DC Pandey Solutions (JEE Main): Interference and Diffraction of Light | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Energy Distribution in Interference 
Q 1.  Two waves of the same frequency and same amplitude a are reaching a point simultaneously. 
What should be the phase difference between the waves so that the amplitude of the resultant wave 
be : 
  (i) 2a (ii) 2a (iii) a and (iv) zero? 
Q 2.  Two waves of equal frequencies have their amplitude in the ratio of 5 :3. They are superimposed 
on each other. Calculate the ratio of the maximum to minimum intensities of the resultant wave. 
Q 3.  In a Young's double slit experiment ? = 500 nm, d = 1.0 mm and D = 1.0m. Find the minimum 
distance from the central maximum for which the intensity is half of the maximum intensity. 
Q 4.  In a Young's double slit interference experiment the fringe pattern is observed on a screen placed 
at a distance D from the slits. The slits are separated by a distance d and are illuminated by 
monochromatic light of wavelength ?. Find the distance from the central point where the intensity 
falls to (a) half the maximum, (b) one fourth of the maximum. 
Q 5.  In a two-slit interference pattern, the maximum intensity is I
0
. 
(a) At a point in the pattern where the phase difference between the waves from the two slits is 
60°, what is the intensity? 
(b) What is the path difference for 480 nm light from the two slits at a point where the phase angle 
is 60°?  
  Conditions for Interference 
Q 6.  Two coherent sources A and B of radio waves are 5.00 m apart. Each source emits waves with 
wavelength 6.00 m. Consider points along the line between the two sources. At what distances, if 
any, from A is the interference (a) constructive, (b) destructive? 
Q 7.  A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that 
radiate in phase. Antenna B is 9.00 m to the right of antenna A. Consider point P between the 
antennas and along the line connecting them, a horizontal distance x to the right of antenna A. For 
what values of x will constructive interference occur at point P ? 
  Young ’s Double Slit Experiment 
Q 8.  Coherent light from a sodium-vapour lamp is passed through a filter that blocks every thing except 
for light of a single wavelength. It then falls on two slits separated by 0.460 mm. In the resulting 
interference pattern on a screen 2.20 m away, adjacent bright fringes are separated by 2.82 mm. 
What is the wavelength? 
Q 9.  Find the angular separation between the consecutive bright fringes in a Young's double slit 
experiment with blue-green light of wavelength 500 nm. The separation between the slits is 2.0 x 
10
-3
m. 
Page 2


