DC Pandey Solutions (JEE Main): Refraction of Light- 1 | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


Exercises 
For JEE Main 
Note In different books refractive index has been represented by the symbol n and ?. So in our 
book we have used both symbols at different places. 
  Subjective Questions 
  Refraction of Light 
Q 1.  A ray of light falls on a glass plate of refractive index n = 1.5. What is the angle of incidence of 
the ray if the angle between the reflected and refracted rays is 90°? 
Q 2.  The laws of reflection or refraction are the same for sound as for light. The index of refraction of a 
medium (for sound) is defined as the ratio of the speed of sound in air 343 m/s to the speed of 
sound in the medium. 
  (a) What is the index of refraction (for sound) of water (v = 1498 m/s)? 
  (b) What is the critical angle ?, for total reflection of sound from water? 
Q 3.  Light from a sodium lamp ( ?
0
 
= 589 run) passes through a tank of glycerin (refractive index 
=1.47) 20 m long in a time t
1
. If it takes a time t
2
 to transverse the same tank when filled with 
carbon disulfide (index = 1.63),determine the difference t
2
 - t
1
. 
Q 4.  A light beam of wavelength 600 run in air passes through film 1 (n
1
 = 1.2) of thickness 1.0 ?m, 
then through film 2 (air) of thickness 1.5 ?m, and finally through film 3 (n
3
 = 18) of thickness l.0 
?m. 
  (a) Which film does the light cross in the least time, and what is that least time? 
  (b) What are the total number of wavelengths (at any instant) across all three films together? 
Q 5.  A plane harmonic infrared wave travelling through a transparent medium is given by  
   
14
x 0x 7
y
E (y, t) E sin 2 3 10 t
5 10
?
??
? ? ? ?
??
?
??
 
in SI units. Determine refractive index of the medium at that frequency, and the vacuum 
wavelength of the disturbance. 
  Refraction from Plane and Spherical Surface 
Q 6.  A plate with plane parallel faces having refractive index 1.8 rests on a plane mirror. A light ray is 
incident on the upper face of the plate at 60°. How far from the entry point will the ray emerge 
after reflection by the mirror. The plate is 6 cm thick? 
 
Q 7.  A pile 4 m high driven into the bottom of a lake is 1 m above the water. Determine the length of 
the shadow of the pile on the bottom of the lake if the sun rays make an angle of 45° with the 
water surface. The refractive index of water is 4/3. 
Page 2


Exercises 
For JEE Main 
Note In different books refractive index has been represented by the symbol n and ?. So in our 
book we have used both symbols at different places. 
  Subjective Questions 
  Refraction of Light 
Q 1.  A ray of light falls on a glass plate of refractive index n = 1.5. What is the angle of incidence of 
the ray if the angle between the reflected and refracted rays is 90°? 
Q 2.  The laws of reflection or refraction are the same for sound as for light. The index of refraction of a 
medium (for sound) is defined as the ratio of the speed of sound in air 343 m/s to the speed of 
sound in the medium. 
  (a) What is the index of refraction (for sound) of water (v = 1498 m/s)? 
  (b) What is the critical angle ?, for total reflection of sound from water? 
Q 3.  Light from a sodium lamp ( ?
0
 
= 589 run) passes through a tank of glycerin (refractive index 
=1.47) 20 m long in a time t
1
. If it takes a time t
2
 to transverse the same tank when filled with 
carbon disulfide (index = 1.63),determine the difference t
2
 - t
1
. 
Q 4.  A light beam of wavelength 600 run in air passes through film 1 (n
1
 = 1.2) of thickness 1.0 ?m, 
then through film 2 (air) of thickness 1.5 ?m, and finally through film 3 (n
3
 = 18) of thickness l.0 
?m. 
  (a) Which film does the light cross in the least time, and what is that least time? 
  (b) What are the total number of wavelengths (at any instant) across all three films together? 
Q 5.  A plane harmonic infrared wave travelling through a transparent medium is given by  
   
14
x 0x 7
y
E (y, t) E sin 2 3 10 t
5 10
?
??
? ? ? ?
??
?
??
 
in SI units. Determine refractive index of the medium at that frequency, and the vacuum 
wavelength of the disturbance. 
  Refraction from Plane and Spherical Surface 
Q 6.  A plate with plane parallel faces having refractive index 1.8 rests on a plane mirror. A light ray is 
incident on the upper face of the plate at 60°. How far from the entry point will the ray emerge 
after reflection by the mirror. The plate is 6 cm thick? 
 
