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

 Page 1


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  A bird is flying over a swimming pool at a height of 2 m from the water surface. If the bottom is 
perfectly plane reflecting surface and depth of swimming pool is 1 m, then the distance of final 
image of bird from the bird itself is ?
w
 = 4/3. 
 (a) 
11
m
3
   (b) 
23
m
3
   (c) 
11
m
4
   (d) 
11
m
2
 
Q 2.  A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius R 
and refractive index ? = 1.5
 
as shown. The position of the
 
image formed by refraction at the 
spherical surface only is 
 
 (a) 
R
2
   (b) 3R   (c) 
R
3
    (d) 2R 
Q 3.  Consider the situation as shown in figure. The point O is the centre . The light ray forms an angle 
of 60° with the normal. The normal makes an angle 60° with the horizontal and each mirror makes 
an angle 60° with the normal. The value of refractive
 
index of that spherical portion so that light 
ray retraces its path is 
 
 (a) 2   (b) 
2
3
   (c) 
3
2
    (d) 3 
Q 4.  The figure shows an equi-convex lens. What should be the condition of the refractive
 
indices so 
that the lens becomes diverging ? 
 
 (a) 2 ?
3
 > ?
1
 - ?
2
 (b) 2 ?
2
 < ?
1
 + ?
3
 (c) 2 ?
2
 > 2 ?
1
 - ?
3
 (d) None of these 
Q 5.  An object is kept at a distance of 16 cm from a thin lens and the image formed is real. If the object 
is kept at a distance of 6 cm from the same lens the image formed is virtual. If the size of the 
image formed are equal, the focal length of the lens will be 
  (a) 19 cm   (b) 17 cm   (c) 21cm   (d) 11cm 
Page 2


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  A bird is flying over a swimming pool at a height of 2 m from the water surface. If the bottom is 
perfectly plane reflecting surface and depth of swimming pool is 1 m, then the distance of final 
image of bird from the bird itself is ?
w
 = 4/3. 
 (a) 
11
m
3
   (b) 
23
m
3
   (c) 
11
m
4
   (d) 
11
m
2
 
Q 2.  A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius R 
and refractive index ? = 1.5
 
as shown. The position of the
 
image formed by refraction at the 
spherical surface only is 
 
 (a) 
R
2
   (b) 3R   (c) 
R
3
    (d) 2R 
Q 3.  Consider the situation as shown in figure. The point O is the centre . The light ray forms an angle 
of 60° with the normal. The normal makes an angle 60° with the horizontal and each mirror makes 
an angle 60° with the normal. The value of refractive
 
index of that spherical portion so that light 
ray retraces its path is 
 
 (a) 2   (b) 
2
3
   (c) 
3
2
    (d) 3 
Q 4.  The figure shows an equi-convex lens. What should be the condition of the refractive
 
indices so 
that the lens becomes diverging ? 
 
 (a) 2 ?
3
 > ?
1
 - ?
2
 (b) 2 ?
2
 < ?
1
 + ?
3
 (c) 2 ?
2
 > 2 ?
1
 - ?
3
 (d) None of these 
Q 5.  An object is kept at a distance of 16 cm from a thin lens and the image formed is real. If the object 
is kept at a distance of 6 cm from the same lens the image formed is virtual. If the size of the 
image formed are equal, the focal length of the lens will be 
  (a) 19 cm   (b) 17 cm   (c) 21cm   (d) 11cm 
Q 6.  The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of 
x cm/min when water is being drained out at a constant rate. The amount of water drained in 
cc/minute is (n
1
 = refractive index of air, n
2
 = refractive index of water) 
 (a) 
2
1
2
x R n
n
?
   (b) 
2
2
1
x R n
n
?
   (c) 
1
2
2 Rn
n
?
   (d) ?R
2
x 
Q 7.  A ray of light makes normal incidence on the diagonal face of a right- angled prism as shown in 
figure. If ? = 37?
 
then the angle of deviation after second step (from AS) is (sin 37° = 3/5) 
 
  (a) 53°   (b) 74°   (c) 106°   (d) 90° 
Q 8.  A bird in air looks at a fish directly below it inside in a transparent liquid in a tank. If the distance 
of the fish as estimated by the bird is h
1
 and that of the bird as estimated by the fish is h
2
, then the 
refractive index of the liquid is 
 (a) 
2
1
h
h
   (b) 
1
2
h
h
   (c) 
12
12
hh
hh
?
?
   (d) 
12
12
hh
hh
?
?
 
