WAVE OPTICS

KEY CONCEPT
1. If two coherent waves with intensity I1 and I2 are superimposed with a phase difference of I, the resulting
wave intensity is
I = I1 + I2 + 2 I1I 2 cos I
(i) For maxima, optical path difference = nO [optical path = P (geometrical path)]
1 1
(ii) For minima, optical path difference = (n – )O or (n + )O
2 2
2S
(iii) Phase difference I = (optical path difference)
O
O : Wavelength in vacuum

2. The phase difference between two waves at a point will depend upon
(i) the difference in path lengths of two waves from their respective sources.( geometrical path difference)
(ii) the refractive index of the medium (media)
(iii) phase difference at source (if any).
(iv) In case, the waves suffer reflection, the reflected wave differs in phase by S with respect to the incident
wave if the incidence occurs in rarer medium. There would be no phase difference if incidence occures
in denser medium.
3. Young's Double Slit Experiment

Fig. in Young’s interference experiment, incident monochromatic light is diffracted by slit S0, which then
acts as a point source of ligh that emits semicircular wavefronts. As that light reaches screen B, it is
diffracted by slits S1 and.S2, which then act as two point sources of light. The light waves traveling from
slits S1 and S2 overlap and undergo interference, forming an interference pattern of maxima and minima
on viewing screen C. This figure is a cross section; the screens, slits, and interference pattern extend into
and out of the page. Between screens Band C, the semicircular wavefront’s centered on S2 depict the
waves that would be there if only S2 were open. Similarly, those centered on S1 depict waves that would
be there if only S1 were open.

(i) If d << D
'x = S2P – S1P = d sin T
If O << d then sin T| T | tan T as when P is close to D so T is small.
dy
'x =
D
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dy
(ii) For maxima = nO
D
DO 2 DO
or y = 0, ± ,±
d d
dy
(iii) For minima = [n + (1/2)]O
D
DO 3DO 5DO
or y = ± ,± ,± , so on
2d 2d 2d
OD
(iv) Fringe width, E =
d

4. Displacement of fringe Pattern

When a film of thickness 't' and refractive index 'P' is introduced in the path of one of the source's of
light, then fringe shift occurs as the optical path difference changes.
Optical path difference at P.
'x = S2P – [S1P + Pt – t]
= S2P – S1P (P – 1) t = y. (d/D) – (P– 1)t
D(P  1) t
Ÿ The fringe shift is given by 'y =
d
5. Intensity Variation on Screen

If I0 is the intensity of light beam coming from each slit, the

resultant intensity at a point where they have a phase
difference of I is
I 2S(d sin T)
I = 4I0 cos2 , where I =
2 O