Q 7.  A pile 4 m high driven into the bottom of a lake is 1 m above the water. Determine the length of 
the shadow of the pile on the bottom of the lake if the sun rays make an angle of 45° with the 
water surface. The refractive index of water is 4/3. 
Q 8.  An object is at a distance of d = 2.5 cm from the surface of a glass sphere with a radius R = 10cm 
Find the position of the final image produced by the sphere. The refractive index of glass is ?
 
= 
1.5. 
Q 9.  An air bubble is seen inside a solid sphere of glass (n = 1.5) of 4.0 cm diameter at a distance of 1.0 
cm from the surface of the sphere (on seeing along the diameter). Determine the real position of 
the bubble inside the sphere. 
Q 10.  Find the position of final image of an object O as shown in figure. 
 
Q 11.  One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm infront of the 
unsilvered face forms an image 10 cm behind the silvered face. Find the refractive index of glass. 
Consider all the three steps. 
Q 12.  A shallow glass dish is 4.00 cm wide at the bottom, as shown in figure. When an observer's eye is 
positioned as shown, the observer sees the edge of the bottom of the empty dish. When this dish is 
filled with water, the observer sees the centre
 
of the bottom of the dish. Find the height of the dish 
?
w
 
= 4/3. 
 
Q 13.  A glass prism in the shape of a quarter-cylinder lies on a horizontal table. A uniform, horizontal 
light beam falls on its vertical plane surface, as shown in the figure. If the radius of the cylinder is 
R = 5 cm and the refractive index of the glass is n = 1.5, where, on the table beyond the cylinder, 
will a path of light be found? 
 
Q 14.  A glass sphere with 10 cm radius has a 5 cm radius spherical hole at its centre. A narrow beam of 
parallel light is directed into the sphere. Where, if anywhere, will the sphere produce an image? 
The index of refraction of the glass is 1.50. 
Q 15.  A glass sphere has a radius of 5.0 cm and a refractive index of 1.6. A paperweight is constructed 
by slicing through the sphere on a plate that is 2.0 cm from the centre of the sphere and 
perpendicular to a radius of the sphere that passes through the centre of the circle formed by the 
intersection of the plane and the sphere. The paperweight is placed on a table and viewed from 
directly above an observer who is 8.0 cm from the tabletop, as shown in figure. When viewed 
through the paperweight, how far away does the tabletop appear to the observer? 
Page 3


Exercises 
For JEE Main 
Note In different books refractive index has been represented by the symbol n and ?. So in our 
book we have used both symbols at different places. 
  Subjective Questions 
  Refraction of Light 
Q 1.  A ray of light falls on a glass plate of refractive index n = 1.5. What is the angle of incidence of 
the ray if the angle between the reflected and refracted rays is 90°? 
Q 2.  The laws of reflection or refraction are the same for sound as for light. The index of refraction of a 
medium (for sound) is defined as the ratio of the speed of sound in air 343 m/s to the speed of 
sound in the medium. 
  (a) What is the index of refraction (for sound) of water (v = 1498 m/s)? 
  (b) What is the critical angle ?, for total reflection of sound from water? 
Q 3.  Light from a sodium lamp ( ?
0
 
= 589 run) passes through a tank of glycerin (refractive index 
=1.47) 20 m long in a time t
1
. If it takes a time t
2
 to transverse the same tank when filled with 
carbon disulfide (index = 1.63),determine the difference t
2
 - t
1
. 
Q 4.  A light beam of wavelength 600 run in air passes through film 1 (n
1
 = 1.2) of thickness 1.0 ?m, 
then through film 2 (air) of thickness 1.5 ?m, and finally through film 3 (n
3
 = 18) of thickness l.0 
?m. 
  (a) Which film does the light cross in the least time, and what is that least time? 
  (b) What are the total number of wavelengths (at any instant) across all three films together? 
Q 5.  A plane harmonic infrared wave travelling through a transparent medium is given by  
   
14
x 0x 7
y
E (y, t) E sin 2 3 10 t
5 10
?
??
? ? ? ?
??
?
??
 
in SI units. Determine refractive index of the medium at that frequency, and the vacuum 
wavelength of the disturbance. 
  Refraction from Plane and Spherical Surface 
Q 6.  A plate with plane parallel faces having refractive index 1.8 rests on a plane mirror. A light ray is 
incident on the upper face of the plate at 60°. How far from the entry point will the ray emerge 
after reflection by the mirror. The plate is 6 cm thick? 
 