Q 9.  Diameter of the flat surface of a circular plano-convex lens is 6 cm and thickness at the centre is 3 
mm. The radius of curvature of the curved part is 
  (a) 15 cm   (b) 20 cm   (c) 30 cm   (d) 10cm 
Q 10.  When the object is at distances ?
1
 and ?
2
 
from the optical centre of a convex lens, a real and a 
virtual image of the same magnification are obtained . The focal length of the lens is 
 (a) 
12
2
? ? ?
   (b) ?
1
 + ?
2
  (c) 
12
??   (d) 
12
2
? ? ?
 
Q 11.  Two convex lenses placed in contact from the image of a distant object at P. If the lens B is moved 
to the right, the image will 
 
  (a) move to the left (b) move to the right (c) remain at P 
  (d) move either to the left or right, depending upon focal lengths of the lenses 
Q 12.  Two light rays 1 and 2 are incident on two faces AB and A C on an isosceles prism as shown in 
the figure. The rays emerge from the side BC. Then 
 
  (a) minimum deviation of ray 1 > minimum deviation of ray 2 
Page 3


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  A bird is flying over a swimming pool at a height of 2 m from the water surface. If the bottom is 
perfectly plane reflecting surface and depth of swimming pool is 1 m, then the distance of final 
image of bird from the bird itself is ?
w
 = 4/3. 
 (a) 
11
m
3
   (b) 
23
m
3
   (c) 
11
m
4
   (d) 
11
m
2
 
Q 2.  A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius R 
and refractive index ? = 1.5
 
as shown. The position of the
 
image formed by refraction at the 
spherical surface only is 
 
 (a) 
R
2
   (b) 3R   (c) 
R
3
    (d) 2R 
Q 3.  Consider the situation as shown in figure. The point O is the centre . The light ray forms an angle 
of 60° with the normal. The normal makes an angle 60° with the horizontal and each mirror makes 
an angle 60° with the normal. The value of refractive
 
index of that spherical portion so that light 
ray retraces its path is 
 
 (a) 2   (b) 
2
3
   (c) 
3
2
    (d) 3 
Q 4.  The figure shows an equi-convex lens. What should be the condition of the refractive
 
indices so 
that the lens becomes diverging ? 
 
 (a) 2 ?
3
 > ?
1
 - ?
2
 (b) 2 ?
2
 < ?
1
 + ?
3
 (c) 2 ?
2
 > 2 ?
1
 - ?
3
 (d) None of these 
Q 5.  An object is kept at a distance of 16 cm from a thin lens and the image formed is real. If the object 
is kept at a distance of 6 cm from the same lens the image formed is virtual. If the size of the 
image formed are equal, the focal length of the lens will be 
  (a) 19 cm   (b) 17 cm   (c) 21cm   (d) 11cm 
Q 6.  The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of 
x cm/min when water is being drained out at a constant rate. The amount of water drained in 
cc/minute is (n
1
 = refractive index of air, n
2
 = refractive index of water) 
 (a) 
2
1
2
x R n
n
?
   (b) 
2
2
1
x R n
n
?
   (c) 
1
2
2 Rn
n
?
   (d) ?R
2
x 
Q 7.  A ray of light makes normal incidence on the diagonal face of a right- angled prism as shown in 
figure. If ? = 37?
 
then the angle of deviation after second step (from AS) is (sin 37° = 3/5) 
 
  (a) 53°   (b) 74°   (c) 106°   (d) 90° 
Q 8.  A bird in air looks at a fish directly below it inside in a transparent liquid in a tank. If the distance 
of the fish as estimated by the bird is h
1
 and that of the bird as estimated by the fish is h
2
, then the 
refractive index of the liquid is 
 (a) 
2
1
h
h
   (b) 
1
2
h
h
   (c) 
12
12
hh
hh
?
?
   (d) 
12
12
hh
hh
?
?
 