6. Interference at thin film

optical path difference = 2Pt cos r
= 2Pt (in case of near normal incidence)
For interference in reflected light
(i) Condition of minima 2Pt cos r = nO
§ 1·
(ii) Condition of maxima 2Pt cos r = ¨ n  ¸ O
© 2¹
 WAVE OPTICS
EXERCISE – I
Q.1 Two coherent waves are described by the expressions.
§ 2Sx1 S·
E1 E 0 sin ¨  2Sft  ¸
© O 6¹
§ 2Sx 2 S·
E2 E 0 sin ¨  2Sft  ¸
© O 8¹
Determine the relationship between x1 and x2 that produces constructive interference when the two
waves are superposed.
Q.2 In a Young's double slit experiment for interference of light, the slits are 0.2 cm apart and are illuminated
by yellow light (O = 600 nm). What would be the fringe width on a screen placed 1 m from the plane of
slits if the whole system is immersed in water of index 4/3?
Q.3 In Young's double slit experiment the slits are 0.5 mm apart and the interference is observed on a screen at
a distance of 100 cm from the slit. It is found that the 9th bright fringe is at a distance of 7.5 mm from the
second dark fringe from the centre of the fringe pattern on same side. Find the wavelength of the light used.
Q.4 Light of wavelength 520 nm passing through a double slit,
produces interference pattern of relative intensity versus
deflection angle T as shown in the figure. find the separation d
between the slits.
Q.5 In a YDSE apparatus, d = 1mm, O = 600nm and D = 1m. The slits individually produce same intensity
on the screen. Find the minimum distance between two points on the screen having 75% intensity of the
maximum intensity.
Q.6 The distance between two slits in a YDSE apparatus is 3mm. The distance of the screen from the slits is
1m. Microwaves of wavelength 1 mm are incident on the plane of the slits normally. Find the distance of
the first maxima on the screen from the central maxima. Also find the total number of maxima on the
screen.
Q.7 One slit of a double slit experiment is covered by a thin glass plate of refractive index 1.4 and the other
by a thin glass plate of refractive index 1.7. The point on the screen, where central bright fringe was
formed before the introduction of the glass sheets, is now occupied by the 5th bright fringe. Assuming
that both the glass plates have same thickness and wavelength of light used is 4800 Å, find their thickness.
Q.8 A monochromatic light of O = 5000 Å is incident on two slits separated by a distance of 5 × 104 m . The
interference pattern is seen on a screen placed at a distance of 1 m from the slits . A thin glass plate of
thickness 1.5 × 106 m & refractive index P = 1.5 is placed between one of the slits & the screen. Find
the intensity at the centre of the screen, if the intensity there is I0 in the absence of the plate . Also find the
lateral shift of the central maximum.
Q.9 One radio transmitter A operating at 60.0 MHz is 10.0 m from another similar transmitter B that is 180°
out of phase with transmitter A. How far must an observe move from transmitter A toward transmitter B
along the line connecting A and B to reach the nearest point where the two beams are in phase?
Q.10 Two microwave coherent point sources emitting waves of wavelength O are
placed at 5O distance apart. The interference is being observed on a flat
non-reflecting surface along a line passing through one source, in a direction
perpendicular to the line joining the two sources (refer figure)
Considering O as 4 mm, calculate the positions of maxima and draw shape of
interference pattern. Take initial phase difference between the two sources to be zero.
 WAVE OPTICS
Q.11 Our discussion of the techniques for determining constructive and destructive interference by reflection
from a thin film in air has been confined to rays striking the film at nearly normal incidence. Assume that
a ray is incident at an angle of 45° (relative to the normal) on a film with an index of refraction of 2 .
Calculate the minimum thickness for constructive interference if the light is sodium light with a wavelength
of 600 nm.

Q.12 A ray of light of intensity I is incident on a parallel glass-slab at a point A

as shown in figure. It undergoes partial reflection and refraction. At each
reflection 20% of incident energy is reflected. The rays AB and Ac
Bcundergo interference. Find the ratio Imax/Imin.
[Neglect the absorption of light]

Q.13 A lens (P =1.5) is coated with a thin film of refractive index 1.2 in order to reduce the reflection from its
surface at O= 4800 Å. Find the minimum thickness of the film which will minimize the intensity of the
reflected light. [Assume near normal incidence]

Q.14 A broad source of light of wavelength 680nm illuminates normally two glass
plates 120mm long that meet at one end and are separated by a wire 0.048
mm in diameter at the other end. Find the number of bright fringes formed
over the 120mm distance.

EXERCISE – II
Q.1 If the slits of the double slit were moved symmetrically apart with relative velocity v, calculate the number
of fringes passing per unit time at a distance y from the centre of the fringe system formed on a screen x
distance away from the double slits if wavelength of light is O. Assume x >> d & d >> O.

Q.2 A thin glass plate of thickness t and refractive index P is inserted between screen & one of the slits in a
Young's experiment. If the intensity at the centre of the screen is I, what was the intensity at the same
point prior to the introduction of the sheet.

Q.3 In Young's experiment, the source is red light of wavelength 7 × 107 m . When a thin glass plate of
refractive index 1.5 at this wavelength is put in the path of one of the interfering beams, the central bright
fringe shifts by 103 m to the position previously occupied by the 5th bright fringe . Find the thickness of
the plate . When the source is now changed to green light of wavelength 5 × 107 m, the central fringe
shifts to a position initially occupied by the 6th bright fringe due to red light without the plate. Find the
refractive index of glass for the green light . Also estimate the change in fringe width due to the change in
wavelength.