Q 7.  A pile 4 m high driven into the bottom of a lake is 1 m above the water. Determine the length of 
the shadow of the pile on the bottom of the lake if the sun rays make an angle of 45° with the 
water surface. The refractive index of water is 4/3. 
Q 8.  An object is at a distance of d = 2.5 cm from the surface of a glass sphere with a radius R = 10cm 
Find the position of the final image produced by the sphere. The refractive index of glass is ?
 
= 
1.5. 
Q 9.  An air bubble is seen inside a solid sphere of glass (n = 1.5) of 4.0 cm diameter at a distance of 1.0 
cm from the surface of the sphere (on seeing along the diameter). Determine the real position of 
the bubble inside the sphere. 
Q 10.  Find the position of final image of an object O as shown in figure. 
 
Q 11.  One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm infront of the 
unsilvered face forms an image 10 cm behind the silvered face. Find the refractive index of glass. 
Consider all the three steps. 
Q 12.  A shallow glass dish is 4.00 cm wide at the bottom, as shown in figure. When an observer's eye is 
positioned as shown, the observer sees the edge of the bottom of the empty dish. When this dish is 
filled with water, the observer sees the centre
 
of the bottom of the dish. Find the height of the dish 
?
w
 
= 4/3. 
 
Q 13.  A glass prism in the shape of a quarter-cylinder lies on a horizontal table. A uniform, horizontal 
light beam falls on its vertical plane surface, as shown in the figure. If the radius of the cylinder is 
R = 5 cm and the refractive index of the glass is n = 1.5, where, on the table beyond the cylinder, 
will a path of light be found? 
 
Q 14.  A glass sphere with 10 cm radius has a 5 cm radius spherical hole at its centre. A narrow beam of 
parallel light is directed into the sphere. Where, if anywhere, will the sphere produce an image? 
The index of refraction of the glass is 1.50. 
Q 15.  A glass sphere has a radius of 5.0 cm and a refractive index of 1.6. A paperweight is constructed 
by slicing through the sphere on a plate that is 2.0 cm from the centre of the sphere and 
perpendicular to a radius of the sphere that passes through the centre of the circle formed by the 
intersection of the plane and the sphere. The paperweight is placed on a table and viewed from 
directly above an observer who is 8.0 cm from the tabletop, as shown in figure. When viewed 
through the paperweight, how far away does the tabletop appear to the observer? 
 
Q 16.  A fish is rising up vertically inside a pond with velocity 4 cm/s, and notices a bird, which is diving 
downward and its velocity appears to be 16 cm/s (to the fish). What is the real velocity of the 
diving bird, if refractive index of water is 4/3 ? 
  Thin Lenses 
Q 17.  A lens with a focal length of 16 cm produces a sharp image of an object in two positions, which 
are 60 cm apart. Find the distance from the object to the screen. 
Q 18.  Two glasses with refractive indices of 1.5 and 1.7 are used to make two identical double convex 
lenses. 
  (a) Find the ratio between their focal lengths. 
(b) How will each of these lenses act on a ray parallel to its optical axis if the lenses are 
submerged into a transparent liquid with a refractive index of 1.6? 
Q 19.  A converging beam of rays is incident on a diverging lens. Having passed through the lens the 
rays intersect at a point 15 cm from the lens. If the lens is removed, the point where the rays meet, 
move 5 cm closer to the mounting that holds the lens. Find the focal length of the lens. 
Q 20.  The distance between two point sources of light is 24 cm. Find out where would you place a 
converging lens of focal length of 9 cm, so that the images of both the sources are formed at the 
same point. 
Q 21.  Two thin converging lenses are placed on a common axis so that the centre of one of them 
coincides with the focus of the other. An object is placed at a distance twice the focal length from 
the left-hand lens. Where will its image be? What is the lateral magnification? The focal length of 
each lens is f. 
Q 22.  A source of light is located at double focal length from a convergent lens. The focal length of the 
lens is f = 30 cm At what distance from the lens should a flat mirror be placed so that the rays 
reflected from the mirror are parallel after passing through the lens for the second time? 
Q 23.  A parallel beam of rays is incident on a convergent lens with a focal length of 40 cm. Where a 
divergent lens with a focal length of 15 cm be placed for the beam of rays to remain parallel after 
passing through the two lenses. 
Q 24.  An optical system consists of two convergent lenses with focal lengths f
1
 = 20 cm and f
2
 = 10 cm 
The distance between the lenses is d = 30 cm An object is placed at a distance of 30 cm from the 
first lens. At what distance from the second lens will the image be obtained? 
Q 25.  Determine the position of the image produced by an optical system consisting of a concave mirror 
with a focal length of 10 cm and a convergent lens with a focal length of 20 cm. The distance from 
the mirror to the lens is 30 cm and from the lens to the object is 40 cm. Consider only two steps. 
Plot the image. 
Page 4