Q 9.  Diameter of the flat surface of a circular plano-convex lens is 6 cm and thickness at the centre is 3 
mm. The radius of curvature of the curved part is 
  (a) 15 cm   (b) 20 cm   (c) 30 cm   (d) 10cm 
Q 10.  When the object is at distances ?
1
 and ?
2
 
from the optical centre of a convex lens, a real and a 
virtual image of the same magnification are obtained . The focal length of the lens is 
 (a) 
12
2
? ? ?
   (b) ?
1
 + ?
2
  (c) 
12
??   (d) 
12
2
? ? ?
 
Q 11.  Two convex lenses placed in contact from the image of a distant object at P. If the lens B is moved 
to the right, the image will 
 
  (a) move to the left (b) move to the right (c) remain at P 
  (d) move either to the left or right, depending upon focal lengths of the lenses 
Q 12.  Two light rays 1 and 2 are incident on two faces AB and A C on an isosceles prism as shown in 
the figure. The rays emerge from the side BC. Then 
 
  (a) minimum deviation of ray 1 > minimum deviation of ray 2 
  (b) minimum deviation of ray 1 < minimum deviation of ray 2 
  (c) minimum deviation of ray 1 = minimum deviation of ray 2 
  (d) Cannot be determined 
Q 13.  A ray of light travelling in glass > ( ?
g
= 3/2)
 
is incident on a glass air surface at the critical angle. 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 emerge into air at the water air surface ? 
  (a) 60°   (b) 30°   (c) 45°   (d) 90° 
Q 14.  Refractive index of a prism is 
7
3
and the angle of prism is 60°. The limiting angle of incidence of 
a ray that will be transmitted through the prism is approximately  
  (a) 30°   (b) 45°   (c) 15°   (d) None of these 
Q 15.  A plano-convex thin lens of focal length 10 cm is silvered at its plane surface. The distance d at 
which an object must be kept in order to get its image on itself is 
 
   (a) 5 cm   (b) 20 cm  (c) 10 cm   (d) 2.5 cm 
Q 16.  There is a small black dot at the centre C of a solid glass sphere of refractive index When seen 
from outside, the dot will appear to be located 
  (a) Away from the C for all values of ?  (b) At C for all values of ? 
  (c) At C for ? = 1.5, but away from C for not ? equal to 1.5 
  (d) At C for 2< ?
 
< 1.5 
Q 17.  In the figure ABC is the cross-section of a right angled prism and BCDE is the cross-section of a 
glass slab. The value of ? so that light incident normally on the face
 
AB does not cross the face 
BC is (Given sin-
1
 3/5 = 37° ) 
 
 (a) ? < 37?  (b) ? < 53?  (c) ? ? 37?  (d) ? ? 53? 
Q 18.  An object O is kept in air in front of a thin plano-convex lens of radius of curvature 10 cm. Its 
refractive index is 3/2 and the medium towards right of the plane surface is water of refractive 
index 4/3. What should be distance x of the object so that the rays become parallel finally? 
 
  (a) 5 cm   (b) 10 cm  (c) 20 cm   (d) 15 cm 
Page 4


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  A bird is flying over a swimming pool at a height of 2 m from the water surface. If the bottom is 
perfectly plane reflecting surface and depth of swimming pool is 1 m, then the distance of final 
image of bird from the bird itself is ?
w
 = 4/3. 
 (a) 
11
m
3
   (b) 
23
m
3
   (c) 
11
m
4
   (d) 
11
m
2
 
Q 2.  A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius R 
and refractive index ? = 1.5
 
as shown. The position of the
 
image formed by refraction at the 
spherical surface only is 
 
 (a) 
R
2
   (b) 3R   (c) 
R
3
    (d) 2R 
Q 3.  Consider the situation as shown in figure. The point O is the centre . The light ray forms an angle 
of 60° with the normal. The normal makes an angle 60° with the horizontal and each mirror makes 
an angle 60° with the normal. The value of refractive
 
index of that spherical portion so that light 
ray retraces its path is 
 
 (a) 2   (b) 
2
3
   (c) 
3
2
    (d) 3 
Q 4.  The figure shows an equi-convex lens. What should be the condition of the refractive
 
indices so 
that the lens becomes diverging ? 
 