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Energy Distribution in Interference 
Q 1.  Two waves of the same frequency and same amplitude a are reaching a point simultaneously. 
What should be the phase difference between the waves so that the amplitude of the resultant wave 
be : 
  (i) 2a (ii) 2a (iii) a and (iv) zero? 
Q 2.  Two waves of equal frequencies have their amplitude in the ratio of 5 :3. They are superimposed 
on each other. Calculate the ratio of the maximum to minimum intensities of the resultant wave. 
Q 3.  In a Young's double slit experiment ? = 500 nm, d = 1.0 mm and D = 1.0m. Find the minimum 
distance from the central maximum for which the intensity is half of the maximum intensity. 
Q 4.  In a Young's double slit interference experiment the fringe pattern is observed on a screen placed 
at a distance D from the slits. The slits are separated by a distance d and are illuminated by 
monochromatic light of wavelength ?. Find the distance from the central point where the intensity 
falls to (a) half the maximum, (b) one fourth of the maximum. 
Q 5.  In a two-slit interference pattern, the maximum intensity is I
0
. 
(a) At a point in the pattern where the phase difference between the waves from the two slits is 
60°, what is the intensity? 
(b) What is the path difference for 480 nm light from the two slits at a point where the phase angle 
is 60°?  
  Conditions for Interference 
Q 6.  Two coherent sources A and B of radio waves are 5.00 m apart. Each source emits waves with 
wavelength 6.00 m. Consider points along the line between the two sources. At what distances, if 
any, from A is the interference (a) constructive, (b) destructive? 
Q 7.  A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that 
radiate in phase. Antenna B is 9.00 m to the right of antenna A. Consider point P between the 
antennas and along the line connecting them, a horizontal distance x to the right of antenna A. For 
what values of x will constructive interference occur at point P ? 
  Young ’s Double Slit Experiment 
Q 8.  Coherent light from a sodium-vapour lamp is passed through a filter that blocks every thing except 
for light of a single wavelength. It then falls on two slits separated by 0.460 mm. In the resulting 
interference pattern on a screen 2.20 m away, adjacent bright fringes are separated by 2.82 mm. 
What is the wavelength? 
Q 9.  Find the angular separation between the consecutive bright fringes in a Young's double slit 
experiment with blue-green light of wavelength 500 nm. The separation between the slits is 2.0 x 
10
-3
m. 
Q 10.  A Young's double slit apparatus has slits separated by 0.25 mm and a screen 48 cm away from the 
slits. The whole apparatus is immersed in water and the slits are illuminated by the red light ( ? = 
700 nm in vacuum). Find the fringe-width of the pattern formed on the screen. ( ?
w
 = 4/3) 
Q 11.  In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some 
distance from the slits. If the screen is moved by 1.5 × 10
-2
 m towards the slits, the change in 
fringe-width is 3 × 10
-5
 m. If the distance between the slits is 10
-3
 m, calculate the wavelength of 
the light used. 
Q 12.  In a double slit experiment the distance between the slits is 5.0 mm and the slits are 1.0 m from the 
screen. Two interference patterns can be seen on the screen one due to light with wavelength 480 
nm, and the other due to light with wavelength 600 nm. What is the separation on the screen 
between the third order bright fringes of the two interference patterns? 
Q 13.  Two slits spaced 0.450 mm apart are placed 75.0 cm from a screen. What is the distance between 
the second and third dark lines of the interference pattern on the screen when the slits are 
illuminated with coherent light with a wavelength of 500 nm? 
Q 14.  Coherent light with wavelength 600 nm passes through two very narrow slits and the interference 
pattern is observed on a screen 3.00 m from the slits. The first-order bright fringe is at 4.94 mm 
from the centre of the central bright fringe. For what wavelength of light will the first-order dark 
fringe be observed at this same point on the screen? 
Q 15.  Two very narrow slits are spaced 1.80 ?m apart and are placed 35.0 cm from a screen. What is the 
distance between the first and second dark lines of the interference pattern when the slits are 
illuminated with coherent light of ?
 
= 550 nm? (Hint: The angle ? is not small). 
Q 16.  A narrow beam of 100 eV electrons is fired at two parallel slits very close to each other. The 
distance between the slits is 10Å. The electron waves after passing through the slits interfere on a 
screen 3 m away from slits and form interference fringes. Find the width of the fringe. 
Q 17.  In a Young's double slit set up the wavelength of light used is 546 nm. The distance of screen from 
slits is 1 m. The slit separation is 0.3 mm. 
(a) Compare the intensity at a point P distant 10 mm from the central fringe where the intensity is  
I
0
. 
  (b) Find the number of bright fringes between P and the central fringe. 
Q 18.  Interference pattern with Young's double slits 1.5 mm apart are formed on a screen at a distance 
1.5 m from the plane of slits. In the path of the beam of one of the slits, a transparent film of 10-
micron thickness and of refractive index 1.6 is interposed while in the path of the beam from the 
other slit a transparent film of 15 micron thickness and of refractive index 1.2 is interposed. Find 
the displacement of the fringe pattern. 
Q 19.  In a Young's double slit experiment using monochromatic light the fringe pattern shifts by a 
certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 
microns is introduced in the path of one of the interfering waves. The mica sheet is then removed 
and the distance between the slits and screen is doubled. It is found that the distance between 
successive maxima (or minima) now is the same as observed fringe shift upon the introduction of 
the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment. 
Page 3