Q.4 In a Young's experiment, the upper slit is covered by a thin glass plate of refractive index 1.4 while the
lower slit is covered by another glass plate having the same thickness as the first one but having refractive
index 1.7 . Interference pattern is observed using light of wavelength 5400 Å . It is found that the point
P on the screen where the central maximum (n = 0) fell before the glass plates were inserted now has
3/4 the original intensity . It is further observed that what used to be the 5th maximum earlier, lies below
the point P while the 6th minimum lies above P. Calculate the thickness of the glass plate.
(Absorption of light by glass plate may be neglected).
 WAVE OPTICS
Q.5 A screen is at a distance D = 80 cm from a diaphragm having two
narrow slits S1 and S2 which are d = 2 mm apart. Slit S1 is covered by
a transparent sheet of thickness t1 = 2.5 Pm and S2 by another sheet of
thickness t2 = 1.25 Pm as shown in figure. Both sheets are made of
same material having refractive index P = 1.40. Water is filled in space
between diaphragm and screen. A monochromatic light beam of wavelength O = 5000 Å is incident
normally on the diaphragm. Assuming intensity of beam to be uniform and slits of equal width, calculate
ratio of intensity at C to maximum intensity of interference pattern obtained on the screen, where C is
foot of perpendicular bisector of S1S2. (Refractive index of water, Pw = 4/3)

Q.6 A coherent parallel beam of microwaves of wavelength

O = 0.5 mm falls on a Young's double slit apparatus. The separation
between the slits is 1.0 mm. The intensity of microwaves is measured on
screen placed parallel to the plane of the slits at a distance of 1.0 m from
it, as shown in the figure.
(a) If the incident beam falls normally on the double slit apparatus, find the
ycoordinates of all the interference minima on the screen .
(b) If the incident beam makes an angle of 30º with the xaxis (as in the dotted arrow shown in the figure),
find the ycoordinates of the first minima on either side of the central maximum.

Q.7 In a YDSE two thin transparent sheets are used in front of the slits S1 and
S2. P1 = 1.6 and P2 = 1.4. If both sheets have thickness t, the central
maximum is observed at a distance of 5 mm from centre O. Now the
sheets are replaced by two sheets of same material of refractive index
P1  P 2 t1  t 2
but having thickness t1& t2 such that t = . Now central
2 2
maximum is observed at distance of 8mm from centre O on the same side
as before. Find the thickness t1(in Pm)
[Given: d = 1 mm. D = 1m].

Q.8 Radio waves coming at ‘D to vertical are recieved by a radar after reflection
from a nearby water surface & directly. What should be height of antenna from
water surface so that it records a maximum intensity. (wavelength = O).

EXERCISE – III
Q.1 The Young's double slit experiment is done in a medium of refractive index
4/3. A light of 600 nm wavelength is falling on the slits having 0.45 mm
separation. The lower slit S2 is covered by a thin glass sheet of thickness
10.4 Pm and refractive index 1.5. The interference pattern is observed on
a screen placed 1.5 m from the slits as shown
(a) Find the location of the central maximum (bright fringe with zero path difference) on the y-axis.
(b) Find the light intensity at point O relative to the maximum fringe intensity.
(c) Now, if 600 nm light is replaced by white light of range 400 to 700 nm, find the wavelengths of the light
that form maxima exactly at point O .
[All wavelengths in this problem are for the given medium of refractive index 4/3. Ignore dispersion]
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Q.2 A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice
is placed on a flat glass plate as shown. The observed interference fringes from
this combination shall be
(A) straight
(B) circular
(C) equally spaced (D) having fringe spacing which increases as we go outwards.
Q.3 In a double slit experiment, when the width of one slit is made twice as wide as the other in contrast to
normal YDSE having slits of equal width. Then, in the interference pattern
(A) the intensities of both the maxima and the minima increase.
(B) the intensity of the maxima increases and the minima has zero intensity.
(C) the intensity of the maxima decreases and that of the minima increases.
(D) the intensity of the maxima decreases and the minima has zero intensity.
Q.4 A glass plate kept in air of refractive index 1.5 is coated with a thin layer of thickness t and refractive
index 1.8. Light of wavelength O travelling in air is incident normally on the layer . It is partly reflected at
the upper and the lower surfaces of the layer and the two reflected rays interfere. Write the condition for
their constructive interference assume rays to be incident normally. If O = 648 nm, obtain the least value
of t for which the rays interfere constructively.

