Wave & Ray Optics MCQ ACE Class 12 Notes | EduRev

Class 12 : Wave & Ray Optics MCQ ACE Class 12 Notes | EduRev

 Page 1


                                   [1] 
 
 
 
(Wave & Ray Optics)  
1. In Young’s double slit experiment if the slit 
widths are in the ratio 1 : 9, the ratio of the 
intensity at minima to that at maxima will be   
(a) 1 (b) 1/9 
(c) 1/4 (d) 1/3 
2. Which of the following statements are true for 
light waves but not for sound waves ?  
(i)  the speed of wave is greater in vacuum than 
in a medium  
(ii) waves of different frequencies travels with 
different speeds in a medium   
(iii)  Waves travel with different speeds in 
different media.  
Choose your answer according to the code given 
below : 
(a) (i) and (ii) (b) (i) and (iii)  
(c) (ii) and (iii)  (d) (i), (ii) and (iii)  
3. For sustained interference we need two sources 
which emit radiation :  
(a) with same intensity  
(b) with same amplitude  
(c) having constant phase difference  
(d) in a narrow beam. 
4. The intensity of the light emerging from the two 
slits in Young’s experiment is in the ratio 1 to 4. 
The intensity of the minimum to the consecutive 
maximum  will be in the ratio of :  
(a) 1 : 2 (b) 1 : 4 
(c)  1: 9 (d) none of these  
5. A thin film is viewed in white light. The colour of 
the film seen at a particular point depends upon: 
(a) width of the source  
(b) distance of the source  
(c) location of the observer  
(d) none of these  
6. In Young’s double slit experiment the 7
th
 
maximum with wavelength ?
1
 is at a distance d
1
 
and that with wavelength ?
2
 is at distance d
2
. 
Then d
1
/d
2
 =  
(a) ?
1
/ ?
2 
(b) ?
2
/ ?
1
 
(c) ?
2
1
/ ?
2
2
 (d) ?
2
2
/ ?
2
1
 
7. A light of 6000 Å is used to produce interference 
pattern. The observed fringe width is 0.12 mm. 
The angle between two interfering wave trains is 
(a) 2 x 10
–3
radian  (b)3 x 10
–3
radian 
(c) 4x 10
–3
radian  (d) 5x 10
–3
 radian. 
8. In a biprism experiment by using light of 
wavelength 5000 Å, 5 mm wide fringes are 
obtained on a screen 1.0 m away from the 
coherent sources. The separation between the two 
coherent sources is 
(a) 1.0mm   (b) 0.1mm 
(c) 0.05mm   (d) 0.01mm 
9. When the light is incident at the plarising angle, 
which of the following is completely polarised ? ? 
(a) Refracted light   
(b) Reflected light  
(c) both reflected as well as refracted  
(d) neither reflected nor refracted light  
10. In Young’s double slit experiment, if the widths of 
the slit are in the ratio 4 : 9, ratio of intensity of 
maxima to intensity of minima will be 
(a) 25:1 (b)  9:4 
(c) 3:2 (d)  81:16. 
11. Doppler shift for the light of wavelength 6000Å 
emitted from the sun is 0.04Å. If radius of the sun 
is 7 x 10
8
m then time period of rotation of the sun 
will be 
(a) 30days (b) 365 days 
(c) 24 hours (d) 25 days. 
12. In young’s double slit experiment a maximum is 
obtained when the path difference between the 
interfering waves is  
(Given that n = 1, 2, 3, 4….) 
(a) n
2
?
 
(b) n ? 
(c) (2n + 1)
2
?
 
(d) other than that given above  
13. A piano-convex lens when silvered on the plane 
side behaves like a concave mirror of focal length 
30 cm. When silvered on convex side, it behaves 
like a concave mirror of focal length 10 cm. The 
refractive index of material is 
(a)  3.0 (b)  2.0 
(c)  2.5 (d)  1.5 
14. Fig. shows the path of ray through an equiangular 
glass prism. It is incident on face AC at the critical 
angle for glass air interface. The angle of deviation 
of ray is 108°. Find the refractive index of glass 
prism. 
(a)  1.01 (b)  2.02 
(c)  1.45 (d)  1.72 
Page 2


                                   [1] 
 
 
 
(Wave & Ray Optics)  
1. In Young’s double slit experiment if the slit 
widths are in the ratio 1 : 9, the ratio of the 
intensity at minima to that at maxima will be   
(a) 1 (b) 1/9 
(c) 1/4 (d) 1/3 
2. Which of the following statements are true for 
light waves but not for sound waves ?  
(i)  the speed of wave is greater in vacuum than 
in a medium  
(ii) waves of different frequencies travels with 
different speeds in a medium   
(iii)  Waves travel with different speeds in 
different media.  
Choose your answer according to the code given 
below : 
(a) (i) and (ii) (b) (i) and (iii)  
(c) (ii) and (iii)  (d) (i), (ii) and (iii)  
3. For sustained interference we need two sources 
which emit radiation :  
(a) with same intensity  
(b) with same amplitude  
(c) having constant phase difference  
(d) in a narrow beam. 
4. The intensity of the light emerging from the two 
slits in Young’s experiment is in the ratio 1 to 4. 
The intensity of the minimum to the consecutive 
maximum  will be in the ratio of :  
(a) 1 : 2 (b) 1 : 4 
(c)  1: 9 (d) none of these  
5. A thin film is viewed in white light. The colour of 
the film seen at a particular point depends upon: 
(a) width of the source  
(b) distance of the source  
(c) location of the observer  
(d) none of these  
6. In Young’s double slit experiment the 7
th
 
maximum with wavelength ?
1
 is at a distance d
1
 
and that with wavelength ?
2
 is at distance d
2
. 
Then d
1
/d
2
 =  
(a) ?
1
/ ?
2 
(b) ?
2
/ ?
1
 
(c) ?
2
1
/ ?
2
2
 (d) ?
2
2
/ ?
2
1
 
7. A light of 6000 Å is used to produce interference 
pattern. The observed fringe width is 0.12 mm. 
The angle between two interfering wave trains is 
(a) 2 x 10
–3
radian  (b)3 x 10
–3
radian 
(c) 4x 10
–3
radian  (d) 5x 10
–3
 radian. 
8. In a biprism experiment by using light of 
wavelength 5000 Å, 5 mm wide fringes are 
obtained on a screen 1.0 m away from the 
coherent sources. The separation between the two 
coherent sources is 
(a) 1.0mm   (b) 0.1mm 
(c) 0.05mm   (d) 0.01mm 
9. When the light is incident at the plarising angle, 
which of the following is completely polarised ? ? 
(a) Refracted light   
(b) Reflected light  
(c) both reflected as well as refracted  
(d) neither reflected nor refracted light  
10. In Young’s double slit experiment, if the widths of 
the slit are in the ratio 4 : 9, ratio of intensity of 
maxima to intensity of minima will be 
(a) 25:1 (b)  9:4 
(c) 3:2 (d)  81:16. 
11. Doppler shift for the light of wavelength 6000Å 
emitted from the sun is 0.04Å. If radius of the sun 
is 7 x 10
8
m then time period of rotation of the sun 
will be 
(a) 30days (b) 365 days 
(c) 24 hours (d) 25 days. 
12. In young’s double slit experiment a maximum is 
obtained when the path difference between the 
interfering waves is  
(Given that n = 1, 2, 3, 4….) 
(a) n
2
?
 