 (a) 2 ?
3
 > ?
1
 - ?
2
 (b) 2 ?
2
 < ?
1
 + ?
3
 (c) 2 ?
2
 > 2 ?
1
 - ?
3
 (d) None of these 
Q 5.  An object is kept at a distance of 16 cm from a thin lens and the image formed is real. If the object 
is kept at a distance of 6 cm from the same lens the image formed is virtual. If the size of the 
image formed are equal, the focal length of the lens will be 
  (a) 19 cm   (b) 17 cm   (c) 21cm   (d) 11cm 
Q 6.  The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of 
x cm/min when water is being drained out at a constant rate. The amount of water drained in 
cc/minute is (n
1
 = refractive index of air, n
2
 = refractive index of water) 
 (a) 
2
1
2
x R n
n
?
   (b) 
2
2
1
x R n
n
?
   (c) 
1
2
2 Rn
n
?
   (d) ?R
2
x 
Q 7.  A ray of light makes normal incidence on the diagonal face of a right- angled prism as shown in 
figure. If ? = 37?
 
then the angle of deviation after second step (from AS) is (sin 37° = 3/5) 
 
  (a) 53°   (b) 74°   (c) 106°   (d) 90° 
Q 8.  A bird in air looks at a fish directly below it inside in a transparent liquid in a tank. If the distance 
of the fish as estimated by the bird is h
1
 and that of the bird as estimated by the fish is h
2
, then the 
refractive index of the liquid is 
 (a) 
2
1
h
h
   (b) 
1
2
h
h
   (c) 
12
12
hh
hh
?
?
   (d) 
12
12
hh
hh
?
?
 
Q 9.  Diameter of the flat surface of a circular plano-convex lens is 6 cm and thickness at the centre is 3 
mm. The radius of curvature of the curved part is 
  (a) 15 cm   (b) 20 cm   (c) 30 cm   (d) 10cm 
Q 10.  When the object is at distances ?
1
 and ?
2
 
from the optical centre of a convex lens, a real and a 
virtual image of the same magnification are obtained . The focal length of the lens is 
 (a) 
12
2
? ? ?
   (b) ?
1
 + ?
2
  (c) 
12
??   (d) 
12
2
? ? ?
 
Q 11.  Two convex lenses placed in contact from the image of a distant object at P. If the lens B is moved 
to the right, the image will 
 
  (a) move to the left (b) move to the right (c) remain at P 
  (d) move either to the left or right, depending upon focal lengths of the lenses 
Q 12.  Two light rays 1 and 2 are incident on two faces AB and A C on an isosceles prism as shown in 
the figure. The rays emerge from the side BC. Then 
 
  (a) minimum deviation of ray 1 > minimum deviation of ray 2 
  (b) minimum deviation of ray 1 < minimum deviation of ray 2 
  (c) minimum deviation of ray 1 = minimum deviation of ray 2 
  (d) Cannot be determined 
Q 13.  A ray of light travelling in glass > ( ?
g
= 3/2)
 
is incident on a glass air surface at the critical angle. 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 emerge into air at the water air surface ? 
  (a) 60°   (b) 30°   (c) 45°   (d) 90° 
Q 14.  Refractive index of a prism is 
7
3
and the angle of prism is 60°. The limiting angle of incidence of 
a ray that will be transmitted through the prism is approximately  
  (a) 30°   (b) 45°   (c) 15°   (d) None of these 
Q 15.  A plano-convex thin lens of focal length 10 cm is silvered at its plane surface. The distance d at 
which an object must be kept in order to get its image on itself is 
 
   (a) 5 cm   (b) 20 cm  (c) 10 cm   (d) 2.5 cm 
Q 16.  There is a small black dot at the centre C of a solid glass sphere of refractive index When seen 
from outside, the dot will appear to be located 
  (a) Away from the C for all values of ?  (b) At C for all values of ? 
  (c) At C for ? = 1.5, but away from C for not ? equal to 1.5 
  (d) At C for 2< ?
 
< 1.5 
Q 17.  In the figure ABC is the cross-section of a right angled prism and BCDE is the cross-section of a 
glass slab. The value of ? so that light incident normally on the face
 
AB does not cross the face 
BC is (Given sin-
1
 3/5 = 37° ) 
 
 (a) ? < 37?  (b) ? < 53?  (c) ? ? 37?  (d) ? ? 53? 
Q 18.  An object O is kept in air in front of a thin plano-convex lens of radius of curvature 10 cm. Its 
refractive index is 3/2 and the medium towards right of the plane surface is water of refractive 
index 4/3. What should be distance x of the object so that the rays become parallel finally? 
 