Q.5 Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase
difference between the beams is S/2 at point A and S at point B. Then the difference between the
resultant intensities at A and B is
(A) 2I (B) 4I (C) 5I (D) 7I

Q.6 In a young double slit experiment, 12 fringes are observed to be formed in a certain segment of the screen
when light of wavelength 600 nm is used. If the wavelength of light is changed to 400 nm, number of
fringes observed in the same segment of the screen is given by
(A) 12 (B) 18 (C) 24 (D) 30

Q.7 A vessel ABCD of 10 cm width has two small slits S1 and S2 sealed with
identical glass plates of equal thickness. The distance between the slits is
0.8 mm. POQ is the line perpendicular to the plane AB and passing through
O, the middle point of S1 and S2. A monochromatic light source is kept at
S, 40 cm below P and 2 m from the vessel, to illuminate the slits as shown
in the figure below. Calculate the position of the central bright fringe on the
other wall CD with respect to the line OQ. Now, a liquid is poured into the vessel and filled up to OQ.
The central bright fringe is found to be at Q. Calculate the refractive index of the liquid.

Q.8 A point source S emitting light of wavelength 600 nm is placed at a very

small height h above the flat reflecting surface AB (see figure). The
intensity of the reflected light is 36% of the incident intensity. Interference
fringes are observed on a screen placed parallel to the reflecting surface
at a very large distance D from it.
(a) What is the shape of the interference fringes on the screen?
(b) Calculate the ratio of the minimum to the maximum intensities in the interference fringes formed near the
point P (shown in the figure).
(c) If the intensities at point P corresponds to a maximum, calculate the minimum distance through which the
reflecting surface AB should be shifted so that the intensity at P again becomes maximum.
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Q.9 In the adjacent diagram, CP represents a wavefront and AO and BP, the
corresponding two rays. Find the condition on T for constructive interference
at P between the ray BP and reflected ray OP.
3O O
(A) cosT = 2 d (B) cosT = 4 d
O 4O
(C) secT – cosT = (D) secT – cosT =
d d
Q.10 A prism (PP = 3 ) has an angle of prism A = 30°. A thin film (Pf = 2.2) is coated
on face AC as shown in the figure. Light of wavelength 550 nm is incident on the
face AB at 60° angle of incidence. Find
(i) the angle of its emergence from the face AC and
(ii) the minimum thickness (in nm) of the film for which the emerging light is
of maximum possible intensity.
Q.11 In a YDSE bi-chromatic light of wavelengths 400 nm and 560 nm are used. The distance between the
slits is 0.1 mm and the distance between the plane of the slits and the screen is 1 m. The minimum
distance between two successive regions of complete darkness is
(A) 4 mm (B) 5.6 mm (C) 14 mm (D) 28 mm
Q.12 In a Young's double slit experiment, two wavelengths of 500 nm and 700 nm were used. What is the
minimum distance from the central maximum where their maximas coincide again?
Take D/d = 103. Symbols have their usual meanings.
Q.13 In Young's double slit experiment maximum intensity is I then the angular position where the intensity
I
becomes is:
4
§O· § O · § O · § O ·
(A) sin–1 ¨ ¸ (B) sin–1 ¨ ¸ (C) sin–1 ¨ ¸ (D) sin–1 ¨ ¸
©d¹ © 3d ¹ © 2d ¹ © 4d ¹
Paragraph for Question Nos. 14 to 16 (3 questions)
The figure shows a surface XY separating two transparent media, medium-1 and medium-2. The lines
ab and cd represent wavefronts of a light wave traveling in medium-1 and incident on XY. The lines ef
and gh represent wavefronts of the light wave in medium-2 after refraction.

Q.14 Light travels as a

(A) parallel beam in each medium (B) convergent beam in each medium
(C) divergent beam in each medium
(D) divergent beam in one medium and convergent beam in the other medium
Q.15 The phases of the light wave at c, d, e and f are Ic, Id, Ie and If respectively. It is given that Ic zIf.
(A) Ic cannot be equal to Id (B) Id can be equal to Ie
(C) (Id – If) is equal to (Ic – Ie) (D) (Id – Ic) is not equal to (If – Ie)
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Q.16 Speed of light is
(A) the same in medium-1 and medium-2 (B) larger in medium-1 than in medium-2
(C) larger in medium-2 than in medium-1 (D) different at b and d
Q.17 In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the
light is O. The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the
correct choice(s).
(A) If d = O, the screen will contain only one maximum
(B) If O < d < 2O, at least one more maximum (besides the central maximum) will be observed on the
screen
(C) If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the intensities
of the observed dark and bright fringes will increase
(D) If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the
intensities of the observed dark and bright fringes will increase
Q.18 Column I shows four situations of standard Young’s double slit arrangement with the screen placed far
away from the slits S1 and S2. In each of these cases S1P0 = S2P0, S1P1 – S2P1 = O/4 and
S1P2 – S2P2 =O/3,, where O is the wavelength of the light used. In the cases B, C and D, a transparent
sheet of refractive index µ and thickness t is pasted on slit S2. The thicknesses of the sheets are different
in different cases. The phase difference between the light waves reaching a point P on the screen from the
two slits is denoted by G(P) and the intensity by I(P). Match each situation given in Column I with the
statement(s) in Column II valid for that situation.
Column-I
Column-II