(b) n ? 
(c) (2n + 1)
2
?
 
(d) other than that given above  
13. A piano-convex lens when silvered on the plane 
side behaves like a concave mirror of focal length 
30 cm. When silvered on convex side, it behaves 
like a concave mirror of focal length 10 cm. The 
refractive index of material is 
(a)  3.0 (b)  2.0 
(c)  2.5 (d)  1.5 
14. Fig. shows the path of ray through an equiangular 
glass prism. It is incident on face AC at the critical 
angle for glass air interface. The angle of deviation 
of ray is 108°. Find the refractive index of glass 
prism. 
(a)  1.01 (b)  2.02 
(c)  1.45 (d)  1.72 
                                   [2] 
 
 
 
 
15. A thin prism of angle 5° is placed at a distance of 
10 cm from the object. What is distance of image 
from the object? 
(a)  0.25 cm (b) 0.43 cm 
(c)  0.52 cm (d) 0.61 cm 
16. The refractive index of the material of                            
equilateral prism is 3 . The angle of minimum 
deviation for the prism is 
(a) 30°  (b) 41° 
(c) 49°  (d) 60°. 
17. A light bulb is placed between two plane mirrors 
inclined at an angle of 60 °. The number of images 
formed are : 
(a) 6 (b) 2 
(c) 5  (d) 4 
18. What causes changes in the colours of the thin 
soap or oil films for the given beam of light ?  
(a) angle of incidence  
(b) angle of reflection  
(c) thickness of the film  
(d) none of these  
19. Instead of using two slits as in Young’s 
experiment, if we use two separate but identical 
sodium lamps, which of the following will occur ? 
(a) General illumination  
(b) Widely separate interference  
(c) Very bright maximum  
(d) Very dark minimum  
20. In Fresnel’s biprism experiment, bands of width 
0.185 mm are observed at a distance one meter 
from the slit. The image of the coherent sources is 
then produced at the same distance from the slit 
by placing a convex lens at 30 cm from the slit. 
The images are found to be separated by a 
distance of 0.70 cm. The wavelength of the light 
used is 
(a) 1295Å (b) 5550Å 
(c) 6000Å (d) 6500 Å 
21. If two mirrors are kept at 60 ° to each other, then 
the number of images formed by them is 
(a)  5 (b)  6 
(c)  7 (d)  8. 
22. A light source approaches the observer with 
velocity 0.5c. Doppler shift for light of wavelength 
5500 Å is 
(a) 616 Å (b)  1833 Å 
(c) 5500 Å (d)  6160 Å 
23. On introducing a thin mica sheet of thickness           
2 x 10
–6
 m and refractive index 1.5 in the path of 
one of the waves, central bright maxima shifts by 
n fringes. Wavelength of the wave used is 5000 Å, 
then n is 
(a) 1 (b) 2 
(c)  5 (d)  10. 
24. The focal length of a lens in a camera is marked ƒ: 
2.8 is 8 cm. What is diameter of lens? 
(a) 1.4 cm (b) 2.8 cm 
(c) 3.2 cm (d) 4.0 cm 
25. A plano-convex lens fits exactly into a plano-
concave lens. Their plane surfaces are parallel to 
each other. If the lenses are made of different 
materials, what is focal length of combination ? 
Given 
ƒ 1
 = focal length of piano-concave 
lens 
ƒ
2 
= focal length of piano-convex 
lens 
µ
1 
= ref. index of material of 
piano-concave lens 
µ
2
 = ref. index of material of 
piano convex lens. 
(a)  
R
1 2
µ - µ
 (b)  
1 2
R
µ - µ
   
(c)  
R
2
1
µ
µ
 (d) 
R
1
2
µ
µ
 
In every question a statement of ASSERTION is 
followed by a statement of REASON. Mark the 
correct answer out of the following choices:  
(a) If both ASSERTION and REASON are true 
and reason is the correct explanation of the 
assertion. 
(b) If both ASSERTION and REASON are true 
but reason is not the correct explanation of the 
assertion. 
(c) If ASSERTION is true but REASON is false. 
(d) If ASSERTION is false but REASON is true. 
26. Assertion: According to dual theory, light has a 
particle and wave nature at the same time.  
Reason: Any, particle or wave nature of light may 
be needed to explain a particular phenomenon.  
27. Assertion: Light emerging from a convex lens 
when a point source is placed at its focus 
produces a plane wavefront. 
Page 3


                                   [1] 
 
 
 
(Wave & Ray Optics)  
1. In Young’s double slit experiment if the slit 
widths are in the ratio 1 : 9, the ratio of the 
intensity at minima to that at maxima will be   
(a) 1 (b) 1/9 
(c) 1/4 (d) 1/3 
2. Which of the following statements are true for 
light waves but not for sound waves ?  
(i)  the speed of wave is greater in vacuum than 
in a medium  
(ii) waves of different frequencies travels with 
different speeds in a medium   
(iii)  Waves travel with different speeds in 
different media.  
Choose your answer according to the code given 
below : 
(a) (i) and (ii) (b) (i) and (iii)  
(c) (ii) and (iii)  (d) (i), (ii) and (iii)  
3. For sustained interference we need two sources 
which emit radiation :  
(a) with same intensity  
(b) with same amplitude  
(c) having constant phase difference  
(d) in a narrow beam. 
4. The intensity of the light emerging from the two 
slits in Young’s experiment is in the ratio 1 to 4. 
The intensity of the minimum to the consecutive 
maximum  will be in the ratio of :  
(a) 1 : 2 (b) 1 : 4 
(c)  1: 9 (d) none of these  
5. A thin film is viewed in white light. The colour of 
the film seen at a particular point depends upon: 
(a) width of the source  
(b) distance of the source  
(c) location of the observer  
(d) none of these  
6. In Young’s double slit experiment the 7
th
 
maximum with wavelength ?
1
 is at a distance d
1
 
and that with wavelength ?
2
 is at distance d
2
. 
Then d
1
/d
2
 =  
(a) ?
1
/ ?
2 
(b) ?
2
/ ?
1
 
(c) ?
2
1
/ ?
2
2
 (d) ?
2
2
/ ?
2
1
 
7. A light of 6000 Å is used to produce interference 
pattern. The observed fringe width is 0.12 mm. 
The angle between two interfering wave trains is 
(a) 2 x 10
–3
radian  (b)3 x 10
–3
radian 
(c) 4x 10
–3
radian  (d) 5x 10
–3
 radian. 
8. In a biprism experiment by using light of 
wavelength 5000 Å, 5 mm wide fringes are 
obtained on a screen 1.0 m away from the 
coherent sources. The separation between the two 
coherent sources is 
(a) 1.0mm   (b) 0.1mm 
(c) 0.05mm   (d) 0.01mm 
9. When the light is incident at the plarising angle, 
which of the following is completely polarised ? ? 
(a) Refracted light   
(b) Reflected light  
(c) both reflected as well as refracted  
(d) neither reflected nor refracted light  
10. In Young’s double slit experiment, if the widths of 
the slit are in the ratio 4 : 9, ratio of intensity of 
maxima to intensity of minima will be 
(a) 25:1 (b)  9:4 
(c) 3:2 (d)  81:16. 
11. Doppler shift for the light of wavelength 6000Å 
emitted from the sun is 0.04Å. If radius of the sun 
is 7 x 10
8
m then time period of rotation of the sun 
will be 
(a) 30days (b) 365 days 
(c) 24 hours (d) 25 days. 
12. In young’s double slit experiment a maximum is 
obtained when the path difference between the 
interfering waves is  
(Given that n = 1, 2, 3, 4….) 
(a) n
2
?
 