Exercises 
For JEE Main 
Note In different books refractive index has been represented by the symbol n and ?. So in our 
book we have used both symbols at different places. 
  Subjective Questions 
  Refraction of Light 
Q 1.  A ray of light falls on a glass plate of refractive index n = 1.5. What is the angle of incidence of 
the ray if the angle between the reflected and refracted rays is 90°? 
Q 2.  The laws of reflection or refraction are the same for sound as for light. The index of refraction of a 
medium (for sound) is defined as the ratio of the speed of sound in air 343 m/s to the speed of 
sound in the medium. 
  (a) What is the index of refraction (for sound) of water (v = 1498 m/s)? 
  (b) What is the critical angle ?, for total reflection of sound from water? 
Q 3.  Light from a sodium lamp ( ?
0
 
= 589 run) passes through a tank of glycerin (refractive index 
=1.47) 20 m long in a time t
1
. If it takes a time t
2
 to transverse the same tank when filled with 
carbon disulfide (index = 1.63),determine the difference t
2
 - t
1
. 
Q 4.  A light beam of wavelength 600 run in air passes through film 1 (n
1
 = 1.2) of thickness 1.0 ?m, 
then through film 2 (air) of thickness 1.5 ?m, and finally through film 3 (n
3
 = 18) of thickness l.0 
?m. 
  (a) Which film does the light cross in the least time, and what is that least time? 
  (b) What are the total number of wavelengths (at any instant) across all three films together? 
Q 5.  A plane harmonic infrared wave travelling through a transparent medium is given by  
   
14
x 0x 7
y
E (y, t) E sin 2 3 10 t
5 10
?
??
? ? ? ?
??
?
??
 
in SI units. Determine refractive index of the medium at that frequency, and the vacuum 
wavelength of the disturbance. 
  Refraction from Plane and Spherical Surface 
Q 6.  A plate with plane parallel faces having refractive index 1.8 rests on a plane mirror. A light ray is 
incident on the upper face of the plate at 60°. How far from the entry point will the ray emerge 
after reflection by the mirror. The plate is 6 cm thick? 
 
Q 7.  A pile 4 m high driven into the bottom of a lake is 1 m above the water. Determine the length of 
the shadow of the pile on the bottom of the lake if the sun rays make an angle of 45° with the 
water surface. The refractive index of water is 4/3. 
Q 8.  An object is at a distance of d = 2.5 cm from the surface of a glass sphere with a radius R = 10cm 
Find the position of the final image produced by the sphere. The refractive index of glass is ?
 
= 
1.5. 
Q 9.  An air bubble is seen inside a solid sphere of glass (n = 1.5) of 4.0 cm diameter at a distance of 1.0 
cm from the surface of the sphere (on seeing along the diameter). Determine the real position of 
the bubble inside the sphere. 
Q 10.  Find the position of final image of an object O as shown in figure. 
 
Q 11.  One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm infront of the 
unsilvered face forms an image 10 cm behind the silvered face. Find the refractive index of glass. 
Consider all the three steps. 
Q 12.  A shallow glass dish is 4.00 cm wide at the bottom, as shown in figure. When an observer's eye is 
positioned as shown, the observer sees the edge of the bottom of the empty dish. When this dish is 
filled with water, the observer sees the centre
 
of the bottom of the dish. Find the height of the dish 
?
w
 
= 4/3. 
 