(A) (p) G(P0) = 0

(B) (µ – 1) t = O/4 (q) G(P1) = 0

(C) (µ – 1) t = O/2 (r) I(P1) = 0

(D) (µ – 1) t = 3O/4 (s) I(P0) > I(P1)

(t) I(P2) > I(P1)

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QUESTION BANK
ONLY ONE OPTION IS CORRECT.
Take approx. 2 minutes for answering each question.
Q.1 Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and
minimum possible intensities in the resulting beam are :
(A) 5I and I (B) 5I and 3I (C) 9I and I (D) 9I and 3I

Q.2 Figure shows plane waves refracted from air to water using Huygen's
principle a, b, c, d, e are lengths on the diagram. The refractive index of
water wrt air is the ratio.
(A) a/e (B) b/e (C) b/d (D) d/b

Q.3 When light is refracted into a denser medium,

(A) its wavelength and frequeny both increase
(B) its wavelength increases but frequency remains unchanged
(C) its wavelength decreases but frequency remains unchanged
(D) its wavelength and frequency both decrease.
Q.4 In YDSE how many maxima can be obtained on the screen if wavelength of light used is 200nm and
d = 700 nm:
(A) 12 (B) 7 (C) 18 (D) none of these

Q.5 In a YDSE, the central bright fringe can be identified :

(A) as it has greater intensity than the other bright fringes.
(B) as it is wider than the other bright fringes.
(C) as it is narrower than the other bright fringes.
(D) by using white light instead of single wavelength light.

Q.6 In Young's double slit experiment, the wavelength of red light is 7800 Å and that of blue light is 5200 Å.
The value of n for which nth bright band due to red light coincides with (n + 1)th bright band due to blue
light, is :
(A) 1 (B) 2 (C) 3 (D) 4

Q.7 Two identical narrow slits S1 and S2 are illuminated by light of wavelength O from a point source P.

If, as shown in the diagram above, the light is then allowed to fall on a screen, and if n is a positive
integer, the condition for destructive interference at Q is
(A) (l1 – l2) = (2n + 1)O/2 (B) (l3 – l4) = (2n + 1)O/2
(C) (l1 + l2) – (l3 + l4) = nO (D) (l1 + l3) – (l2 + l4) = (2n + 1)O/2

Q.8 In Young's double slit experiment, the two slits act as coherent sources of equal amplitude A and wavelength
O. In another experiment with the same setup the two slits are sources of equal amplitude A and wavelength
O but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case to that
in the second case is
(A) 1 : 1 (B) 2 : 1 (C) 4 : 1 (D) none of these
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Q.9 In a Young's double slit experiment, a small detector measures an intensity of illumination of I units at the
centre of the fringe pattern. If one of the two (identical) slits is now covered, the measured intensity will be
(A) 2I (B) I (C) I/4 (D) I/2

Q.10 In a Young's double slit experiment D equals the distance of screen and d is the separation between the
slit. The distance of the nearest point to the central maximum where the intensity is same as that due to a
single slit, is equal to
DO DO DO 2DO
(A) (B) 2 d (C) 3 d (D)
d d

Q.11 Two point monochromatic and coherent sources of light of wavelength O are placed on the dotted line in
front of a large screen. The source emit waves in phase with each other. The distance between S1 and S2
is 'd' while their distance from the screen is much larger. Then,
(1) o If d = 7O/2, O will be a minima
(2) o If d = 4.3O, there will be a total of 8 minima on y axis.
(3) o If d = 7O, O will be a maxima.
(4) o If d = O, there will be only one maxima on the screen.
Which is the set of correct statement :
(A) 1, 2 & 3 (B) 2, 3 & 4 (C) 1, 2, 3 & 4 (D) 1, 3 & 4

Q.12 A plane wavefront AB is incident on a concave mirror as shown.