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Energy Distribution in Interference 
Q 1.  Two waves of the same frequency and same amplitude a are reaching a point simultaneously. 
What should be the phase difference between the waves so that the amplitude of the resultant wave 
be : 
  (i) 2a (ii) 2a (iii) a and (iv) zero? 
Q 2.  Two waves of equal frequencies have their amplitude in the ratio of 5 :3. They are superimposed 
on each other. Calculate the ratio of the maximum to minimum intensities of the resultant wave. 
Q 3.  In a Young's double slit experiment ? = 500 nm, d = 1.0 mm and D = 1.0m. Find the minimum 
distance from the central maximum for which the intensity is half of the maximum intensity. 
Q 4.  In a Young's double slit interference experiment the fringe pattern is observed on a screen placed 
at a distance D from the slits. The slits are separated by a distance d and are illuminated by 
monochromatic light of wavelength ?. Find the distance from the central point where the intensity 
falls to (a) half the maximum, (b) one fourth of the maximum. 
Q 5.  In a two-slit interference pattern, the maximum intensity is I
0
. 
(a) At a point in the pattern where the phase difference between the waves from the two slits is 
60°, what is the intensity? 
(b) What is the path difference for 480 nm light from the two slits at a point where the phase angle 
is 60°?  
  Conditions for Interference 
Q 6.  Two coherent sources A and B of radio waves are 5.00 m apart. Each source emits waves with 
wavelength 6.00 m. Consider points along the line between the two sources. At what distances, if 
any, from A is the interference (a) constructive, (b) destructive? 
Q 7.  A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that 
radiate in phase. Antenna B is 9.00 m to the right of antenna A. Consider point P between the 
antennas and along the line connecting them, a horizontal distance x to the right of antenna A. For 
what values of x will constructive interference occur at point P ? 
  Young ’s Double Slit Experiment 
Q 8.  Coherent light from a sodium-vapour lamp is passed through a filter that blocks every thing except 
for light of a single wavelength. It then falls on two slits separated by 0.460 mm. In the resulting 
interference pattern on a screen 2.20 m away, adjacent bright fringes are separated by 2.82 mm. 
What is the wavelength? 
Q 9.  Find the angular separation between the consecutive bright fringes in a Young's double slit 
experiment with blue-green light of wavelength 500 nm. The separation between the slits is 2.0 x 
10
-3
m. 
Q 10.  A Young's double slit apparatus has slits separated by 0.25 mm and a screen 48 cm away from the 
slits. The whole apparatus is immersed in water and the slits are illuminated by the red light ( ? = 
700 nm in vacuum). Find the fringe-width of the pattern formed on the screen. ( ?
w
 = 4/3) 
Q 11.  In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some 
distance from the slits. If the screen is moved by 1.5 × 10
-2
 m towards the slits, the change in 
fringe-width is 3 × 10
-5
 m. If the distance between the slits is 10
-3
 m, calculate the wavelength of 
the light used. 
Q 12.  In a double slit experiment the distance between the slits is 5.0 mm and the slits are 1.0 m from the 
screen. Two interference patterns can be seen on the screen one due to light with wavelength 480 
nm, and the other due to light with wavelength 600 nm. What is the separation on the screen 
between the third order bright fringes of the two interference patterns? 
Q 13.  Two slits spaced 0.450 mm apart are placed 75.0 cm from a screen. What is the distance between 
the second and third dark lines of the interference pattern on the screen when the slits are 
illuminated with coherent light with a wavelength of 500 nm? 
Q 14.  Coherent light with wavelength 600 nm passes through two very narrow slits and the interference 
pattern is observed on a screen 3.00 m from the slits. The first-order bright fringe is at 4.94 mm 
from the centre of the central bright fringe. For what wavelength of light will the first-order dark 
fringe be observed at this same point on the screen? 
Q 15.  Two very narrow slits are spaced 1.80 ?m apart and are placed 35.0 cm from a screen. What is the 
distance between the first and second dark lines of the interference pattern when the slits are 
illuminated with coherent light of ?
 
