $\displaystyle { 22 }^{ \circ }$
  4. $\displaystyle { 1 }^{ \circ }$
Question 6 Multiple Choice (Single Answer)

If a solid transparent object has an refractive index of $2.90$ and a clear liquid has a refractive index of $1.45$ then, which of the following must be true for total internal reflection to occur at the interface between these two media?

  1. Incident beam originates in the solid at an angle of incidence greater than $30^o$
  2. Incident beam originates in the liquid at an angle of incidence greater than $30^o$
  3. Incident beam originates in the solid at an angle of incidence greater than $60^o$
  4. Incident beam originates in the liquid at an angle of incidence greater than $60^o$
  5. Total internal reflection cannot occur
Question 7 Multiple Choice (Single Answer)

The index of refraction for diamond is $2.42$. For a diamond in the air (index of refraction = $1.00$), what is the smallest angle that a light ray inside the diamond can make with a normal and completely reflect back inside the diamond (the critical angle)?

  1. $90^o$
  2. $45^o$
  3. $68^o$
  4. $66^o$
  5. $24^o$
Question 8 Multiple Choice (Single Answer)

The critical angle for a medium with respect to air is $45^o$. The refractive index of that medium with respect to air is

  1. $\dfrac{\sqrt 3}{2}$
  2. $\dfrac{2}{\sqrt 3}$
  3. $\sqrt 2$
  4. $\dfrac{1}{\sqrt 2}$
Question 9 Multiple Choice (Single Answer)

A green light is incident from the water to the air - water interface at the critical angle ($\theta$). Select the correct statement.

  1. The spectrum of visible light whose frequency is more than that of green light will come out to the air medium.
  2. The entire spectrum of visible light will come out of the water at various angles to the normal.
  3. The entire spectrum of visible light will come out of the water at an angle of $90^o$ to the normal.
  4. The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.
Question 10 Multiple Choice (Single Answer)

A vertical pencil of rays comes from bottom of a tank filled with a liquid. When it is accelerated with an acceleration of 7.5 m/s$^2$, the ray is seen to be totally reflected by liquid surface. What is minimum possible refractive index of liquid?

  1. slightly greater than 4/3
  2. slightly greater than 5/3
  3. slightly greater than 1.5
  4. slightly greater than 1.75
Question 11 Multiple Choice (Single Answer)

If a ray of light passes from a denser medium to a rarer medium in a straight line, the angle of incidence must be ______

  1. $0^o$
  2. $30^o$
  3. $60^o$
  4. $90^o$
Question 12 Multiple Choice (Single Answer)

If the critical angle for the medium of prism is $C$ and the angle of prism is $A$, then there will be no emergent ray when-

  1. $A< 2C$
  2. $A=2C$
  3. $A> 2C$
  4. $A\ge 2C$
Question 13 Multiple Choice (Multiple Answers)

A ray of light traveling in a transparent medium falls on a surface separating the medium from air, at an angle of $ { 45 }^{ \circ  }$. The ray undergoes total internal reflection. if 'n' is the refractive index of the medium with respect to air, select the possible values of 'n' from the following.

  1. 1.3
  2. 1.4
  3. 1.5
  4. 1.6
Question 14 Multiple Choice (Single Answer)

When ray of light enters from one medium to another its velocity in second medium becomes double. the maximum value of angle of incidence so that total internal reflection may not take place will be

  1. $ { 60 }^{ \circ }$
  2. $ { 180 }^{ \circ }$
  3. $ { 90 }^{ \circ }$
  4. $ { 30 }^{ \circ }$
Question 15 Multiple Choice (Single Answer)

The speed of light in two media  I and II are $2.2\times 10^8 m/s$ and $ 2.4\times { 10 }^{ 8 }{ m }/{ s }$ respectively. The critical angle for light refracting from I to II medium will be

  1. $\sin^{-1}( { \frac { 12 }{ 11 } } )$
  2. $ \sin^{-1} ({ \frac { 11 }{ 12 } } )$
  3. $ \sin^{-1} ({ \frac { 12 }{ 24 } } )$
  4. $ \sin^{-1}( { \frac { 12 }{ 21 } }) $
Question 16 Multiple Choice (Single Answer)