Then, the wavefront just after reflection is

(A) (B) (C) (D) None of the above

Q.13 In a Young's Double slit experiment, first maxima is observed at a fixed point P on the screen. Now the
screen is continuously moved away from the plane of slits. The ratio of intensity at point P to the intensity
at point O (centre of the screen)
(A) remains constant
(B) keeps on decreasing
(C) first decreases and then increases
(D) First decreases and then becomes constant

Q.14 Two slits are separated by 0.3 mm. A beam of 500 nm light strikes the slits
producing an interference pattern. The number of maxima observed in the angular
range – 30° < T < 30°.
(A) 300 (B) 150
(C) 599 (D) 601
Q.15 In the figure shown if a parallel beam of white light is incident on the
plane of the slits then the distance of the white spot on the screen from
O is [Assume d << D, O << d]
(A) 0 (B) d/2
(C) d/3 (D) d/6
Q.16 In the above question if the light incident is monochromatic and point O is a maxima, then the wavelength
of the light incident cannot be
(A) d 2 3D (B) d 2 6D (C) d 2 12D (D) d 2 18D
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Q.17 In Young's double slit arrangement, water is filled in the space between screen and slits. Then :
(A) fringe pattern shifts upwards but fringe width remains unchanged.
(B) fringe width decreases and central bright fringe shifts upwards.
(C) fringe width increases and central bright fringe does not shift.
(D) fringe width decreases and central bright fringe does not shift.
Q.18 Light of wavelength O in air enters a medium of refractive index P. Two points in this medium, lying along
the path of this light, are at a distance x apart. The phase difference between these points is :
2SPx 2Sx 2S(P  1) x 2S x
(A) (B) P O (C) (D)
O O (P  1)O
Q.19 In YDSE, the source placed symmetrically with respect to the slit is
now moved parallel to the plane of the slits so that it is closer to the
upper slit, as shown. Then,
(A) the fringe width will increase and fringe pattern will shift down.
(B) the fringe width will remain same but fringe pattern will shift up.
(C) the fringe width will decrease and fringe pattern will shift down.
(D) the fringe width will remain same but fringe pattern will shift down.
Q.20 In the figure shown in YDSE, a parallel beam of light is incident on the slit from a medium of refractive
index n1. The wavelength of light in this medium is O1. A transparent slab of thickness ‘t’ and refractive
index n3 is put infront of one slit. The medium between the screen and the plane of the slits is n2. The
phase difference between the light waves reaching point ‘O’ (symmetrical, relative to the slits) is :
2S 2S
(A) n O (n3 – n2) t (B) (n – n ) t
1 1 O1 3 2
2 S n1 §n · 2 S n1
(C) ¨¨ 3  1¸¸ t (D) O (n3 – n1) t
n 2 O1 © n2 ¹ 1

Q.21 In a YDSE experiment if a slab whose refractive index can be varied is placed in front of one of the slits
then the variation of resultant intensity at mid-point of screen with ‘P’ will be best represented by
(P t 1).[Assume slits of equal width and there is no absorption by slab]

(A) (B) (C) (D)

Q.22 In the YDSE shown the two slits are covered with thin sheets having thickness t & 2t and refractive index
2P and P. Find the position (y) of central maxima
tD
(A) zero (B)
d
tD
(C)  (D) None
d

Q.23 In a YDSE with two identical slits, when the upper slit is covered with a thin, perfectly transparent sheet
of mica, the intensity at the centre of screen reduces to 75% of the initial value. Second minima is
observed to be above this point and third maxima below it. Which of the following can not be a possible
value of phase difference caused by the mica sheet.
S 13S 17S 11S
(A) (B) (C) (D)
3 3 3 3
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Q.24 Two monochromatic and coherent point sources of light are placed at a certain distance from each other
in the horizontal plane. The locus of all those points in the horizontal plane which have constructive
interference will be
(A) a hyperbola (B) family of hyperbolas (C) family of straight lines (D) family of parabolas

Q.25 A circular planar wire loop is dipped in a soap solution and after taking it out, held with its plane vertical
in air. Assuming thickness of film at the top to be very small, as sunlight falls on the soap film, & observer
receive reflected light
(A) the top portion appears dark while the first colour to be observed as one moves down is red.
(B) the top portion appears violet while the first colour to be observed as one moves down is indigo.
(C) the top portion appears dark while the first colour to be observed as one move down is violet.
(D) the top portion appears dark while the first colour to be observed as one move down depends on
the refractive index of the soap solution.

