Page 1 of 6 CPP - SANKALP_WO–2-PH-II
CPP
WAVE OPTICS - SHEET: 2(Lecture-1)
LEVEL -I
1. Two identical light waves, propagating in the same direction, have a phase difference. After they
superpose, find the intensity of the resulting wave.
2. Two monochromatic light waves whose intensities are in the ratio of 1 : 9 superimpose to produce
interference fringes. What is the ratio of the maximum to the minimum intensity in this fringe
pattern?
3. Consider the situation shown in figure, if the mirror
S
reflects only 64% of the light energy falling on it, what screen
will be the ratio of the maximum to the minimum intensity
in the interference pattern observed on the screen? mirror
4. During superposition of two coherent waves the intensity at a point where the path difference is
6
I
( being the wavelength of the light used) is I. If I0 denotes the maximum intensity, find .
I0
5. For constructive interference to take place between two monochromatic light waves of wavelength
, the path difference should be
l l l
(A) (2n - 1) (B) (2n - 1) (C) n (D) (2n + 1)
4 2 2
6. If two light waves having same frequency have intensity ratio 4 : 1 and they interfere, the ratio of
maximum to minimum intensity in the pattern will be
(A) 9 : 1 (B) 3 : 1 (C) 25 : 9 (D) 16 : 25
æ pö
7. If two waves represented by y1 = 4 sin wt and y 2 = 3 sin çwt + ÷ interfere at a point, the
è 3ø
amplitude of the resulting wave will be about
(A) 7 (B) 6 (C) 5 (D) 3.5
8. The two waves represented by y1 = a sin(wt) and y 2 = b cos( wt) have a phase difference of
p p
(A) 0 (B) (C) (D)
2 4
9. Two coherent sources of intensities, I1 and I 2 produce an interference pattern. The maximum
intensity in the interference pattern will be
(A) I1 + I 2 (B) I12 + I 22 (C) (I1 + I 2 )2 (D) ( I1 + I 2 )2
10. Two beams of light having intensities and 4 interfere to produce a fringe pattern on a screen. The
p
phase difference between the beams is at point A and at point B. Then the difference between
2
the resultant intensities at A and B is
(A) 2 (B) 4 (C) 5 (D) 7
11. What is the path difference of destructive interference?
(n + 1)l (2n + 1)l
(A) n (B) n( l + 1) (C) (D)
2 2
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Page 2 of 6 CPP - SANKALP_WO–2-PH-II
12. To demonstrate the phenomenon of interference, we require two source which emit radiation
(A) Of the same frequency and having a define phase relationship
(B) Of nearly the same frequency
(C) Of the same frequency (D) Of different wavelengths
13. Two waves of intensity undergo Interference. The maximum intensity obtained is
(A) /2 (B) (C) 2 (D) 4
LEVEL -II
1. Three coherent beams of light get superposed on a point O. The intensity corresponding to each is I
at point O. But phase of first wave is less than that of the second by 2/3 and greater than that of
2
the third by . What is the resultant intensity at point O?
3
2. Two coherent rays of wavelenght of emante from source O to
interfere at P fr constructive interference as shown. Write the
condition of nth maxima. II
d
(A) Cosec – cot = (2n – 1)
4d
(B) Cosec + cot = (2n – 1) O I
4d P
(C) Cosec – cot = n
2d
(D) Cosec + cot =n
2d
3. Consider two coherent monochromatic (wavelength ) sources S1
P
S1 and S2 separated by distance d. The ratio of intensity of S1
and that of S2 (which is responsible for interference at point P, d
where detector is located) is 4. Find the distance of point P
S2
9
from S1. (if the resultant intensity at point P is equal to times of intensity of S1)
4
[Given S2 S1P is 90] (d > 0, n is a positive integer)
4. Three coherent sound sources producing plane wave S1 S2 S3 P
fronts towards right of same amplitude and wavelength
( = 3 cm) are situated on a line as shown in the d1 d2 D
diagram. If an observer P also lies on
the same line and observes no sound when sources S1, S2 and S3 are switched on simultaneously.
Taking all suitable approximations and d1 & d2 <<< D. Find values of d1 and d2.
5. Two source S1 and S2 emitting light of wavelength 600 nm are placed a distance 1.0 102 cm
apart. A detector can be moved on the line S1P which is perpendicular to S1S2. (a) What would be
the minimum and maximum path difference at the detector as it is moved along the line S1P? (b)
Locate the position of the farthest minimum detected.
6. Two coherent point sources S1 and S2 vibrating in phase emit light of wavelength . The separation
between the sources is 2. Consider a line passing through S2 and perpendicular to the line S1S2.
What is the smallest distance from S2 where a minimum of intensity occurs?
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7. In the figure shows three equidistant slits being illuminated by a C
d
monochromatic parallel beam of light. Let BP0 AP0 = /3 and D >> . B
d A
2D P0
a) Show that in this case d .
3 D
(b) Show that the intensity at P0 is three times the intensity due to any of the
three slits individually.