  (a) 5 cm   (b) 10 cm  (c) 20 cm   (d) 15 cm 
Q 19.  If a symmetrical bi-concave thin lens is cut into two identical halves, and they are placed in 
different ways as shown, then 
 
  (a) three images will be formed in case (i) (b) two images will be formed in case (ii) 
  (c) the ratio of focal lengths in (ii) and (iii) is 1 
 (d) the ratio of focal lengths in (ii) and (iii) is 2 
Q 20.  If an object is placed at A (OA > f); where f is the focal length of the lens, the image is formed at 
B. A perpendicular is erected at O and C is chosen on it such that the angle ?BCA is a right angle. 
Then the value of f will be 
 
 (a) 
2
AB
OC
   (b) 
(AC)(BC)
OC
  (c) 
2
OC
AB
   (d) 
(OC)(AB)
AC BC ?
 
Q 21.  An object is seen through a glass slab of thickness 36 cm and refractive index 3/2. The observer, 
 and the slab are dipped in water ( ? = 4/3). The shift produced in the position of the object is 
  (a) 12 cm   (b) 4 cm   (c) 6 cm   (d) 8 cm 
Q 22.  How much water should be filled in a container of height 21 cm, so that it appears half filled to the 
observer when viewed from the top of the container ( ? = 4/3).  
  (a) 8 cm   (b) 10.5 cm   (c) 12 cm   (d) 14 cm 
Q 23.  Optic axis of a thin equi-convex lens is the x-axis. The co-ordinates of a point object and its image 
are (- 40 cm, 1 cm) and (50 cm, - 2 cm) respectively. Lens is located at 
  (a) x = 20cm   (b) x = -30 cm  (c) x = -10 cm   (d) origin 
Q 24.  A thin plano-convex lens acts like a concave mirror of radius of curvature 20 cm when its plane 
surface is silvered. The radius of curvature of the curved surface if index of refraction of its 
material is 1.5 will be  
  (a) 40 cm   (b) 30 cm   (c) 10 cm   (d) 20 cm 
Q 25.  A thin lens, made of glass of refractive index 3/2, produces a real and magnified image of an 
object in air. If the whole system, maintaining the same distance between the object and the lens, 
is immersed in water (RI = 4/3) then the image formed will be 
  (a) real, magnified  (b) real, diminished  (c) virtual, magnified  (d) virtual, diminished 
Q 26.  The maximum value of refractive index of a prism which permits the transmission of light through 
it when the refracting angle of the prism is 90°, is given by 
Page 5


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  A bird is flying over a swimming pool at a height of 2 m from the water surface. If the bottom is 
perfectly plane reflecting surface and depth of swimming pool is 1 m, then the distance of final 
image of bird from the bird itself is ?
w
 = 4/3. 
 (a) 
11
m
3
   (b) 
23
m
3
   (c) 
11
m
4
   (d) 
11
m
2
 
Q 2.  A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius R 
and refractive index ? = 1.5
 
as shown. The position of the
 
image formed by refraction at the 
spherical surface only is 
 
 (a) 
R
2
   (b) 3R   (c) 
R
3
    (d) 2R 
Q 3.  Consider the situation as shown in figure. The point O is the centre . The light ray forms an angle 
of 60° with the normal. The normal makes an angle 60° with the horizontal and each mirror makes 
an angle 60° with the normal. The value of refractive
 
index of that spherical portion so that light 
ray retraces its path is 
 
 (a) 2   (b) 
2
3
   (c) 
3
2
    (d) 3 
Q 4.  The figure shows an equi-convex lens. What should be the condition of the refractive
 
indices so 
that the lens becomes diverging ? 
 
 (a) 2 ?
3
 > ?
1
 - ?
2
 (b) 2 ?
2
 < ?
1
 + ?
3
 (c) 2 ?
2
 > 2 ?
1
 - ?
3
 (d) None of these 
Q 5.  An object is kept at a distance of 16 cm from a thin lens and the image formed is real. If the object 
is kept at a distance of 6 cm from the same lens the image formed is virtual. If the size of the 
image formed are equal, the focal length of the lens will be 
  (a) 19 cm   (b) 17 cm   (c) 21cm   (d) 11cm 
Q 6.  The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of 
x cm/min when water is being drained out at a constant rate. The amount of water drained in 
cc/minute is (n
1
 = refractive index of air, n
2
 = refractive index of water) 
 (a) 
2
1
2
x R n
n
?
   (b) 
2
2
1
x R n
n
?
   (c) 
1
2
2 Rn
n
?
   (d) ?R
2
x 
Q 7.  A ray of light makes normal incidence on the diagonal face of a right- angled prism as shown in 
figure. If ? = 37?
 