(b) n ? 
(c) (2n + 1)
2
?
 
(d) other than that given above  
13. A piano-convex lens when silvered on the plane 
side behaves like a concave mirror of focal length 
30 cm. When silvered on convex side, it behaves 
like a concave mirror of focal length 10 cm. The 
refractive index of material is 
(a)  3.0 (b)  2.0 
(c)  2.5 (d)  1.5 
14. Fig. shows the path of ray through an equiangular 
glass prism. It is incident on face AC at the critical 
angle for glass air interface. The angle of deviation 
of ray is 108°. Find the refractive index of glass 
prism. 
(a)  1.01 (b)  2.02 
(c)  1.45 (d)  1.72 
                                   [2] 
 
 
 
 
15. A thin prism of angle 5° is placed at a distance of 
10 cm from the object. What is distance of image 
from the object? 
(a)  0.25 cm (b) 0.43 cm 
(c)  0.52 cm (d) 0.61 cm 
16. The refractive index of the material of                            
equilateral prism is 3 . The angle of minimum 
deviation for the prism is 
(a) 30°  (b) 41° 
(c) 49°  (d) 60°. 
17. A light bulb is placed between two plane mirrors 
inclined at an angle of 60 °. The number of images 
formed are : 
(a) 6 (b) 2 
(c) 5  (d) 4 
18. What causes changes in the colours of the thin 
soap or oil films for the given beam of light ?  
(a) angle of incidence  
(b) angle of reflection  
(c) thickness of the film  
(d) none of these  
19. Instead of using two slits as in Young’s 
experiment, if we use two separate but identical 
sodium lamps, which of the following will occur ? 
(a) General illumination  
(b) Widely separate interference  
(c) Very bright maximum  
(d) Very dark minimum  
20. In Fresnel’s biprism experiment, bands of width 
0.185 mm are observed at a distance one meter 
from the slit. The image of the coherent sources is 
then produced at the same distance from the slit 
by placing a convex lens at 30 cm from the slit. 
The images are found to be separated by a 
distance of 0.70 cm. The wavelength of the light 
used is 
(a) 1295Å (b) 5550Å 
(c) 6000Å (d) 6500 Å 
21. If two mirrors are kept at 60 ° to each other, then 
the number of images formed by them is 
(a)  5 (b)  6 
(c)  7 (d)  8. 
22. A light source approaches the observer with 
velocity 0.5c. Doppler shift for light of wavelength 
5500 Å is 
(a) 616 Å (b)  1833 Å 
(c) 5500 Å (d)  6160 Å 
23. On introducing a thin mica sheet of thickness           
2 x 10
–6
 m and refractive index 1.5 in the path of 
one of the waves, central bright maxima shifts by 
n fringes. Wavelength of the wave used is 5000 Å, 
then n is 
(a) 1 (b) 2 
(c)  5 (d)  10. 
24. The focal length of a lens in a camera is marked ƒ: 
2.8 is 8 cm. What is diameter of lens? 
(a) 1.4 cm (b) 2.8 cm 
(c) 3.2 cm (d) 4.0 cm 
25. A plano-convex lens fits exactly into a plano-
concave lens. Their plane surfaces are parallel to 
each other. If the lenses are made of different 
materials, what is focal length of combination ? 
Given 
ƒ 1
 = focal length of piano-concave 
lens 
ƒ
2 
= focal length of piano-convex 
lens 
µ
1 
= ref. index of material of 
piano-concave lens 
µ
2
 = ref. index of material of 
piano convex lens. 
(a)  
R
1 2
µ - µ
 (b)  
1 2
R
µ - µ
   
(c)  
R
2
1
µ
µ
 (d) 
R
1
2
µ
µ
 
In every question a statement of ASSERTION is 
followed by a statement of REASON. Mark the 
correct answer out of the following choices:  
(a) If both ASSERTION and REASON are true 
and reason is the correct explanation of the 
assertion. 
(b) If both ASSERTION and REASON are true 
but reason is not the correct explanation of the 
assertion. 
(c) If ASSERTION is true but REASON is false. 
(d) If ASSERTION is false but REASON is true. 
26. Assertion: According to dual theory, light has a 
particle and wave nature at the same time.  
Reason: Any, particle or wave nature of light may 
be needed to explain a particular phenomenon.  
27. Assertion: Light emerging from a convex lens 
when a point source is placed at its focus 
produces a plane wavefront. 
                                   [3] 
 
 
 
Reason: A spherical wavefront on entering an 
inhomogenous anisotropic medium becomes a 
plane wavefront. 
28. Assertion: In Young’s double slit experiment if 
the point on the screen directly opposite to a slit is 
dark then the wavelength of the source is 
proportional to square of the distance between the 
slits.  
Reason: A minima is obtained when the path 
difference is (2n + 1) 
2
?
 and the phase difference 
is (2n + 1) p. 
29. Assertion: A narrow pulse of light, through a 
medium retains its shape as it travels through the 
medium. 
Reason: A narrow pulse of light is made of 
harmonic waves with a large range of 
wavelengths. 
30. Assertion: One of the two polaroids crossed to 
each other is rotated through 30 °. Only 1/8th of 
the incident unpolarised light passes through the 
combination. 
Reason: The amount of light going through the 
Polaroid is determined by Malus’ law. 
 
 
ANSWER KEY 
 
1 C 6 A 11 
D 
16 
D 
21 A 26 D 
2 A 7 D 12 
B 
17 
C 
22 B 27 C 
3 C 8 B 13 
D 
18 
C 
23 
B 
28 A 
4 C 9 B 14 
C 
19 A 24 
B 
29 D 
5 C 10 A 15 
B 
20 B 25 
B 
30 A 
 
SOLUTIONS 
1. Amplitude of the superimposing waves are  
A
1
/A
2
 = (1/9)
1/2
 = 1/3  
4
1
) A A (
) A A (
I
I
2
2 1
2
2 1
ima max
ima min
=
+
-
=  
2. Speed of sound in vacuum is zero. Also there is 
no dispersion of sound wave. So both (i) and (ii) 
are not valid for sound waves. 
3. (c) 
4. Amplitude are in the ratio 1 : 2. Hence amplitude 
at minimum will be 1 and that at maximum will 
be 3. 
5. (c) 
6. 7 ß = 7 D ? 1
/d = d
1
 and 7 ß
2
 = 7D ?/d = d
2
           
Hence ?
1
/ ?
2
 = d
1
/d
2
 
7. Here ß = 
d
D ?
 Angle ? between two waves train is  
? = 
ß
?
=
D
d
 or     ? = 
3
10
10 12 . 0
10 6000
-
-
×
×
\ 
8. use ß = 
d
D ?
 