= 550 nm? (Hint: The angle ? is not small). 
Q 16.  A narrow beam of 100 eV electrons is fired at two parallel slits very close to each other. The 
distance between the slits is 10Å. The electron waves after passing through the slits interfere on a 
screen 3 m away from slits and form interference fringes. Find the width of the fringe. 
Q 17.  In a Young's double slit set up the wavelength of light used is 546 nm. The distance of screen from 
slits is 1 m. The slit separation is 0.3 mm. 
(a) Compare the intensity at a point P distant 10 mm from the central fringe where the intensity is  
I
0
. 
  (b) Find the number of bright fringes between P and the central fringe. 
Q 18.  Interference pattern with Young's double slits 1.5 mm apart are formed on a screen at a distance 
1.5 m from the plane of slits. In the path of the beam of one of the slits, a transparent film of 10-
micron thickness and of refractive index 1.6 is interposed while in the path of the beam from the 
other slit a transparent film of 15 micron thickness and of refractive index 1.2 is interposed. Find 
the displacement of the fringe pattern. 
Q 19.  In a Young's double slit experiment using monochromatic light the fringe pattern shifts by a 
certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 
microns is introduced in the path of one of the interfering waves. The mica sheet is then removed 
and the distance between the slits and screen is doubled. It is found that the distance between 
successive maxima (or minima) now is the same as observed fringe shift upon the introduction of 
the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment. 
Q 20.  In a double slit pattern ( ? = 6000 Å),
 
the first order and tenth order maxima fall at 12.50 mm and 
14.74 mm from a particular reference point. If ? is changed to 5500 Å, find the position of zero 
order and tenth order fringes, other arrangement remaining the same. 
Q 21.  Interference effects are produced at point P on a screen as a result of direct rays from a 500 nm 
source and reflected rays from a mirror, as shown in figure. If the source is 100 m to the left of the 
screen and 1.00 cm above the mirror, find the distance y (in milimetres) to the first dark band 
above the mirror. 
 
Interference in Thin Films 
Q 22.  What is the thinnest film of coating with n = 1.42 on glass (n = 1.52) for which destructive 
interference of the red component (650 nm) of an incident white light beam in air can take place 
by reflection? 
Q 23.  A glass plate (n = 1.53) that is 0.485 um thick and surrounded by air is illuminated by a beam of 
white light normal to the plate. 
(a) What wavelengths (in air) within the limits of the visible spectrum ( ? = 400 to 700 nm) are 
intensified in the reflected beam? 
  (b) What wavelengths within the visible spectrum are intensified in the transmitted light? 
Q 24.  A thick glass slab ( ? = 1.5)
 
is to be viewed in reflected white light. It is proposed to coat the slab 
with a thin layer of a material having refractive index 1.3 so that the wavelength 6000 Å
 
is 
suppressed. Find the minimum thickness of the coating required. 
Q 25.  An oil film covers the surface of a small pond. The refractive index of the oil is greater than that of 
water. At one point on the film, the film has the smallest nonzero thickness for which there will be 
destructive interference in the reflected light when infrared radiation with wavelength 800 nm is 
incident normal to the film. When this film is viewed at normal incidence at this same point, for 
what visible wavelengths, if any, will there be constructive interference? (Visible light has 
wavelengths between 400 nm and 700 nm) 
Solutions 
1.  a
R
 = 2a cos 
2
?
 
  (i) For a
R
 = 2a, ?
 
= 0° 
  (ii) For a
R
 = 2a , ?
 