8. There are two coherent light sources. Assume intensity of each source is I0 and K1 is equal to
I0
difference of maximum and minimum intensity. Now intensity of one source is made and K2 is
4
K1
again difference of maximum and minimum intensity. Then find .
K2
9. A person views the interference pattern, produced by two slits illuminated by white light, on placing
a green fitter in front of his eyes, then
(A) he will see sharply distinguishable dark and bright fringes.
(B) the fringes will not be sharp but differentiable.
(C) on replacing the green filter by blue filter the fringes will be again sharp but closer than those by
the green filter.
(D) on using both the filters simultaneously the central bands will be maximum bright.
Paragraph-1
A narrow tube is bent in the form of a circle of radius R, as shown in
the figure. Two small holes S and D are made in the tube at the
positions right angle to each other. A source placed at S generates a R
wave of intensity I0 which is equally divided into two parts: one part S
travels along the longer path, while the other travels along the shorter
path. Both the part waves meet at the point D where a detector is
placed.
D
10. If a maxima is formed at a detector then, the magnitude of wavelength of the wave produced is
given by
R R
(A) R (B) (C) (D) all of these
2 4
11. If a minima is formed at the detector then, the magnitude of wavelength of the wave produced is
given by
3 2
(A) 2R (B) R (C) R (D) None of these
2 5
12. The maximum intensity produced at D is given by
(A) 4I0 (B) 2I0 (C) I0 (D) 3I0
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WAVE OPTICS - SHEET: 2(Lecture-2)
Answers
LEVEL – I
1. I = 4I2 cos2 /2
2. 4:1
A1 1
I A2 A = I
A2 3
2 2
Imax A1 A 2 (3 1)2 4
Imin
2
2
4 :1
A1 A 2 (3 1) 2
3. 81 : 1
4. 3/4
5. C
l
5. For constructive interference path difference is even multiple of .
2
2
æ I1 ö æ 4 ö
+ 1÷
Imax ç I2 ç 1 + 1÷ 9
6. (A) =ç ÷ =ç ÷=
Imin ç I1 ÷ ç 4 1
ç - 1÷ ç - 1÷
÷
è I2 ø è 1 ø
7. (B) f = p / 3, a1 = 4, a2 = 3
So, A = a12 + a22 + 2a1 ×a2 cos f Þ A»6
æ pö
8. (B) y1 = a sin wt, and y 2 = bcos wt = b sin çw t + ÷
è 2ø
So phase difference f = p / 2
9. (D) Resultant intensity IR = I1 + I 2 + 2 I1 I 2 cos f
For maximum IR , f = 0°
Þ IR = I1 + I 2 + I1 I 2 = ( I1 + I 2 )2
10. (B) At point A, resultant intensity
I A = I1 + I 2 = 5I ; and at point B
IB = I1 + I 2 + 2 I1 I 2 cos p = 5I + 4I
IB = 9I so IB - I A = 4I .
l
11. (D) For destructive interference path difference is odd multiple of .
2
12. (A) For interference frequency must be same and phase difference must be constant.
13. (D) For maximum intensity f = 0°
\ I = I1 + I 2 + 2 I1 I 2 cos f = I + I + 2 I I cos0° = 4I
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Page 5 of 6 CPP - SANKALP_WO–2-PH-II
LEVEL - II
1. zero
A r A1 A 2 A 3
A
=0 2/3
2/3
Ir = 0 A
A
2. A
d2 n2 2
3.
2n
9
intensity of S1 = 9 times of intensity S2
4
2
Intensity of maxima = I1 I2 = 9 I2
S2P – S1P = n for maxima
d2 n2 2
d2 x 2 x n x=
2n
4. 3 cm, 4 cm
Making phase diagram
d1 will be 1, 4, 7, ….. cm
d2 will be 1, 4, 7, ….. cm
120o
S3
S2 o
120
S1
5. (a) The path difference is maximum when the detector is just at the position of S1 and its value ie
equal to 1.0 102 cm. The path difference is minimum when the detector is at a large distance from
S1. The path difference is then close to zero.
(b) The farthest minimum occurs at S2
point P when where the path difference
is /2. If S1P = D d
S2P S1P = /2
or, D2 d 2 D S1 P
2 D
D = 1.7 cm
7
6.
12
7. 2
K1 4I0 0
In second case
2 2
1 9 1 I
I max I0 1 I 0 ; I min I 0 1 0
2 4 2 4
9I I K
K 2 0 0 2I 0 ; 1 2
4 4 K2
8. A, C
9. D
3
Path difference produced is p R R R
2 2
For maxima : p = n
n = R
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Page 6 of 6 CPP - SANKALP_WO–2-PH-II
R
= ,n 1,2,3,...
n
æ2n + 1ö
pR = ç l
è 2 ÷ ø
Thus, the possible values of are
2 2 2
2R, R, R, R,.....
3 5 7
10. A
2
Maximum intensity, Imax I1 I2
I0
Here I1 I2
2
given
2
I I
Imax 0 0 2I0
2 2
11. B
From 31 : max = R for a
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