9. (b) 
10. 
4
9
I
I
W
W
2
1
2
1
= = ?  
4
9
a
a
2
2
2
1
= 
2
3
a
a
2
1
= a
max
 = a
1
 + a
2
 
 a
min
 = a
1
 - a
2
  ? 
min
max
I
I
= 
1
25
) a a (
) a a (
2 1
2 1
=
-
+
 
11. Doppler’s shift is given by ? ? = ?
?
?
?
?
? ?
? = ?
c
. R
c
v
 ? = 
T
2 p
 ? R. ?
?
?
?
?
? p
T
2
. ? =
?
d
c
  T = days 25 c / .
dr
2 . R
= ?
p
 
12. (b) 
13. Focal length of plano -convex lens  f
1
 = 
1
R
- µ
…(1) 
(i) Focal length equivalent concave mirror, when 
one side of lens is silvered 
m m l
f
1
R
) 1 ( 2
f
1
f
2
F
1
+
- µ
= + = ……..(2) (ii) When 
plane side is silvered, then f
m
 = 8 , so eqn. (2) 
gives 
8
+
- µ
=
1
R
) 1 ( 2
F
1
1
 
R
) 1 ( 2
30
1 - µ
= (iii) When 
convex side of its silvered  f
m
 = 
2
R
, so eqn. (2) 
gives 
R
2
R
2
R
) 1 ( 2
F
1
2
µ
= +
- µ
= 
R
2
10
1 µ
= …(4). 
Dividing (3) by (4)  
µ
- µ
=
1
30
10
?    µ = 3 ( µ - 1)  or 
µ = 1.5 
14. Let i be angle of incidence at Q. Then angle of 
refraction at Q is  90 ° - (180 ° - A - 90 ° + C)  = A - 
C. Angle of incidence at S is also (A - C), so angle 
Page 4


                                   [1] 
 
 
 
(Wave & Ray Optics)  
1. In Young’s double slit experiment if the slit 
widths are in the ratio 1 : 9, the ratio of the 
intensity at minima to that at maxima will be   
(a) 1 (b) 1/9 
(c) 1/4 (d) 1/3 
2. Which of the following statements are true for 
light waves but not for sound waves ?  
(i)  the speed of wave is greater in vacuum than 
in a medium  
(ii) waves of different frequencies travels with 
different speeds in a medium   
(iii)  Waves travel with different speeds in 
different media.  
Choose your answer according to the code given 
below : 
(a) (i) and (ii) (b) (i) and (iii)  
(c) (ii) and (iii)  (d) (i), (ii) and (iii)  
3. For sustained interference we need two sources 
which emit radiation :  
(a) with same intensity  
(b) with same amplitude  
(c) having constant phase difference  
(d) in a narrow beam. 
4. The intensity of the light emerging from the two 
slits in Young’s experiment is in the ratio 1 to 4. 
The intensity of the minimum to the consecutive 
maximum  will be in the ratio of :  
(a) 1 : 2 (b) 1 : 4 
(c)  1: 9 (d) none of these  
5. A thin film is viewed in white light. The colour of 
the film seen at a particular point depends upon: 
(a) width of the source  
(b) distance of the source  
(c) location of the observer  
(d) none of these  
6. In Young’s double slit experiment the 7
th
 
maximum with wavelength ?
1
 is at a distance d
1
 
and that with wavelength ?
2
 is at distance d
2
. 
Then d
1
/d
2
 =  
(a) ?
1
/ ?
2 
(b) ?
2
/ ?
1
 
(c) ?
2
1
/ ?
2
2
 (d) ?
2
2
/ ?
2
1
 
7. A light of 6000 Å is used to produce interference 
pattern. The observed fringe width is 0.12 mm. 
The angle between two interfering wave trains is 
(a) 2 x 10
–3
radian  (b)3 x 10
–3
radian 
(c) 4x 10
–3
radian  (d) 5x 10
–3
 radian. 
8. In a biprism experiment by using light of 
wavelength 5000 Å, 5 mm wide fringes are 
obtained on a screen 1.0 m away from the 
coherent sources. The separation between the two 
coherent sources is 
(a) 1.0mm   (b) 0.1mm 
(c) 0.05mm   (d) 0.01mm 
9. When the light is incident at the plarising angle, 
which of the following is completely polarised ? ? 
(a) Refracted light   
(b) Reflected light  
(c) both reflected as well as refracted  
(d) neither reflected nor refracted light  
10. In Young’s double slit experiment, if the widths of 
the slit are in the ratio 4 : 9, ratio of intensity of 
maxima to intensity of minima will be 
(a) 25:1 (b)  9:4 
(c) 3:2 (d)  81:16. 
11. Doppler shift for the light of wavelength 6000Å 
emitted from the sun is 0.04Å. If radius of the sun 
is 7 x 10
8
m then time period of rotation of the sun 
will be 
(a) 30days (b) 365 days 
(c) 24 hours (d) 25 days. 
12. In young’s double slit experiment a maximum is 
obtained when the path difference between the 
interfering waves is  
(Given that n = 1, 2, 3, 4….) 
(a) n
2
?
 
(b) n ? 
(c) (2n + 1)
2
?
 
(d) other than that given above  
13. A piano-convex lens when silvered on the plane 
side behaves like a concave mirror of focal length 
30 cm. When silvered on convex side, it behaves 
like a concave mirror of focal length 10 cm. The 
refractive index of material is 
(a)  3.0 (b)  2.0 
(c)  2.5 (d)  1.5 
14. Fig. shows the path of ray through an equiangular 
glass prism. It is incident on face AC at the critical 
angle for glass air interface. The angle of deviation 
of ray is 108°. Find the refractive index of glass 
prism. 
(a)  1.01 (b)  2.02 
(c)  1.45 (d)  1.72 
                                   [2] 
 
 
 