An optical fiber ($\mu=1.72$) has a coating of glass ($\mu=1.5$). The critical angle for total internal reflection is

  1. $ { sin }^{ -1 }\left( \dfrac { 75 }{ 86 } \right) $
  2. $ { sin }^{ -1 }\left( \dfrac { 86 }{ 75 } \right) $
  3. $ { sin }^{ -1 }\left( 0.8 \right) $
  4. $ { sin }^{ -1 }\left( 0.82 \right) $
Question 17 Multiple Choice (Single Answer)

If the refractive index of water is 4/3 and that of glass is 5/3, then the critical angle of light entering from glass into water will be

  1. $ \sin^{-1} ({ \dfrac { 4 }{ 5 } } )$
  2. $ \sin^{-1} ({ \dfrac { 3 }{ 4 } }) $
  3. $ \sin^{-1} ({ \dfrac { 1 }{ 2 } } )$
  4. $ \sin^{-1} ({ \dfrac { 2 }{ 3 } }) $
Question 18 Multiple Choice (Single Answer)

The velocity of light in a medium is half its velocity in air. If a ray of light emerges from such a medium into air, the angle of incidence, at which it will be totally internally reflected, is

  1. $15^o$
  2. $30^o$
  3. $45^o$
  4. $60^o$
Question 19 Multiple Choice (Single Answer)

A ray of light traveling in glass $(\mu=3/2)$ is incident on a horizontal glass-air surface at the critical angle $\theta _C$. If a thin layer of water $(\mu =4/3)$ is now poured on the glass-air surface, the angle at which the ray emerges into air at the water-air surface is

  1. $60^o$
  2. $45^o$
  3. $90^o$
  4. $180^o$
Question 20 Multiple Choice (Single Answer)

A ray of light from a denser medium strikes a rarer medium at an angle of incidence $i$. The reflected and refracted rays make an angle of $\pi/2$ with each other. If the angles of reflection and refraction are $r$ and $r'$, then the critical angle will be

  1. $\tan^{-1}(\sin i)$
  2. $\sin^{-1}(\sin r)$
  3. $\sin^{-1}(\tan i)$
  4. $\sin^{-1}(\tan r)$
Question 21 Multiple Choice (Single Answer)

A fish looks upward at an unobstructed overcast sky. What total angle does the sky appear to subtend? (Take refractive index of water is $\sqrt 2)$

  1. $180^o$
  2. $90^o$
  3. $75^o$
  4. $60^o$
Question 22 Multiple Choice (Multiple Answers)

A ray of light traveling in a transparent medium falls on a surface separating the medium from air at an angle of incidence of $45^o$. The ray undergoes total internal reflection. If n is the refractive index of the medium with respect to air, select the possible value(s) of n from the following

  1. 1.3
  2. 1.4
  3. 1.5
  4. 1.6
Question 23 Multiple Choice (Single Answer)

The critical angle for glass-air is $45^o$ for the light of yellow colour. State whether it will be less than, equal to, or more than $45^o$ for  blue light?

  1. more than $45^o$
  2. less than $45^o$
  3. same as $45^o$
  4. cant say
Question 24 Multiple Choice (Single Answer)

The critical angle for glass-air is $45^o$ for the light of yellow colour. State whether it will be less than , equal to, or more than $45^o$ for  red light?

  1. more than $45^o$
  2. less than $45^o$
  3. same as $45^o$
  4. can't say
Question 25 Multiple Choice (Single Answer)

State the approximate value of the critical angle for (a) glass-air surface, (b) water-air surface (Given $\mu _{glass} =1.5, \mu _{water}=1.33$)

  1. (a) $49^o$, (b)$49^o$
  2. (a) $42^o$, (b)$42^o$
  3. (a) $42^o$, (b)$49^o$
  4. (a) $49^o$, (b)$42^o$
Question 26 Multiple Choice (Single Answer)

