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# 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.
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
(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
–3
(c) 4x 10
–3
–3
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.
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
(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
–3
(c) 4x 10
–3
–3
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.
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
(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
–3
(c) 4x 10
–3
–3
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.

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.
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
(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
–3
(c) 4x 10
–3
–3
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.

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.
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
(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
–3
(c) 4x 10
–3
–3
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.

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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