 
15. A thin prism of angle 5° is placed at a distance of 
10 cm from the object. What is distance of image 
from the object? 
(a)  0.25 cm (b) 0.43 cm 
(c)  0.52 cm (d) 0.61 cm 
16. The refractive index of the material of                            
equilateral prism is 3 . The angle of minimum 
deviation for the prism is 
(a) 30°  (b) 41° 
(c) 49°  (d) 60°. 
17. A light bulb is placed between two plane mirrors 
inclined at an angle of 60 °. The number of images 
formed are : 
(a) 6 (b) 2 
(c) 5  (d) 4 
18. What causes changes in the colours of the thin 
soap or oil films for the given beam of light ?  
(a) angle of incidence  
(b) angle of reflection  
(c) thickness of the film  
(d) none of these  
19. Instead of using two slits as in Young’s 
experiment, if we use two separate but identical 
sodium lamps, which of the following will occur ? 
(a) General illumination  
(b) Widely separate interference  
(c) Very bright maximum  
(d) Very dark minimum  
20. In Fresnel’s biprism experiment, bands of width 
0.185 mm are observed at a distance one meter 
from the slit. The image of the coherent sources is 
then produced at the same distance from the slit 
by placing a convex lens at 30 cm from the slit. 
The images are found to be separated by a 
distance of 0.70 cm. The wavelength of the light 
used is 
(a) 1295Å (b) 5550Å 
(c) 6000Å (d) 6500 Å 
21. If two mirrors are kept at 60 ° to each other, then 
the number of images formed by them is 
(a)  5 (b)  6 
(c)  7 (d)  8. 
22. A light source approaches the observer with 
velocity 0.5c. Doppler shift for light of wavelength 
5500 Å is 
(a) 616 Å (b)  1833 Å 
(c) 5500 Å (d)  6160 Å 
23. On introducing a thin mica sheet of thickness           
2 x 10
–6
 m and refractive index 1.5 in the path of 
one of the waves, central bright maxima shifts by 
n fringes. Wavelength of the wave used is 5000 Å, 
then n is 
(a) 1 (b) 2 
(c)  5 (d)  10. 
24. The focal length of a lens in a camera is marked ƒ: 
2.8 is 8 cm. What is diameter of lens? 
(a) 1.4 cm (b) 2.8 cm 
(c) 3.2 cm (d) 4.0 cm 
25. A plano-convex lens fits exactly into a plano-
concave lens. Their plane surfaces are parallel to 
each other. If the lenses are made of different 
materials, what is focal length of combination ? 
Given 
ƒ 1
 = focal length of piano-concave 
lens 
ƒ
2 
= focal length of piano-convex 
lens 
µ
1 
= ref. index of material of 
piano-concave lens 
µ
2
 = ref. index of material of 
piano convex lens. 
(a)  
R
1 2
µ - µ
 (b)  
1 2
R
µ - µ
   
(c)  
R
2
1
µ
µ
 (d) 
R
1
2
µ
µ
 
In every question a statement of ASSERTION is 
followed by a statement of REASON. Mark the 
correct answer out of the following choices:  
(a) If both ASSERTION and REASON are true 
and reason is the correct explanation of the 
assertion. 
(b) If both ASSERTION and REASON are true 
but reason is not the correct explanation of the 
assertion. 
(c) If ASSERTION is true but REASON is false. 
(d) If ASSERTION is false but REASON is true. 
26. Assertion: According to dual theory, light has a 
particle and wave nature at the same time.  
Reason: Any, particle or wave nature of light may 
be needed to explain a particular phenomenon.  
27. Assertion: Light emerging from a convex lens 
when a point source is placed at its focus 
produces a plane wavefront. 
                                   [3] 
 
 
 
Reason: A spherical wavefront on entering an 
inhomogenous anisotropic medium becomes a 
plane wavefront. 
28. Assertion: In Young’s double slit experiment if 
the point on the screen directly opposite to a slit is 
dark then the wavelength of the source is 
proportional to square of the distance between the 
slits.  
Reason: A minima is obtained when the path 
difference is (2n + 1) 
2
?
 and the phase difference 
is (2n + 1) p. 
29. Assertion: A narrow pulse of light, through a 
medium retains its shape as it travels through the 
medium. 
Reason: A narrow pulse of light is made of 
harmonic waves with a large range of 
wavelengths. 
30. Assertion: One of the two polaroids crossed to 
each other is rotated through 30 °. Only 1/8th of 
the incident unpolarised light passes through the 
combination. 
Reason: The amount of light going through the 
Polaroid is determined by Malus’ law. 
 
 
ANSWER KEY 
 
1 C 6 A 11 
D 
16 
D 
21 A 26 D 
2 A 7 D 12 
B 
17 
C 
22 B 27 C 
3 C 8 B 13 
D 
18 
C 
23 
B 
28 A 
4 C 9 B 14 
C 
19 A 24 
B 
29 D 
5 C 10 A 15 
B 
20 B 25 
B 
30 A 
 
SOLUTIONS 
1. Amplitude of the superimposing waves are  
A
1
/A
2
 = (1/9)
1/2
 = 1/3  
4
1
) A A (
) A A (
I
I
2
2 1
2
2 1
ima max
ima min
=
+
-
=  
2. Speed of sound in vacuum is zero. Also there is 
no dispersion of sound wave. So both (i) and (ii) 
are not valid for sound waves. 
3. (c) 
4. Amplitude are in the ratio 1 : 2. Hence amplitude 
at minimum will be 1 and that at maximum will 
be 3. 
5. (c) 
6. 7 ß = 7 D ? 1
/d = d
1
 and 7 ß
2
 = 7D ?/d = d
2
           
Hence ?
1
/ ?
2
 = d
1
/d
2
 
7. Here ß = 
d
D ?
 Angle ? between two waves train is  
? = 
ß
?
=
D
d
 or     ? = 
3
10
10 12 . 0
10 6000
-
-
×
×
\ 
8. use ß = 
d
D ?
 
9. (b) 
10. 
4
9
I
I
W
W
2
1
2
1
= = ?  
4
9
a
a
2
2
2
1
= 
2
3
a
a
2
1
= a
max
 = a
1
 + a
2
 
 a
min
 = a
1
 - a
2
  ? 
min
max
I
I
= 
1
25
) a a (
) a a (
2 1
2 1
=
-
+
 
11. Doppler’s shift is given by ? ? = ?
?
?
?
?
? ?
? = ?
c
. R
c
v
 ? = 
T
2 p
 ? R. ?
?
?
?
?
? p
T
2
. ? =
?
d
c
  T = days 25 c / .
dr
2 . R
= ?
p
 
12. (b) 
13. Focal length of plano -convex lens  f
1
 = 
1
R
- µ
…(1) 
(i) Focal length equivalent concave mirror, when 
one side of lens is silvered 
m m l
f
1
R
) 1 ( 2
f
1
f
2
F
1
+
- µ
= + = ……..(2) (ii) When 
plane side is silvered, then f
m
 = 8 , so eqn. (2) 
gives 
8
+
- µ
=
1
R
) 1 ( 2
F
1
1
 
R
) 1 ( 2
30
1 - µ
= (iii) When 
convex side of its silvered  f
m
 = 
2
R
, so eqn. (2) 
gives 
R
2
R
2
R
) 1 ( 2
F
1
2
µ
= +
- µ
= 
R
2
10
1 µ
= …(4). 
Dividing (3) by (4)  
µ
- µ
=
1
30
10
?    µ = 3 ( µ - 1)  or 
µ = 1.5 
14. Let i be angle of incidence at Q. Then angle of 
refraction at Q is  90 ° - (180 ° - A - 90 ° + C)  = A - 
C. Angle of incidence at S is also (A - C), so angle 
                                   [4] 
 
 
 
of emergence at S is also i.  Total deviation is 
algebraic sum of deviation at Q. R and S.  108 ° = i 
- (A - C) + 180 ° - 2C + i - (A -C)  2i - 2A + 180 ° = 
2i - 120 ° + 180 ° or  i = 24 ° µ = 
) C 60 ( sin
24 sin
r sin
i sin
-
°
= 
After solving, µ = 1.45 
15. D = ( µ - 1) A  Distance of image from the object  = 
OI = OE × D  = µ × ( µ - 1) A ? OI = 10 (1.5 - 1) × 
cm 43 . 0
180
5
=
°
× p
 