Q 13.  A glass prism in the shape of a quarter-cylinder lies on a horizontal table. A uniform, horizontal 
light beam falls on its vertical plane surface, as shown in the figure. If the radius of the cylinder is 
R = 5 cm and the refractive index of the glass is n = 1.5, where, on the table beyond the cylinder, 
will a path of light be found? 
 
Q 14.  A glass sphere with 10 cm radius has a 5 cm radius spherical hole at its centre. A narrow beam of 
parallel light is directed into the sphere. Where, if anywhere, will the sphere produce an image? 
The index of refraction of the glass is 1.50. 
Q 15.  A glass sphere has a radius of 5.0 cm and a refractive index of 1.6. A paperweight is constructed 
by slicing through the sphere on a plate that is 2.0 cm from the centre of the sphere and 
perpendicular to a radius of the sphere that passes through the centre of the circle formed by the 
intersection of the plane and the sphere. The paperweight is placed on a table and viewed from 
directly above an observer who is 8.0 cm from the tabletop, as shown in figure. When viewed 
through the paperweight, how far away does the tabletop appear to the observer? 
 
Q 16.  A fish is rising up vertically inside a pond with velocity 4 cm/s, and notices a bird, which is diving 
downward and its velocity appears to be 16 cm/s (to the fish). What is the real velocity of the 
diving bird, if refractive index of water is 4/3 ? 
  Thin Lenses 
Q 17.  A lens with a focal length of 16 cm produces a sharp image of an object in two positions, which 
are 60 cm apart. Find the distance from the object to the screen. 
Q 18.  Two glasses with refractive indices of 1.5 and 1.7 are used to make two identical double convex 
lenses. 
  (a) Find the ratio between their focal lengths. 
(b) How will each of these lenses act on a ray parallel to its optical axis if the lenses are 
submerged into a transparent liquid with a refractive index of 1.6? 
Q 19.  A converging beam of rays is incident on a diverging lens. Having passed through the lens the 
rays intersect at a point 15 cm from the lens. If the lens is removed, the point where the rays meet, 
move 5 cm closer to the mounting that holds the lens. Find the focal length of the lens. 
Q 20.  The distance between two point sources of light is 24 cm. Find out where would you place a 
converging lens of focal length of 9 cm, so that the images of both the sources are formed at the 
same point. 
Q 21.  Two thin converging lenses are placed on a common axis so that the centre of one of them 
coincides with the focus of the other. An object is placed at a distance twice the focal length from 
the left-hand lens. Where will its image be? What is the lateral magnification? The focal length of 
each lens is f. 
Q 22.  A source of light is located at double focal length from a convergent lens. The focal length of the 
lens is f = 30 cm At what distance from the lens should a flat mirror be placed so that the rays 
reflected from the mirror are parallel after passing through the lens for the second time? 
Q 23.  A parallel beam of rays is incident on a convergent lens with a focal length of 40 cm. Where a 
divergent lens with a focal length of 15 cm be placed for the beam of rays to remain parallel after 
passing through the two lenses. 
Q 24.  An optical system consists of two convergent lenses with focal lengths f
1
 = 20 cm and f
2
 = 10 cm 
The distance between the lenses is d = 30 cm An object is placed at a distance of 30 cm from the 
first lens. At what distance from the second lens will the image be obtained? 
Q 25.  Determine the position of the image produced by an optical system consisting of a concave mirror 
with a focal length of 10 cm and a convergent lens with a focal length of 20 cm. The distance from 
the mirror to the lens is 30 cm and from the lens to the object is 40 cm. Consider only two steps. 
Plot the image. 
Q 26.  A parallel beam of light is incident on a system consisting of three thin lenses with a common 
optical axis. The focal lengths of the lenses are equal to f
1
 = +10cm and f
2
 = -20cm, and f
3
 = + 
9cm respectively. The distance between the first and the second lens is 15 cm and between the 
second and the third is 5 cm. Find the position of the point at which the beam converges when it 
leaves the system of lenses. 
Q 27.  Two equi-convex lenses of focal lengths 30 cm and 70 cm, made of material of refractive index = 
1.5, are held in contact coaxially by a rubber band round their edges. A liquid of refractive index 
1.3 is introduced in the space between the lenses filling it completely. Find the position of the 
image of a luminous point object placed on the axis of the combination lens at distance of 90 cm 
from it. 
Total Internal Reflection 
Q 28.  If the speed of light in ice is 2.3 × 10
8
 m/s, what is its index of refraction? What is the critical 
angle of incidence for light going from ice to air? 
Q 29.  In figure, light refracts from material 1 into a thin layer of material 2, crosses that layer, and then 
is incident at the critical angle on the interface between materials 2 and 3. 
 