The critical angle for light going from medium X into medium Y is $\theta$. The speed of light in medium X is v, then speed of light in medium Y is

  1. $v(1 - cos \theta)$
  2. $v/sin \theta$
  3. $v/ cos \theta$
  4. $v cos \theta$
Question 27 Multiple Choice (Single Answer)

Light takes $t _1$ sec to travel a distance 'x' in vacuum and the same light takes $'t _2'$ sec to travel 10 cm in a medium. Critical angle for corresponding medium will be

  1. $\displaystyle sin^{-1} \left ( \frac{10 t _2}{t _1 x} \right )$
  2. $\displaystyle sin^{-1} \left ( \frac{t _2 x}{10 t _1 } \right )$
  3. $\displaystyle sin^{-1} \left ( \frac{10 t _1}{t _2 x } \right )$
  4. $\displaystyle sin^{-1} \left ( \frac{t _1 x}{10 t _2 } \right )$
Question 28 Multiple Choice (Single Answer)

A ray of light is travelling from glass to air. (Refractive index of glass $=1.5$). The angle of incidence is $50^o$.The deviation of the ray is

  1. $0^o$
  2. 80$^o$
  3. $50^o - sin^{-1} \displaystyle \left [ \frac{sin 50^o}{1.5} \right ]$
  4. $sin^{-1} \displaystyle \left [ \frac{sin 50^o}{1.5} \right ] - 50^o$
Question 29 Multiple Choice (Single Answer)

A light ray is incident at an angle ${30}^{o}$ on a transparent surface separating two media. If the angle of refraction is ${60}^{o}$ then critical angle is

  1. $\sin ^{ -1 }{ \left( \cfrac { 1 }{ \sqrt { 3 } } \right) } $
  2. $\sin ^{ -1 }{ \left( \sqrt { 3 } \right) } $
  3. $\sin ^{ -1 }{ \left( \cfrac { 2 }{ 3 } \right) } $
  4. ${45}^{o}$
Question 30 Multiple Choice (Single Answer)

Which of the following conditions are necessary for total internal reflection to take place at the boundary of two optical media ?
1. Light is passing from optically denser medium to optically rarer medium. 
2. Light is passing from optically rarer medium to optically denser medium. 
3. Angle of incidence is greater than the critical angle. 
4. Angle of incidence is less than the critical angle. 

  1. 1 and 3 only
  2. 2 and 4 only
  3. 3 and 4 only
  4. 1 and 4 only
Question 31 Multiple Choice (Single Answer)

A ray of light passing through an equilateral triangular prism gets deviated at least by $30^\circ$. Then, the refractive index of the material of the prism must be 

  1. $\leq \sqrt{2}$
  2. $\geq \sqrt{2}$
  3. $\leq \sqrt{3}$
  4. $\geq \sqrt{3}$
Question 32 Multiple Choice (Single Answer)

If the velocity of light in water is $2.25 \times {10}^{10}   cm$ per second and that is glass is $2 \times {10}^{10}   cm$ per second. A slab of this glass is immersed in water, what will be the critical angle of incidence of a ray of light tending to go from glass slab to water ?

  1. $\sin ^{ -1 }{ { 3 }/{ 5 } } $
  2. $\sin ^{ -1 }{ { 8 }/{ 9 } } $
  3. $\sin ^{ -1 }{ { 4 }/{ 5 } } $
  4. $\sin ^{ -1 }{ { 3 }/{ 4 } } $
Question 33 Multiple Choice (Single Answer)

A plane sound wave travelling with velocity $v$ in a medium $A$ reaches a point on the interface of medium $A$ and medium $B$. If velocity of sound in medium $B$ is $2v$, the angle of incidence for total internal reflection of the wave will be greater than ($\sin{30} = 0.5$ and $\sin{90} = 1$)

  1. $15$
  2. $30$
  3. $45$
  4. $90$
Question 34 Multiple Choice (Single Answer)

In vacuum, to travel distance $d$, light takes time $t$ and in medium to travel $5d$, it takes time $T$. The critical angle of the medium is :