Q.26 A thin film of thickness t and index of refraction 1.33 coats a glass with index of refraction 1.50. What is
the least thickness t that will strongly reflect light with wavelength 600 nm incident normally?
(A) 225 nm (B) 300 nm (C) 400 nm (D) 450 nm

Q.27 It is necessary to coat a glass lens with a non-reflecting layer. If the wavelength of the light in the coating
is O, the best choice is a layer of material having an index of refraction between those of glass and air and
a minimum thickness of
O 3O
(A) (B) O (C) (D) O
4 2 8
Q.28 In a double slit experiment, the separation between the slits is d = 0.25 cm and the distance of the screen
D = 100 cm from the slits. If the wavelength of light used is O = 6000Å and I0 is the intensity of the
central bright fringe, the intensity at a distance x = 4 × 10–5 m from the central maximum is
(A) I0 (B) I 0 2 (C) 3I 0 4 (D) I 0 3

Q.29 Spherical wave fronts shown in figure, strike a plane mirror. Reflected
wave fronts will be as shown in

(A) (B) (C) (D)

ASSERTION AND REASON

Q.1 Statement-1 : In YDSE, as shown in figure, central bright fringe is formed at O. If a liquid is filled
between plane of slits and screen, the central bright fringe is shifted in upward direction.
Statement-2 : If path difference at O increases y-coordinate of central bright fringe will change.

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
(C) Statement-1 is true, statement-2 is false.
(D) Statement-1 is false, statement-2 is true.
 WAVE OPTICS
Q.2 Statement-1 : In glass, red light travels faster than blue light.
Statement-2 : Red light has a wavelength longer than blue.
(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
(C) Statement-1 is true, statement-2 is false.
(D) Statement-1 is false, statement-2 is true.

Q.3 Statement-1 : In standard YDSE set up with visible light, the position on screen where phase difference
is zero appears bright.
Statement-2 : In YDSE set up magnitude of electromagnetic field at central bright fringe is not varying
with time.
(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
(C) Statement-1 is true, statement-2 is false.
(D) Statement-1 is false, statement-2 is true.

ONE OR MORE THAN ONE OPTION MAY BE CORRECT

Take approx. 3 minutes for answering each question.

Q.1 To observe a sustained interference pattern formed by two light waves, it is not necessary that they must
have :
(A) the same frequency (B) same amplitude
(C) a constant phase difference (D) the same intensity
Q.2 In a YDSE apparatus, if we use white light then :
(A) the fringe next to the central will be red (B) the central fringe will be white.
(C) the fringe next to the central will be violet (D) there will not be a completely dark fringe.

Q.3 If the source of light used in a Young's Double Slit Experiment is changed from red to blue, then
(A) the fringes will become brighter
(B) consecutive fringes will come closer
(C) the number of maxima formed on the screen increases
(D) the central bright fringe will become a dark fringe.

Q.4 In a Young's double slit experiment, green light is incident on the

two slits. The interference pattern is observed on a screen. Which
of the following changes would cause the observed fringes to
be more closely spaced?
(A) Reducing the separation between the slits
(B) Using blue light instead of green light
(C) Used red light instead of green light
(D) Moving the light source further away from the slits.

Q.5 Consider a case of thin film interference as shown. Thickness of film is equal to wavelength of light in P2.
(A) Reflected light will be maxima if P1 < P2 < P3
(B) Reflected light will be maxima if P1 < P2 > P3
(C) Transmitted light will be maxima if P1 > P2 > P3
(D) Transmitted light will be maxima if P1 > P2 < P3
 WAVE OPTICS
Q.6 If one of the slits of a standard YDSE apparatus is covered by a thin parallel sided glass slab so that it
transmit only one half of the light intensity of the other, then :
(A) the fringe pattern will get shifted towards the covered slit.
(B) the fringe pattern will get shifted away from the covered slit.
(C) the bright fringes will be less bright and the dark ones will be more bright.
(D) the fringe width will remain unchanged.
Q.7 To make the central fringe at the centre O, a mica sheet of refractive
index 1.5 is introduced. Choose the correct statements (s).
(A) The thickness of sheet is 2( 2  1) d in front of S1.
(B) The thickness of sheet is ( 2  1) d in front of S2.
(C) The thickness of sheet is 2 2 d in front of S1.
(D) The thickness of sheet is (2 2  1) d in front of S1.