then the angle of deviation after second step (from AS) is (sin 37° = 3/5) 
 
  (a) 53°   (b) 74°   (c) 106°   (d) 90° 
Q 8.  A bird in air looks at a fish directly below it inside in a transparent liquid in a tank. If the distance 
of the fish as estimated by the bird is h
1
 and that of the bird as estimated by the fish is h
2
, then the 
refractive index of the liquid is 
 (a) 
2
1
h
h
   (b) 
1
2
h
h
   (c) 
12
12
hh
hh
?
?
   (d) 
12
12
hh
hh
?
?
 
Q 9.  Diameter of the flat surface of a circular plano-convex lens is 6 cm and thickness at the centre is 3 
mm. The radius of curvature of the curved part is 
  (a) 15 cm   (b) 20 cm   (c) 30 cm   (d) 10cm 
Q 10.  When the object is at distances ?
1
 and ?
2
 
from the optical centre of a convex lens, a real and a 
virtual image of the same magnification are obtained . The focal length of the lens is 
 (a) 
12
2
? ? ?
   (b) ?
1
 + ?
2
  (c) 
12
??   (d) 
12
2
? ? ?
 
Q 11.  Two convex lenses placed in contact from the image of a distant object at P. If the lens B is moved 
to the right, the image will 
 
  (a) move to the left (b) move to the right (c) remain at P 
  (d) move either to the left or right, depending upon focal lengths of the lenses 
Q 12.  Two light rays 1 and 2 are incident on two faces AB and A C on an isosceles prism as shown in 
the figure. The rays emerge from the side BC. Then 
 
  (a) minimum deviation of ray 1 > minimum deviation of ray 2 
  (b) minimum deviation of ray 1 < minimum deviation of ray 2 
  (c) minimum deviation of ray 1 = minimum deviation of ray 2 
  (d) Cannot be determined 
Q 13.  A ray of light travelling in glass > ( ?
g
= 3/2)
 
is incident on a glass air surface at the critical angle. 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 emerge into air at the water air surface ? 
  (a) 60°   (b) 30°   (c) 45°   (d) 90° 
Q 14.  Refractive index of a prism is 
7
3
and the angle of prism is 60°. The limiting angle of incidence of 
a ray that will be transmitted through the prism is approximately  
  (a) 30°   (b) 45°   (c) 15°   (d) None of these 
Q 15.  A plano-convex thin lens of focal length 10 cm is silvered at its plane surface. The distance d at 
which an object must be kept in order to get its image on itself is 
 
   (a) 5 cm   (b) 20 cm  (c) 10 cm   (d) 2.5 cm 
Q 16.  There is a small black dot at the centre C of a solid glass sphere of refractive index When seen 
from outside, the dot will appear to be located 
  (a) Away from the C for all values of ?  (b) At C for all values of ? 
  (c) At C for ? = 1.5, but away from C for not ? equal to 1.5 
  (d) At C for 2< ?
 
< 1.5 
Q 17.  In the figure ABC is the cross-section of a right angled prism and BCDE is the cross-section of a 
glass slab. The value of ? so that light incident normally on the face
 
AB does not cross the face 
BC is (Given sin-
1
 3/5 = 37° ) 
 
 (a) ? < 37?  (b) ? < 53?  (c) ? ? 37?  (d) ? ? 53? 
Q 18.  An object O is kept in air in front of a thin plano-convex lens of radius of curvature 10 cm. Its 
refractive index is 3/2 and the medium towards right of the plane surface is water of refractive 
index 4/3. What should be distance x of the object so that the rays become parallel finally? 
 