  (a) What is the angle ? ? 
  (b) If ?
 
is decreased, is there refraction of light into material 3? 
Q 30.  A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 
5/ 3. A person is viewing the source from above the surface. There is an opaque disc of radius 1 
cm floating on the surface. The centre of the disc lies vertically above the source S. The liquid 
from the vessel is gradually drained out through a tap. What is the maximum height of the liquid 
for which the source cannot at all be seen from above? 
Q 31.  A ray of light travelling in glass ( ?
g 
= 3/2) is incident on a horizontal glass-air surface at the 
critical angle ?
C
.
 
If a thin layer of water ( ?
w
 = 4/3) is now poured on the glass-air surface, at what 
angle will the ray of light emerges into water at glass-water surface? 
Q 32.  A ray of light is incident on the left vertical face of glass cube of refractive index n
2
, as shown in 
figure. 
The plane of incidence is the plane of the page, and the cube is surrounded by liquid (refractive 
index = n
1
). What is the largest angle of incidence ?
1
 
for which total internal reflection occurs at 
the top surface? 
 
Page 5


Exercises 
For JEE Main 
Note In different books refractive index has been represented by the symbol n and ?. So in our 
book we have used both symbols at different places. 
  Subjective Questions 
  Refraction of Light 
Q 1.  A ray of light falls on a glass plate of refractive index n = 1.5. What is the angle of incidence of 
the ray if the angle between the reflected and refracted rays is 90°? 
Q 2.  The laws of reflection or refraction are the same for sound as for light. The index of refraction of a 
medium (for sound) is defined as the ratio of the speed of sound in air 343 m/s to the speed of 
sound in the medium. 
  (a) What is the index of refraction (for sound) of water (v = 1498 m/s)? 
  (b) What is the critical angle ?, for total reflection of sound from water? 
Q 3.  Light from a sodium lamp ( ?
0
 
= 589 run) passes through a tank of glycerin (refractive index 
=1.47) 20 m long in a time t
1
. If it takes a time t
2
 to transverse the same tank when filled with 
carbon disulfide (index = 1.63),determine the difference t
2
 - t
1
. 
Q 4.  A light beam of wavelength 600 run in air passes through film 1 (n
1
 = 1.2) of thickness 1.0 ?m, 
then through film 2 (air) of thickness 1.5 ?m, and finally through film 3 (n
3
 = 18) of thickness l.0 
?m. 
  (a) Which film does the light cross in the least time, and what is that least time? 
  (b) What are the total number of wavelengths (at any instant) across all three films together? 
Q 5.  A plane harmonic infrared wave travelling through a transparent medium is given by  
   
14
x 0x 7
y
E (y, t) E sin 2 3 10 t
5 10
?
??
? ? ? ?
??
?
??
 
in SI units. Determine refractive index of the medium at that frequency, and the vacuum 
wavelength of the disturbance. 
  Refraction from Plane and Spherical Surface 
Q 6.  A plate with plane parallel faces having refractive index 1.8 rests on a plane mirror. A light ray is 
incident on the upper face of the plate at 60°. How far from the entry point will the ray emerge 
after reflection by the mirror. The plate is 6 cm thick? 
 
Q 7.  A pile 4 m high driven into the bottom of a lake is 1 m above the water. Determine the length of 
the shadow of the pile on the bottom of the lake if the sun rays make an angle of 45° with the 
water surface. The refractive index of water is 4/3. 
Q 8.  An object is at a distance of d = 2.5 cm from the surface of a glass sphere with a radius R = 10cm 
Find the position of the final image produced by the sphere. The refractive index of glass is ?
 