Question No. 8 to 10 (3 questions)

The figure shows a schematic diagram showing the arrangement of Young's
Double Slit Experiment
Q.8 Choose the correct statement(s) related to the wavelength of light used
(A) Larger the wavelength of light larger the fringe width
(B) The position of central maxima depends on the wavelength of light used
(C) If white light is used in YDSE, then the violet colour forms its first maxima closest to the central
maxima
(D) The central maxima of all the wavelengths coincide
Q.9 If the distance D is varied, then choose the correct statement(s)
(A) The angular fringe width does not change
(B) The fringe width changes in direct proportion
(C) The change in fringe width is same for all wavelengths
(D) The position of central maxima remains unchanged
Q.10 If the distance d is varied, then identify the correct statement
(A) The angular width does not change (B) The fringe width changes in inverse proportion
(C) The positions of all maxima change (D) The positions of all minima change
Q.11 In an interference arrangement similar to Young's double- slit experiment, the
slits S1 & S2 are illuminated with coherent microwave sources, each of frequency
106 Hz. The sources are synchronized to have zero phase difference. The
slits are separated by a distance d = 150.0 m . The intensity I(T) is measured as
a function of Tat a large distance from S1 & S2, where T is defined as shown . If
I0 is the maximum intensity then
I(T) for 0 dTd 90º is given by :
I I
(A) I(T) = 0 for T = 30º (B) I(T) = 0 for T = 90º
2 4
(C) I(T) = I0 for T = 0º (D) I(T) is constant for all values of T .

Q.12 In a standard YDSE apparatus a thin film (P = 1.5, t = 2.1 Pm) is placed in front of upper slit. How far
above or below the centre point of the screen are two nearest maxima located? Take D = 1 m, d = 1mm,
O = 4500Å. (Symbols have usual meaning)
(A) 1.5 mm (B) 0.6 mm (C) 0.15 mm (D) 0.3 mm
 WAVE OPTICS
ANSWER KEY
EXERCISE – I
§ 1 ·
Q.1 ¨ n  ¸ O = x1 – x2 Q.2 0.225 mm Q.3 5000Å Q.4 1.99 × 10–2 mm
© 48 ¹

Q.5 0.2 mm Q.6 35.35 cm app., 5 Q.7 8 Pm

32 9
Q.8 0 , 1.5 mm Q.9 1.25 m Q.10 48, 21, , , 0 m.m.;
3 2
Q.11 122.47 nm Q.12 81 : 1 Q.13 10 m Q.14 141

EXERCISE – II
y ª S(P  1) t º 400
Q.1 v Q.2 I0 = I sec 2 « , Q.3 7 Pm , 1.6 , Pm (decrease)
Ox O » 7
¬ ¼
1 3 1 3
Q.4 9.3 Pm Q.5 3 / 4 Q.6 (a) ± m,± m (b) + m, + m
15 7 15 7
O
Q.7 33 Q.8 4 cos D

EXERCISE – III
Q.1 (a) y =  13/3 mm, (b) intensity at O = 0.75Imax (c) 650 nm, 433.33 nm
O 3O O
Q.2 A Q.3 A Q.4 t= , , ...... ; tminimum = = 90 nm
7 .2 7 .2 7 .2
Q.5 B Q.6 B Q.7 (i) y = 2 cm, (ii) m = 1.0016
1
Q.8 (a) circular, (b) , (c) 3000Å Q.9 B Q.10 0, 125 nm Q.11 D
16
Q.12 3.5 mm Q.13 B Q.14 A Q.15 C Q.16 B Q.17 A, B
Q.18 (A) p, s ; (B) q ; (C) t ; (D) r,s,t
QUESTION BANK
ONLY ONE OPTION IS CORRECT.
Q.1 C Q.2 C Q.3 C Q.4 B Q.5 D Q.6 B Q.7 D
Q.8 B Q.9 C Q.10 C Q.11 C Q.12 C Q.13 C Q.14 C
Q.15 D Q.16 A Q.17 D Q.18 A Q.19 D Q.20 A Q.21 C
Q.22 B Q.23 A Q.24 B Q.25 C Q.26 A Q.27 A Q.28 C
Q.29 C

ASSERTION AND REASON

Q.1 D Q.2 A Q.3 C

ONE OR MORE THAN ONE OPTION MAY BE CORRECT

Q.1 B,D Q.2 B;C;D Q.3 B;C Q.4 B Q.5 A;D Q.6 A;C;D
Q.7 A Q.8 A;C;D Q.9 A;B;D Q.10 B;D Q.11 A;C Q.12 C;D