  (a) 5 cm   (b) 10 cm  (c) 20 cm   (d) 15 cm 
Q 19.  If a symmetrical bi-concave thin lens is cut into two identical halves, and they are placed in 
different ways as shown, then 
 
  (a) three images will be formed in case (i) (b) two images will be formed in case (ii) 
  (c) the ratio of focal lengths in (ii) and (iii) is 1 
 (d) the ratio of focal lengths in (ii) and (iii) is 2 
Q 20.  If an object is placed at A (OA > f); where f is the focal length of the lens, the image is formed at 
B. A perpendicular is erected at O and C is chosen on it such that the angle ?BCA is a right angle. 
Then the value of f will be 
 
 (a) 
2
AB
OC
   (b) 
(AC)(BC)
OC
  (c) 
2
OC
AB
   (d) 
(OC)(AB)
AC BC ?
 
Q 21.  An object is seen through a glass slab of thickness 36 cm and refractive index 3/2. The observer, 
 and the slab are dipped in water ( ? = 4/3). The shift produced in the position of the object is 
  (a) 12 cm   (b) 4 cm   (c) 6 cm   (d) 8 cm 
Q 22.  How much water should be filled in a container of height 21 cm, so that it appears half filled to the 
observer when viewed from the top of the container ( ? = 4/3).  
  (a) 8 cm   (b) 10.5 cm   (c) 12 cm   (d) 14 cm 
Q 23.  Optic axis of a thin equi-convex lens is the x-axis. The co-ordinates of a point object and its image 
are (- 40 cm, 1 cm) and (50 cm, - 2 cm) respectively. Lens is located at 
  (a) x = 20cm   (b) x = -30 cm  (c) x = -10 cm   (d) origin 
Q 24.  A thin plano-convex lens acts like a concave mirror of radius of curvature 20 cm when its plane 
surface is silvered. The radius of curvature of the curved surface if index of refraction of its 
material is 1.5 will be  
  (a) 40 cm   (b) 30 cm   (c) 10 cm   (d) 20 cm 
Q 25.  A thin lens, made of glass of refractive index 3/2, produces a real and magnified image of an 
object in air. If the whole system, maintaining the same distance between the object and the lens, 
is immersed in water (RI = 4/3) then the image formed will be 
  (a) real, magnified  (b) real, diminished  (c) virtual, magnified  (d) virtual, diminished 
Q 26.  The maximum value of refractive index of a prism which permits the transmission of light through 
it when the refracting angle of the prism is 90°, is given by 
  (a) 1.500   (b) 1.414   (c) 2.000  (d) 1.732 
Q 27.  When an object is moved along the axis of a lens, two images three times the size of the object are 
obtained when the object is at 16 cm and at 8 cm respectively from the lens. The focal length and 
the nature of the lens are 
  (a) 12 cm, concave  (b) 4 cm, concave  (c) 12 cm, convex  (d) 4 cm, convex 
Q 28.  A glass slab of thickness 4 cm contains the same number of waves as 5 cm of water, when both 
are traversed by the same monochromatic light. If the refractive index of water is 4/3, then 
refractive index of glass is 
  (a) 5/3    (b) 5/4    (c) 16/15   (d) 1.5 
Q 29.  If the optic axis of convex and concave lenses are separated by a distance 5 mm as shown in the 
figure. Find, the co-ordinate of the final image formed by the combination if parallel beam of light 
is incident on lens. Origin is at the optical centre of convex lens 
 
  (a) (25 cm, 0.5 cm)  (b) (25 cm, 0.25 cm)  (c) (25 cm, - 0.5 cm)  (d) (25 cm, - 2.5 cm) 
Q 30.  A light source S is placed at the centre of a glass sphere of radius R and refractive index ?.
 
The 
maximum angle ?
 
with the X-axis (as shown in the figure) an incident light
 
ray can make without 
suffering total internal reflection is 
 
 (a) 
1
1
cos
?
??
??
?
??
   (b) 
1
1
sin
?
??
??
?
??
   (c) 
1
1
tan
?
??
??
?
??
    
  (d) there will never be total internal reflection 
Q 31.  A sphere 
4
3
??
??
??
??
of radius 1 m has a small cavity of diameter 1 cm at its centre. An observer who 
 is looking at it from right, sees the magnification of diameter of the cavity as 
  (a) 
4
3
    (b) 
3
4
    (c) 1    (d) 0.5 
Q 32.  An equi-convex lens of ? = 1.5 and R = 20 cm is cut into two equal parts along its axis. Two parts 
are then separated by a distance of 120 cm (as shown in figure). An object of height 3 mm is 
placed at a distance of 30 cm to the left of first half lens. The final image will form at