16. µ = 
2
A
sin
2
A
sin
r sin
i sin
d +
= 
°
d +
=
30 sin
2
A
sin
3 , because A = 
60 ° or sin ° = =
d +
60 sin
2
3
2
A
or   A + d = 2 × 60 = 
120 °. This gives d = 60 ° 
17. Number of images N = 1
360
-
?
. Where ? is in 
degrees. Here ? = 60 ° . Hence N = 5. 
18. (c) 
19. The superimposing waves will not be in constant 
phase. This leads to general illumination. 
20. Here ß = 0.185 mm = 0.0185 cms  D = 1.0 m = 100 
cm  u = = 30 cm  ? v = 100 - 30 = 70 cm;  Size of 
image, I = 0.70 cm Size of object, d = ?  ? = ?.  We 
know = 
v
u
image of size
object of Size
=  
70
30
I
d
= d = 
cm 30 . 0 7 . 0
70
30
I
70
30
= × = × 
Now ? = 
100
3 . 0 0185 . 0
D
d ×
=
ß
  = 555 × 10
-
7
 
cm  = 5550 ? 
21. (a) n = 
60
360
-1 =5. 
22. v’ = 
' c
v c
?
?
=
+
 ?  ?’ = 3667
c 5 . 0 c
c 5500
v c
c
=
+
×
=
+
?
Å ? 
? ? = 95500 - 3667) = 1833 Å 
23. shift is given by  n ? = ( µ - 1) t.  ? n = 2
t ) 1 (
=
?
- µ
 
24. The meaning of mark f : 2.8 is that f is 2.8 times 
the aperture (diameter) of lens ?  8 = 2.8 × 
diameter or diameter = 
8 . 2
cm 8
= 2.8 cm 
25. 
f
1
= ( µ 1 -1) 
?
?
?
?
?
?
-
2 1
R
1
R
1
, here R
1
 = 8 , R
2
 = R ? 
R
1
f
1 1
1
- µ
- = ? 
?
?
?
?
?
?
- - µ =
2 1
2
2
R
1
R
1
) 1 (
f
1
. here R
1
 = 
R and R
2
 = 8 ?  
R
1
f
1
2
2
- µ
= . Focal length of 
combination is 
R R
1
R
1
f
1
f
1
F
1
1 2 2 1
2 1
µ - µ
+
- µ
+
- µ
- = + = ? F = 
1 2
R
µ - µ
 
26. (d) Assertion is false but reason is true. 
According to the dual character of light, it can act 
as a particle or as a wave but not both 
simultaneously. Some phenomenon, such as 
interference, diffraction can be explained only on 
the basis of its wave nature. Some other 
phenomenon such as photoelectric effect, black 
body radiation can be explained by both the wave 
theory as well as the corpuscular theory of light. 
The assertion is false but the reason is true as a 
special character of light is needed to explain 
some particular phenomenon.  
27. (c) Assertion is true but reason is false. 
In an anisotropic medium the properties are not 
same in all direction. For an inhomogeneous 
medium the electric and magnetic properties 
differ at various positions in the medium. Thus 
the speed with which the secondary disturbance 
travels will vary and the wavefront will have a 
complicated shape. The reason is false a spherical 
wavefront cannot become a plane wavefront. 
Light emerging from a convex lens when a point 
source is placed at its focus is a parallel beam of 
light. This is equivalent to a point source at 
infinity produces a plane wavefront. The assertion 
is true. 
28. (a) Both assertion and reason are true and reason 
is the correct explanation of the assertion. 
Let x be the path difference of the two waves from 
the slits reaching a point P at a distance y from the 
central fringe on the screen. Then x = 
D
yd
 where d 
equals the distance between slits and D the 
perpendicular distance between slits & screen. 
In the case, the point of observation is directly 
opposite one of the slits, therefore y = .
2
d
 
It is also given that the point P lies at the centre of 
the dark fringe (a minimum). Therefore x = (2n + 
1)
2
?
. Combining x = 
. d
2
) 1 n 2 (
D 2
d
D
yd
2
2
? ? ?
?
+ = = 
29. (d) Assertion is false but reason is true. 
The velocity of light in a medium depends upon 
wavelength. A narrow pulse of light is made of a 
Page 5


                                   [1] 
 
 
 
(Wave & Ray Optics)  
1. In Young’s double slit experiment if the slit 
widths are in the ratio 1 : 9, the ratio of the 
intensity at minima to that at maxima will be   
(a) 1 (b) 1/9 
(c) 1/4 (d) 1/3 
2. Which of the following statements are true for 
light waves but not for sound waves ?  
(i)  the speed of wave is greater in vacuum than 
in a medium  
(ii) waves of different frequencies travels with 
different speeds in a medium   
(iii)  Waves travel with different speeds in 
different media.  
Choose your answer according to the code given 
below : 
(a) (i) and (ii) (b) (i) and (iii)  
(c) (ii) and (iii)  (d) (i), (ii) and (iii)  
3. For sustained interference we need two sources 
which emit radiation :  
(a) with same intensity  
(b) with same amplitude  
(c) having constant phase difference  
(d) in a narrow beam. 
4. The intensity of the light emerging from the two 
slits in Young’s experiment is in the ratio 1 to 4. 
The intensity of the minimum to the consecutive 
maximum  will be in the ratio of :  
(a) 1 : 2 (b) 1 : 4 
(c)  1: 9 (d) none of these  
5. A thin film is viewed in white light. The colour of 
the film seen at a particular point depends upon: 
(a) width of the source  
(b) distance of the source  
(c) location of the observer  
(d) none of these  
6. In Young’s double slit experiment the 7
th
 
maximum with wavelength ?
1
 is at a distance d
1
 
and that with wavelength ?
2
 is at distance d
2
. 
Then d
1
/d
2
 =  
(a) ?
1
/ ?
2 
(b) ?
2
/ ?
1
 
(c) ?
2
1
/ ?
2
2
 (d) ?
2
2
/ ?
2
1
 
7. A light of 6000 Å is used to produce interference 
pattern. The observed fringe width is 0.12 mm. 
The angle between two interfering wave trains is 
(a) 2 x 10
–3
radian  (b)3 x 10
–3
radian 
(c) 4x 10
–3
radian  (d) 5x 10
–3
 radian. 
8. In a biprism experiment by using light of 
wavelength 5000 Å, 5 mm wide fringes are 
obtained on a screen 1.0 m away from the 
coherent sources. The separation between the two 
coherent sources is 
(a) 1.0mm   (b) 0.1mm 
(c) 0.05mm   (d) 0.01mm 
9. When the light is incident at the plarising angle, 
which of the following is completely polarised ? ? 
(a) Refracted light   
(b) Reflected light  
(c) both reflected as well as refracted  
(d) neither reflected nor refracted light  
10. In Young’s double slit experiment, if the widths of 
the slit are in the ratio 4 : 9, ratio of intensity of 
maxima to intensity of minima will be 
(a) 25:1 (b)  9:4 
(c) 3:2 (d)  81:16. 
11. Doppler shift for the light of wavelength 6000Å 
emitted from the sun is 0.04Å. If radius of the sun 
is 7 x 10
8
m then time period of rotation of the sun 
will be 
(a) 30days (b) 365 days 
(c) 24 hours (d) 25 days. 
12. In young’s double slit experiment a maximum is 
obtained when the path difference between the 
interfering waves is  
(Given that n = 1, 2, 3, 4….) 
(a) n
2
?
 