= 
1.5. 
Q 9.  An air bubble is seen inside a solid sphere of glass (n = 1.5) of 4.0 cm diameter at a distance of 1.0 
cm from the surface of the sphere (on seeing along the diameter). Determine the real position of 
the bubble inside the sphere. 
Q 10.  Find the position of final image of an object O as shown in figure. 
 
Q 11.  One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm infront of the 
unsilvered face forms an image 10 cm behind the silvered face. Find the refractive index of glass. 
Consider all the three steps. 
Q 12.  A shallow glass dish is 4.00 cm wide at the bottom, as shown in figure. When an observer's eye is 
positioned as shown, the observer sees the edge of the bottom of the empty dish. When this dish is 
filled with water, the observer sees the centre
 
of the bottom of the dish. Find the height of the dish 
?
w
 
= 4/3. 
 
Q 13.  A glass prism in the shape of a quarter-cylinder lies on a horizontal table. A uniform, horizontal 
light beam falls on its vertical plane surface, as shown in the figure. If the radius of the cylinder is 
R = 5 cm and the refractive index of the glass is n = 1.5, where, on the table beyond the cylinder, 
will a path of light be found? 
 
Q 14.  A glass sphere with 10 cm radius has a 5 cm radius spherical hole at its centre. A narrow beam of 
parallel light is directed into the sphere. Where, if anywhere, will the sphere produce an image? 
The index of refraction of the glass is 1.50. 
Q 15.  A glass sphere has a radius of 5.0 cm and a refractive index of 1.6. A paperweight is constructed 
by slicing through the sphere on a plate that is 2.0 cm from the centre of the sphere and 
perpendicular to a radius of the sphere that passes through the centre of the circle formed by the 
intersection of the plane and the sphere. The paperweight is placed on a table and viewed from 
directly above an observer who is 8.0 cm from the tabletop, as shown in figure. When viewed 
through the paperweight, how far away does the tabletop appear to the observer? 
 
Q 16.  A fish is rising up vertically inside a pond with velocity 4 cm/s, and notices a bird, which is diving 
downward and its velocity appears to be 16 cm/s (to the fish). What is the real velocity of the 
diving bird, if refractive index of water is 4/3 ? 
  Thin Lenses 
Q 17.  A lens with a focal length of 16 cm produces a sharp image of an object in two positions, which 
are 60 cm apart. Find the distance from the object to the screen. 
Q 18.  Two glasses with refractive indices of 1.5 and 1.7 are used to make two identical double convex 
lenses. 
  (a) Find the ratio between their focal lengths. 
(b) How will each of these lenses act on a ray parallel to its optical axis if the lenses are 
submerged into a transparent liquid with a refractive index of 1.6? 
Q 19.  A converging beam of rays is incident on a diverging lens. Having passed through the lens the 
rays intersect at a point 15 cm from the lens. If the lens is removed, the point where the rays meet, 
move 5 cm closer to the mounting that holds the lens. Find the focal length of the lens. 
Q 20.  The distance between two point sources of light is 24 cm. Find out where would you place a 
converging lens of focal length of 9 cm, so that the images of both the sources are formed at the 
same point. 
Q 21.  Two thin converging lenses are placed on a common axis so that the centre of one of them 
coincides with the focus of the other. An object is placed at a distance twice the focal length from 
the left-hand lens. Where will its image be? What is the lateral magnification? The focal length of 
each lens is f. 
Q 22.  A source of light is located at double focal length from a convergent lens. The focal length of the 
lens is f = 30 cm At what distance from the lens should a flat mirror be placed so that the rays 
reflected from the mirror are parallel after passing through the lens for the second time? 
Q 23.  A parallel beam of rays is incident on a convergent lens with a focal length of 40 cm. Where a 
divergent lens with a focal length of 15 cm be placed for the beam of rays to remain parallel after 
passing through the two lenses. 
Q 24.  An optical system consists of two convergent lenses with focal lengths f
1
 = 20 cm and f
2
 = 10 cm 
The distance between the lenses is d = 30 cm An object is placed at a distance of 30 cm from the 
first lens. At what distance from the second lens will the image be obtained? 
Q 25.  Determine the position of the image produced by an optical system consisting of a concave mirror 
with a focal length of 10 cm and a convergent lens with a focal length of 20 cm. The distance from 
the mirror to the lens is 30 cm and from the lens to the object is 40 cm. Consider only two steps. 
Plot the image. 
Q 26.  A parallel beam of light is incident on a system consisting of three thin lenses with a common 
optical axis. The focal lengths of the lenses are equal to f
1
 = +10cm and f
2
 = -20cm, and f
3
 = + 
9cm respectively. The distance between the first and the second lens is 15 cm and between the 
second and the third is 5 cm. Find the position of the point at which the beam converges when it 
leaves the system of lenses. 
Q 27.  Two equi-convex lenses of focal lengths 30 cm and 70 cm, made of material of refractive index = 
1.5, are held in contact coaxially by a rubber band round their edges. A liquid of refractive index 
1.3 is introduced in the space between the lenses filling it completely. Find the position of the 
image of a luminous point object placed on the axis of the combination lens at distance of 90 cm 
from it. 
Total Internal Reflection 
Q 28.  If the speed of light in ice is 2.3 × 10
8
 m/s, what is its index of refraction? What is the critical 
angle of incidence for light going from ice to air? 
Q 29.  In figure, light refracts from material 1 into a thin layer of material 2, crosses that layer, and then 
is incident at the critical angle on the interface between materials 2 and 3. 
 
