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
Questions
Critical angle of glass is $\theta _1$ and that of water is $\theta _2$. The critical angle for water and glass surface would be $(\mu _g=3/2, \mu _w=4/3)$
- less than $\theta _2$
- between $\theta _1$ and $\theta _2$
- greater than $\theta _2$
- less than $\theta _1$
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 ?
- $\mu = 1.33$
- $\mu = 1.40$
- $\mu = 1.50$
- $\mu = 1.25$
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?
- $\mu =1.33$
- $\mu =1.40$
- $\mu =1.50$
- $\mu =1.25$
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
- $v\left( 1-\cos { \theta } \right) $
- $\dfrac { v }{ \sin { \theta } } $
- $\dfrac { v }{ \cos { \theta } } $
- $\dfrac { v }{ \left( 1-\sin { \theta } \right) } $
What will be the critical angle of water if $ _a\mu _w=\frac{4}{3}$
- $\displaystyle { 42 }^{ \circ }$
- $\displaystyle { 49 }^{ \circ }$
- $\displaystyle { 22 }^{ \circ }$
- $\displaystyle { 1 }^{ \circ }$
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?
- Incident beam originates in the solid at an angle of incidence greater than $30^o$
- Incident beam originates in the liquid at an angle of incidence greater than $30^o$
- Incident beam originates in the solid at an angle of incidence greater than $60^o$
- Incident beam originates in the liquid at an angle of incidence greater than $60^o$
- Total internal reflection cannot occur
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)?
- $90^o$
- $45^o$
- $68^o$
- $66^o$
- $24^o$
The critical angle for a medium with respect to air is $45^o$. The refractive index of that medium with respect to air is
- $\dfrac{\sqrt 3}{2}$
- $\dfrac{2}{\sqrt 3}$
- $\sqrt 2$
- $\dfrac{1}{\sqrt 2}$
A green light is incident from the water to the air - water interface at the critical angle ($\theta$). Select the correct statement.
- The spectrum of visible light whose frequency is more than that of green light will come out to the air medium.
- The entire spectrum of visible light will come out of the water at various angles to the normal.
- The entire spectrum of visible light will come out of the water at an angle of $90^o$ to the normal.
- The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.
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?
- slightly greater than 4/3
- slightly greater than 5/3
- slightly greater than 1.5
- slightly greater than 1.75
If a ray of light passes from a denser medium to a rarer medium in a straight line, the angle of incidence must be ______
- $0^o$
- $30^o$
- $60^o$
- $90^o$
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-
- $A< 2C$
- $A=2C$
- $A> 2C$
- $A\ge 2C$
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.
- 1.3
- 1.4
- 1.5
- 1.6
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
- $ { 60 }^{ \circ }$
- $ { 180 }^{ \circ }$
- $ { 90 }^{ \circ }$
- $ { 30 }^{ \circ }$
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
- $\sin^{-1}( { \frac { 12 }{ 11 } } )$
- $ \sin^{-1} ({ \frac { 11 }{ 12 } } )$
- $ \sin^{-1} ({ \frac { 12 }{ 24 } } )$
- $ \sin^{-1}( { \frac { 12 }{ 21 } }) $
An optical fiber ($\mu=1.72$) has a coating of glass ($\mu=1.5$). The critical angle for total internal reflection is
- $ { sin }^{ -1 }\left( \dfrac { 75 }{ 86 } \right) $
- $ { sin }^{ -1 }\left( \dfrac { 86 }{ 75 } \right) $
- $ { sin }^{ -1 }\left( 0.8 \right) $
- $ { sin }^{ -1 }\left( 0.82 \right) $
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
- $ \sin^{-1} ({ \dfrac { 4 }{ 5 } } )$
- $ \sin^{-1} ({ \dfrac { 3 }{ 4 } }) $
- $ \sin^{-1} ({ \dfrac { 1 }{ 2 } } )$
- $ \sin^{-1} ({ \dfrac { 2 }{ 3 } }) $
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
- $15^o$
- $30^o$
- $45^o$
- $60^o$
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
- $60^o$
- $45^o$
- $90^o$
- $180^o$
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
- $\tan^{-1}(\sin i)$
- $\sin^{-1}(\sin r)$
- $\sin^{-1}(\tan i)$
- $\sin^{-1}(\tan r)$
A fish looks upward at an unobstructed overcast sky. What total angle does the sky appear to subtend? (Take refractive index of water is $\sqrt 2)$
- $180^o$
- $90^o$
- $75^o$
- $60^o$
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
- 1.3
- 1.4
- 1.5
- 1.6
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?