= 90° etc. 
2.  A
max
 =5 + 3 = 8 units 
  A
min
 = 5 - 3 = 2 units 
Page 4


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Energy Distribution in Interference 
Q 1.  Two waves of the same frequency and same amplitude a are reaching a point simultaneously. 
What should be the phase difference between the waves so that the amplitude of the resultant wave 
be : 
  (i) 2a (ii) 2a (iii) a and (iv) zero? 
Q 2.  Two waves of equal frequencies have their amplitude in the ratio of 5 :3. They are superimposed 
on each other. Calculate the ratio of the maximum to minimum intensities of the resultant wave. 
Q 3.  In a Young's double slit experiment ? = 500 nm, d = 1.0 mm and D = 1.0m. Find the minimum 
distance from the central maximum for which the intensity is half of the maximum intensity. 
Q 4.  In a Young's double slit interference experiment the fringe pattern is observed on a screen placed 
at a distance D from the slits. The slits are separated by a distance d and are illuminated by 
monochromatic light of wavelength ?. Find the distance from the central point where the intensity 
falls to (a) half the maximum, (b) one fourth of the maximum. 
Q 5.  In a two-slit interference pattern, the maximum intensity is I
0
. 
(a) At a point in the pattern where the phase difference between the waves from the two slits is 
60°, what is the intensity? 
(b) What is the path difference for 480 nm light from the two slits at a point where the phase angle 
is 60°?  
  Conditions for Interference 
Q 6.  Two coherent sources A and B of radio waves are 5.00 m apart. Each source emits waves with 
wavelength 6.00 m. Consider points along the line between the two sources. At what distances, if 
any, from A is the interference (a) constructive, (b) destructive? 
Q 7.  A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that 
radiate in phase. Antenna B is 9.00 m to the right of antenna A. Consider point P between the 
antennas and along the line connecting them, a horizontal distance x to the right of antenna A. For 
what values of x will constructive interference occur at point P ? 
  Young ’s Double Slit Experiment 
Q 8.  Coherent light from a sodium-vapour lamp is passed through a filter that blocks every thing except 
for light of a single wavelength. It then falls on two slits separated by 0.460 mm. In the resulting 
interference pattern on a screen 2.20 m away, adjacent bright fringes are separated by 2.82 mm. 
What is the wavelength? 
Q 9.  Find the angular separation between the consecutive bright fringes in a Young's double slit 
experiment with blue-green light of wavelength 500 nm. The separation between the slits is 2.0 x 
10
-3
m. 
Q 10.  A Young's double slit apparatus has slits separated by 0.25 mm and a screen 48 cm away from the 
slits. The whole apparatus is immersed in water and the slits are illuminated by the red light ( ? = 
700 nm in vacuum). Find the fringe-width of the pattern formed on the screen. ( ?
w
 = 4/3) 
Q 11.  In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some 
distance from the slits. If the screen is moved by 1.5 × 10
-2
 m towards the slits, the change in 
fringe-width is 3 × 10
-5
 m. If the distance between the slits is 10
-3
 m, calculate the wavelength of 
the light used. 
Q 12.  In a double slit experiment the distance between the slits is 5.0 mm and the slits are 1.0 m from the 
screen. Two interference patterns can be seen on the screen one due to light with wavelength 480 
nm, and the other due to light with wavelength 600 nm. What is the separation on the screen 
between the third order bright fringes of the two interference patterns? 
Q 13.  Two slits spaced 0.450 mm apart are placed 75.0 cm from a screen. What is the distance between 
the second and third dark lines of the interference pattern on the screen when the slits are 
illuminated with coherent light with a wavelength of 500 nm? 
Q 14.  Coherent light with wavelength 600 nm passes through two very narrow slits and the interference 
pattern is observed on a screen 3.00 m from the slits. The first-order bright fringe is at 4.94 mm 
from the centre of the central bright fringe. For what wavelength of light will the first-order dark 
fringe be observed at this same point on the screen? 
Q 15.  Two very narrow slits are spaced 1.80 ?m apart and are placed 35.0 cm from a screen. What is the 
distance between the first and second dark lines of the interference pattern when the slits are 
illuminated with coherent light of ?
 