(b) n ? 
(c) (2n + 1)
2
?
 
(d) other than that given above  
13. A piano-convex lens when silvered on the plane 
side behaves like a concave mirror of focal length 
30 cm. When silvered on convex side, it behaves 
like a concave mirror of focal length 10 cm. The 
refractive index of material is 
(a)  3.0 (b)  2.0 
(c)  2.5 (d)  1.5 
14. Fig. shows the path of ray through an equiangular 
glass prism. It is incident on face AC at the critical 
angle for glass air interface. The angle of deviation 
of ray is 108°. Find the refractive index of glass 
prism. 
(a)  1.01 (b)  2.02 
(c)  1.45 (d)  1.72 
                                   [2] 
 
 
 
 
15. A thin prism of angle 5° is placed at a distance of 
10 cm from the object. What is distance of image 
from the object? 
(a)  0.25 cm (b) 0.43 cm 
(c)  0.52 cm (d) 0.61 cm 
16. The refractive index of the material of                            
equilateral prism is 3 . The angle of minimum 
deviation for the prism is 
(a) 30°  (b) 41° 
(c) 49°  (d) 60°. 
17. A light bulb is placed between two plane mirrors 
inclined at an angle of 60 °. The number of images 
formed are : 
(a) 6 (b) 2 
(c) 5  (d) 4 
18. What causes changes in the colours of the thin 
soap or oil films for the given beam of light ?  
(a) angle of incidence  
(b) angle of reflection  
(c) thickness of the film  
(d) none of these  
19. Instead of using two slits as in Young’s 
experiment, if we use two separate but identical 
sodium lamps, which of the following will occur ? 
(a) General illumination  
(b) Widely separate interference  
(c) Very bright maximum  
(d) Very dark minimum  
20. In Fresnel’s biprism experiment, bands of width 
0.185 mm are observed at a distance one meter 
from the slit. The image of the coherent sources is 
then produced at the same distance from the slit 
by placing a convex lens at 30 cm from the slit. 
The images are found to be separated by a 
distance of 0.70 cm. The wavelength of the light 
used is 
(a) 1295Å (b) 5550Å 
(c) 6000Å (d) 6500 Å 
21. If two mirrors are kept at 60 ° to each other, then 
the number of images formed by them is 
(a)  5 (b)  6 
(c)  7 (d)  8. 
22. A light source approaches the observer with 
velocity 0.5c. Doppler shift for light of wavelength 
5500 Å is 
(a) 616 Å (b)  1833 Å 
(c) 5500 Å (d)  6160 Å 
23. On introducing a thin mica sheet of thickness           
2 x 10
–6
 m and refractive index 1.5 in the path of 
one of the waves, central bright maxima shifts by 
n fringes. Wavelength of the wave used is 5000 Å, 
then n is 
(a) 1 (b) 2 
(c)  5 (d)  10. 
24. The focal length of a lens in a camera is marked ƒ: 
2.8 is 8 cm. What is diameter of lens? 
(a) 1.4 cm (b) 2.8 cm 
(c) 3.2 cm (d) 4.0 cm 
25. A plano-convex lens fits exactly into a plano-
concave lens. Their plane surfaces are parallel to 
each other. If the lenses are made of different 
materials, what is focal length of combination ? 
Given 
ƒ 1
 = focal length of piano-concave 
lens 
ƒ
2 
= focal length of piano-convex 
lens 
µ
1 
= ref. index of material of 
piano-concave lens 
µ
2
 = ref. index of material of 
piano convex lens. 
(a)  
R
1 2
µ - µ
 (b)  
1 2
R
µ - µ
   
(c)  
R
2
1
µ
µ
 (d) 
R
1
2
µ
µ
 
In every question a statement of ASSERTION is 
followed by a statement of REASON. Mark the 
correct answer out of the following choices:  
(a) If both ASSERTION and REASON are true 
and reason is the correct explanation of the 
assertion. 
(b) If both ASSERTION and REASON are true 
but reason is not the correct explanation of the 
assertion. 
(c) If ASSERTION is true but REASON is false. 
(d) If ASSERTION is false but REASON is true. 
26. Assertion: According to dual theory, light has a 
particle and wave nature at the same time.  
Reason: Any, particle or wave nature of light may 
be needed to explain a particular phenomenon.  
27. Assertion: Light emerging from a convex lens 
when a point source is placed at its focus 
produces a plane wavefront. 
                                   [3] 
 
 
 
Reason: A spherical wavefront on entering an 
inhomogenous anisotropic medium becomes a 
plane wavefront. 
28. Assertion: In Young’s double slit experiment if 
the point on the screen directly opposite to a slit is 
dark then the wavelength of the source is 
proportional to square of the distance between the 
slits.  
Reason: A minima is obtained when the path 
difference is (2n + 1) 
2
?
 and the phase difference 
is (2n + 1) p. 
29. Assertion: A narrow pulse of light, through a 
medium retains its shape as it travels through the 
medium. 
Reason: A narrow pulse of light is made of 
harmonic waves with a large range of 
wavelengths. 
30. Assertion: One of the two polaroids crossed to 
each other is rotated through 30 °. Only 1/8th of 
the incident unpolarised light passes through the 
combination. 
Reason: The amount of light going through the 
Polaroid is determined by Malus’ law. 
 
 
ANSWER KEY 
 
1 C 6 A 11 
D 
16 
D 
21 A 26 D 
2 A 7 D 12 
B 
17 
C 
22 B 27 C 
3 C 8 B 13 
D 
18 
C 
23 
B 
28 A 
4 C 9 B 14 
C 
19 A 24 
B 
29 D 
5 C 10 A 15 
B 
20 B 25 
B 
30 A 
 
SOLUTIONS 
1. Amplitude of the superimposing waves are  
A
1
/A
2
 = (1/9)
1/2
 = 1/3  
4
1
) A A (
) A A (
I
I
2
2 1
2
2 1
ima max
ima min
=
+
-
=  
2. Speed of sound in vacuum is zero. Also there is 
no dispersion of sound wave. So both (i) and (ii) 
are not valid for sound waves. 
3. (c) 
4. Amplitude are in the ratio 1 : 2. Hence amplitude 
at minimum will be 1 and that at maximum will 
be 3. 
5. (c) 
6. 7 ß = 7 D ? 1
/d = d
1
 and 7 ß
2
 = 7D ?/d = d
2
           
Hence ?
1
/ ?
2
 = d
1
/d
2
 
7. Here ß = 
d
D ?
 Angle ? between two waves train is  
? = 
ß
?
=
D
d
 or     ? = 
3
10
10 12 . 0
10 6000
-
-
×
×
\ 
8. use ß = 
d
D ?
 