- more than $45^o$
- less than $45^o$
- same as $45^o$
- cant say
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?
- more than $45^o$
- less than $45^o$
- same as $45^o$
- can't say
State the approximate value of the critical angle for (a) glass-air surface, (b) water-air surface (Given $\mu _{glass} =1.5, \mu _{water}=1.33$)
- (a) $49^o$, (b)$49^o$
- (a) $42^o$, (b)$42^o$
- (a) $42^o$, (b)$49^o$
- (a) $49^o$, (b)$42^o$
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
- $v(1 - cos \theta)$
- $v/sin \theta$
- $v/ cos \theta$
- $v cos \theta$
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
- $\displaystyle sin^{-1} \left ( \frac{10 t _2}{t _1 x} \right )$
- $\displaystyle sin^{-1} \left ( \frac{t _2 x}{10 t _1 } \right )$
- $\displaystyle sin^{-1} \left ( \frac{10 t _1}{t _2 x } \right )$
- $\displaystyle sin^{-1} \left ( \frac{t _1 x}{10 t _2 } \right )$
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
- $0^o$
- 80$^o$
- $50^o - sin^{-1} \displaystyle \left [ \frac{sin 50^o}{1.5} \right ]$
- $sin^{-1} \displaystyle \left [ \frac{sin 50^o}{1.5} \right ] - 50^o$
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
- $\sin ^{ -1 }{ \left( \cfrac { 1 }{ \sqrt { 3 } } \right) } $
- $\sin ^{ -1 }{ \left( \sqrt { 3 } \right) } $
- $\sin ^{ -1 }{ \left( \cfrac { 2 }{ 3 } \right) } $
- ${45}^{o}$
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 and 3 only
- 2 and 4 only
- 3 and 4 only
- 1 and 4 only
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
- $\leq \sqrt{2}$
- $\geq \sqrt{2}$
- $\leq \sqrt{3}$
- $\geq \sqrt{3}$
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 ?
- $\sin ^{ -1 }{ { 3 }/{ 5 } } $
- $\sin ^{ -1 }{ { 8 }/{ 9 } } $
- $\sin ^{ -1 }{ { 4 }/{ 5 } } $
- $\sin ^{ -1 }{ { 3 }/{ 4 } } $
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 $\sin{90} = 1$)
- $15$
- $30$
- $45$
- $90$
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 :
- $\sin ^{ -1 }{ \left( \dfrac { 5T }{ t } \right) } $
- $\sin ^{ -1 }{ \left( \dfrac { 5t }{ 3T } \right) } $
- $\sin ^{ -1 }{ \left( \dfrac { 5t }{ T } \right) } $
- $\sin ^{ -1 }{ \left( \dfrac { 3t }{ 5T } \right) } $
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)?
- $90^{\circ}$
- $45^{\circ}$
- $68^{\circ}$
- $66^{\circ}$
- $24^{\circ}$
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
- 1.245
- 1.324
- 1.414
- 1.524
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 :
- Less than 30$^{\circ}$
- Greater than 30$^{\circ}$
- 30$^{\circ}$
- Cannot be determined
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 :
- $sin^{-1}(10t _{1}/t _{2}$)
- $sin^{-1}(t _{2}/10$)
- $sin^{-1}(1/t _{1}$)
- $sin^{-1}(t _{1}/10t _{2}$)
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)
- 6 x 10$^{8}$m/ s
- 3 x 10$^{8}$m /s
- 1.5 x 10$^{8}$m/ s
- 1 x 10$^{8}$m/s
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 :
- sin$^{-1}$ (tan i)
- cos$^{-1}$ (tan i)
- cot $^{-1}$ (tan i)
- cosec$^{-1}$ (tan i)
The critical angle for a medium with respect to air $45^0$. The refractive index of that medium with respect to air is:
- $\dfrac {\sqrt 3}{2}$
- $\dfrac {2}{\sqrt 3}$
- $\sqrt 2$
- $\dfrac {1}{\sqrt 2}$
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?
- Only a reflected ray and no refracted ray
- Only a refracted ray and no reflected ray
- A reflected ray & a refracted ray and the $\angle$ between them would be less than $180^o-20^0$
- A reflected ray & a refracted ray and the $\angle$ between them would be greater than $180^o-2\theta$
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
- 1.21
- 1.30
- 1.36
- 1.42
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
- $\mu =1.3$
- $\mu =1.4$
- $\mu =1.5$
- $\mu =1.6$