  1. $\sin ^{ -1 }{ \left( \dfrac { 5T }{ t } \right) } $
  2. $\sin ^{ -1 }{ \left( \dfrac { 5t }{ 3T } \right) } $
  3. $\sin ^{ -1 }{ \left( \dfrac { 5t }{ T } \right) } $
  4. $\sin ^{ -1 }{ \left( \dfrac { 3t }{ 5T } \right) } $
Question 35 Multiple Choice (Single Answer)

The index of refraction for diamond is $2.42$. For a diamond in the air (index of refraction $=1.00$), what is the smallest angle that a light ray inside the diamond can make with a normal and completely reflect back inside the diamond (the critical angle)?

  1. $90^{\circ}$
  2. $45^{\circ}$
  3. $68^{\circ}$
  4. $66^{\circ}$
  5. $24^{\circ}$
Question 36 Multiple Choice (Single Answer)

A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence 45$^{\circ}$. The ray undergoes total internal reflection. The possible value of refractive index of the medium with respect to air is

  1. 1.245
  2. 1.324
  3. 1.414
  4. 1.524
Question 37 Multiple Choice (Single Answer)

The critical angle of a medium B with respect another medium A is 45$^{\circ}$ and the critical angle of a medium C with respect the medium B is 30$^{\circ}$. The critical angle of medium C with respect to A is :

  1. Less than 30$^{\circ}$
  2. Greater than 30$^{\circ}$
  3. 30$^{\circ}$
  4. Cannot be determined
Question 38 Multiple Choice (Single Answer)

 Light takes t$ _{1}$ sec to travel a distance x cm in vacuum and takes t$ _{2}$ sec to travel 10x cm in a medium.  The critical angle corresponding to the media is :                         

  1. $sin^{-1}(10t _{1}/t _{2}$)
  2. $sin^{-1}(t _{2}/10$)
  3. $sin^{-1}(1/t _{1}$)
  4. $sin^{-1}(t _{1}/10t _{2}$)
Question 39 Multiple Choice (Single Answer)

If the critical angle of the medium is 30$^{\circ}$, the velocity of light in that medium is :
(velocity of light in air  $3 \times 10^8 $ m/s)

  1. 6 x 10$^{8}$m/ s
  2. 3 x 10$^{8}$m /s
  3. 1.5 x 10$^{8}$m/ s
  4. 1 x 10$^{8}$m/s
Question 40 Multiple Choice (Single Answer)

A ray of light from a denser medium strikes a rarer medium at an angle of incidence $i$. If the reflected and refracted rays are mutually perpendicular to each other then the critical angle is :

  1. sin$^{-1}$ (tan i)
  2. cos$^{-1}$ (tan i)
  3. cot $^{-1}$ (tan i)
  4. cosec$^{-1}$ (tan i)
Question 41 Multiple Choice (Single Answer)

The critical angle for a medium with respect to air $45^0$. The refractive index of that medium with respect to air is:

  1. $\dfrac {\sqrt 3}{2}$
  2. $\dfrac {2}{\sqrt 3}$
  3. $\sqrt 2$
  4. $\dfrac {1}{\sqrt 2}$
Question 42 Multiple Choice (Single Answer)

A ray of light travelling in water is incident on its surface open to air. The angle of incidence is $\theta$, which is less than the critical angle. Then there will be?

  1. Only a reflected ray and no refracted ray
  2. Only a refracted ray and no reflected ray
  3. A reflected ray & a refracted ray and the $\angle$ between them would be less than $180^o-20^0$
  4. A reflected ray & a refracted ray and the $\angle$ between them would be greater than $180^o-2\theta$
Question 43 Multiple Choice (Single Answer)

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular brightspot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is

  1. 1.21
  2. 1.30
  3. 1.36
  4. 1.42
Question 44 Multiple Choice (Multiple Answers)

A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence $45^{\mathrm{o}}$ and undergoes total internal reflection. lf $\mu$ is the refractive index of medium the possible values of $\mu$ are

  1. $\mu =1.3$
  2. $\mu =1.4$
  3. $\mu =1.5$
  4. $\mu =1.6$