  (a) What is the angle ? ? 
  (b) If ?
 
is decreased, is there refraction of light into material 3? 
Q 30.  A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 
5/ 3. A person is viewing the source from above the surface. There is an opaque disc of radius 1 
cm floating on the surface. The centre of the disc lies vertically above the source S. The liquid 
from the vessel is gradually drained out through a tap. What is the maximum height of the liquid 
for which the source cannot at all be seen from above? 
Q 31.  A ray of light travelling in glass ( ?
g 
= 3/2) is incident on a horizontal glass-air surface at the 
critical angle ?
C
.
 
If a thin layer of water ( ?
w
 = 4/3) is now poured on the glass-air surface, at what 
angle will the ray of light emerges into water at glass-water surface? 
Q 32.  A ray of light is incident on the left vertical face of glass cube of refractive index n
2
, as shown in 
figure. 
The plane of incidence is the plane of the page, and the cube is surrounded by liquid (refractive 
index = n
1
). What is the largest angle of incidence ?
1
 
for which total internal reflection occurs at 
the top surface? 
 
Q 33.  Light is incident from glass 
g
3
2
??
??
??
??
to water 
w
4
3
??
??
??
??
.
 
Find the range of the angle of deviation 
for refracted light. 
Q 34.  A point source is placed at a depth h below the surface of water (refractive index = ?).
 
 
(a) Show that light escapes through a circular area on the water surface with its centre directly 
above the point source. 
  (b) Find the angle subtended by a radius of the area on the source. 
Q 35.  Consider the situation shown in figure. Find the maximum angle for which the light suffers total 
internal reflection at the left vertical surface. 
 
  Prism  
Q 36.  The angle of minimum deviation for a glass prism with n = 3 equals the refracting angle of the 
prism. What is the angle of the prism? 
Q 37.  The refracting angle of a glass prism is 30°. A ray is incident onto one of the faces perpendicular 
to it. Find the angle ? between the incident ray and the ray that leaves the prism. The refractive 
index of glass is n = 1.5. 
Q 38.  The perpendicular faces of a right isosceles prism are coated with silver. Prove that the rays 
incident at an arbitrary angle on the hypotenuse face will emerge from the prism parallel to the 
initial direction. 
Q 39.  One face of a prism with a refractive angle of 30° is coated with silver. A ray incident on another 
face at an angle of 45° is refracted and reflected from the silver coated face and retraces its path. 
What is the refractive index of the prism? 
Q 40.  In an isosceles prism of refracting angle 45°, it is found that when the angle of incidence is same 
as the prism angle the emergent ray grazes the emergent surface. Find the refractive index of the 
material of the prism. For what angle of incidence the angle of deviation will be minimum? 
Q 41.  A ray incident on the face of a prism is refracted and escapes through an adjacent face. What is the 
maximum permissible angle of the prism, if it is made of glass with a refractive index of ? = 1.5 ? 
Q 42.  In an equilateral prism of ? = 1.5, the condition for minimum deviation is fulfilled. If face AC is 
polished 
  (a) Find the net deviation. 
(b) If the system is placed in water what will be the net deviation for same angle of incidence? 
Refractive index of water = 
4
3
.