9. (b) 
10. 
4
9
I
I
W
W
2
1
2
1
= = ?  
4
9
a
a
2
2
2
1
= 
2
3
a
a
2
1
= a
max
 = a
1
 + a
2
 
 a
min
 = a
1
 - a
2
  ? 
min
max
I
I
= 
1
25
) a a (
) a a (
2 1
2 1
=
-
+
 
11. Doppler’s shift is given by ? ? = ?
?
?
?
?
? ?
? = ?
c
. R
c
v
 ? = 
T
2 p
 ? R. ?
?
?
?
?
? p
T
2
. ? =
?
d
c
  T = days 25 c / .
dr
2 . R
= ?
p
 
12. (b) 
13. Focal length of plano -convex lens  f
1
 = 
1
R
- µ
…(1) 
(i) Focal length equivalent concave mirror, when 
one side of lens is silvered 
m m l
f
1
R
) 1 ( 2
f
1
f
2
F
1
+
- µ
= + = ……..(2) (ii) When 
plane side is silvered, then f
m
 = 8 , so eqn. (2) 
gives 
8
+
- µ
=
1
R
) 1 ( 2
F
1
1
 
R
) 1 ( 2
30
1 - µ
= (iii) When 
convex side of its silvered  f
m
 = 
2
R
, so eqn. (2) 
gives 
R
2
R
2
R
) 1 ( 2
F
1
2
µ
= +
- µ
= 
R
2
10
1 µ
= …(4). 
Dividing (3) by (4)  
µ
- µ
=
1
30
10
?    µ = 3 ( µ - 1)  or 
µ = 1.5 
14. Let i be angle of incidence at Q. Then angle of 
refraction at Q is  90 ° - (180 ° - A - 90 ° + C)  = A - 
C. Angle of incidence at S is also (A - C), so angle 
                                   [4] 
 
 
 
of emergence at S is also i.  Total deviation is 
algebraic sum of deviation at Q. R and S.  108 ° = i 
- (A - C) + 180 ° - 2C + i - (A -C)  2i - 2A + 180 ° = 
2i - 120 ° + 180 ° or  i = 24 ° µ = 
) C 60 ( sin
24 sin
r sin
i sin
-
°
= 
After solving, µ = 1.45 
15. D = ( µ - 1) A  Distance of image from the object  = 
OI = OE × D  = µ × ( µ - 1) A ? OI = 10 (1.5 - 1) × 
cm 43 . 0
180
5
=
°
× p
 
16. µ = 
2
A
sin
2
A
sin
r sin
i sin
d +
= 
°
d +
=
30 sin
2
A
sin
3 , because A = 
60 ° or sin ° = =
d +
60 sin
2
3
2
A
or   A + d = 2 × 60 = 
120 °. This gives d = 60 ° 
17. Number of images N = 1
360
-
?
. Where ? is in 
degrees. Here ? = 60 ° . Hence N = 5. 
18. (c) 
19. The superimposing waves will not be in constant 
phase. This leads to general illumination. 
20. Here ß = 0.185 mm = 0.0185 cms  D = 1.0 m = 100 
cm  u = = 30 cm  ? v = 100 - 30 = 70 cm;  Size of 
image, I = 0.70 cm Size of object, d = ?  ? = ?.  We 
know = 
v
u
image of size
object of Size
=  
70
30
I
d
= d = 
cm 30 . 0 7 . 0
70
30
I
70
30
= × = × 
Now ? = 
100
3 . 0 0185 . 0
D
d ×
=
ß
  = 555 × 10
-
7
 
cm  = 5550 ? 
21. (a) n = 
60
360
-1 =5. 
22. v’ = 
' c
v c
?
?
=
+
 ?  ?’ = 3667
c 5 . 0 c
c 5500
v c
c
=
+
×
=
+
?
Å ? 
? ? = 95500 - 3667) = 1833 Å 
23. shift is given by  n ? = ( µ - 1) t.  ? n = 2
t ) 1 (
=
?
- µ
 
24. The meaning of mark f : 2.8 is that f is 2.8 times 
the aperture (diameter) of lens ?  8 = 2.8 × 
diameter or diameter = 
8 . 2
cm 8
= 2.8 cm 
25. 
f
1
= ( µ 1 -1) 
?
?
?
?
?
?
-
2 1
R
1
R
1
, here R
1
 = 8 , R
2
 = R ? 
R
1
f
1 1
1
- µ
- = ? 
?
?
?
?
?
?
- - µ =
2 1
2
2
R
1
R
1
) 1 (
f
1
. here R
1
 = 
R and R
2
 = 8 ?  
R
1
f
1
2
2
- µ
= . Focal length of 
combination is 
R R
1
R
1
f
1
f
1
F
1
1 2 2 1
2 1
µ - µ
+
- µ
+
- µ
- = + = ? F = 
1 2
R
µ - µ
 
26. (d) Assertion is false but reason is true. 
According to the dual character of light, it can act 
as a particle or as a wave but not both 
simultaneously. Some phenomenon, such as 
interference, diffraction can be explained only on 
the basis of its wave nature. Some other 
phenomenon such as photoelectric effect, black 
body radiation can be explained by both the wave 
theory as well as the corpuscular theory of light. 
The assertion is false but the reason is true as a 
special character of light is needed to explain 
some particular phenomenon.  
27. (c) Assertion is true but reason is false. 
In an anisotropic medium the properties are not 
same in all direction. For an inhomogeneous 
medium the electric and magnetic properties 
differ at various positions in the medium. Thus 
the speed with which the secondary disturbance 
travels will vary and the wavefront will have a 
complicated shape. The reason is false a spherical 
wavefront cannot become a plane wavefront. 
Light emerging from a convex lens when a point 
source is placed at its focus is a parallel beam of 
light. This is equivalent to a point source at 
infinity produces a plane wavefront. The assertion 
is true. 
28. (a) Both assertion and reason are true and reason 
is the correct explanation of the assertion. 
Let x be the path difference of the two waves from 
the slits reaching a point P at a distance y from the 
central fringe on the screen. Then x = 
D
yd
 where d 
equals the distance between slits and D the 
perpendicular distance between slits & screen. 
In the case, the point of observation is directly 
opposite one of the slits, therefore y = .
2
d
 
It is also given that the point P lies at the centre of 
the dark fringe (a minimum). Therefore x = (2n + 
1)
2
?
. Combining x = 
. d
2
) 1 n 2 (
D 2
d
D
yd
2
2
? ? ?
?
+ = = 
29. (d) Assertion is false but reason is true. 
The velocity of light in a medium depends upon 
wavelength. A narrow pulse of light is made of a 
                                   [5] 
 
 
 
harmonic waves with a large range of 
wavelengths. The reason is the true. Each 
harmonic wave travels with a different speed in 
the medium. Thus the shape of the pulse is 
altered. The assertion is not true.  
30. (a) Both assertion and reason are true and reason 
is correct explanation of the assertion. 
Malus law states that when plane polarized light 
passes through a polarizer, then the intensity I is 
according to I ? cos
2
? or I = I
0
 cos
2
?. Where I
0
 is 
the intensity of plane polarized light and ? is the 
angle between the plane of transmission and the 
polarizer. When one of the polaroids is rotated 
through 30 °, the angle ? between the plane of 
vibration and the axis is = 90 ° - 30 ° = 60 °.         
Therefore, I = I
0
 cos
2 
60 ° = 
4
I
0
. If I’ is the intensity 
of the unpolarised light,       then the intensity of 
plane polarized light produced by the first 
Polaroid is .
2
' I
 Therefore, I = 
8
' I
4
I
2
' I
4
I
0
= = . The 
reason is correct and leads to the correct value 
given in the assertion.  
 
 
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