= 550 nm? (Hint: The angle ? is not small). 
Q 16.  A narrow beam of 100 eV electrons is fired at two parallel slits very close to each other. The 
distance between the slits is 10Å. The electron waves after passing through the slits interfere on a 
screen 3 m away from slits and form interference fringes. Find the width of the fringe. 
Q 17.  In a Young's double slit set up the wavelength of light used is 546 nm. The distance of screen from 
slits is 1 m. The slit separation is 0.3 mm. 
(a) Compare the intensity at a point P distant 10 mm from the central fringe where the intensity is  
I
0
. 
  (b) Find the number of bright fringes between P and the central fringe. 
Q 18.  Interference pattern with Young's double slits 1.5 mm apart are formed on a screen at a distance 
1.5 m from the plane of slits. In the path of the beam of one of the slits, a transparent film of 10-
micron thickness and of refractive index 1.6 is interposed while in the path of the beam from the 
other slit a transparent film of 15 micron thickness and of refractive index 1.2 is interposed. Find 
the displacement of the fringe pattern. 
Q 19.  In a Young's double slit experiment using monochromatic light the fringe pattern shifts by a 
certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 
microns is introduced in the path of one of the interfering waves. The mica sheet is then removed 
and the distance between the slits and screen is doubled. It is found that the distance between 
successive maxima (or minima) now is the same as observed fringe shift upon the introduction of 
the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment. 
Q 20.  In a double slit pattern ( ? = 6000 Å),
 
the first order and tenth order maxima fall at 12.50 mm and 
14.74 mm from a particular reference point. If ? is changed to 5500 Å, find the position of zero 
order and tenth order fringes, other arrangement remaining the same. 
Q 21.  Interference effects are produced at point P on a screen as a result of direct rays from a 500 nm 
source and reflected rays from a mirror, as shown in figure. If the source is 100 m to the left of the 
screen and 1.00 cm above the mirror, find the distance y (in milimetres) to the first dark band 
above the mirror. 
 
Interference in Thin Films 
Q 22.  What is the thinnest film of coating with n = 1.42 on glass (n = 1.52) for which destructive 
interference of the red component (650 nm) of an incident white light beam in air can take place 
by reflection? 
Q 23.  A glass plate (n = 1.53) that is 0.485 um thick and surrounded by air is illuminated by a beam of 
white light normal to the plate. 
(a) What wavelengths (in air) within the limits of the visible spectrum ( ? = 400 to 700 nm) are 
intensified in the reflected beam? 
  (b) What wavelengths within the visible spectrum are intensified in the transmitted light? 
Q 24.  A thick glass slab ( ? = 1.5)
 
is to be viewed in reflected white light. It is proposed to coat the slab 
with a thin layer of a material having refractive index 1.3 so that the wavelength 6000 Å
 
is 
suppressed. Find the minimum thickness of the coating required. 
Q 25.  An oil film covers the surface of a small pond. The refractive index of the oil is greater than that of 
water. At one point on the film, the film has the smallest nonzero thickness for which there will be 
destructive interference in the reflected light when infrared radiation with wavelength 800 nm is 
incident normal to the film. When this film is viewed at normal incidence at this same point, for 
what visible wavelengths, if any, will there be constructive interference? (Visible light has 
wavelengths between 400 nm and 700 nm) 
Solutions 
1.  a
R
 = 2a cos 
2
?
 
  (i) For a
R
 = 2a, ?
 
= 0° 
  (ii) For a
R
 = 2a , ?
 
= 90° etc. 
2.  A
max
 =5 + 3 = 8 units 
  A
min
 = 5 - 3 = 2 units 
   
3.  i = I
max
 
2
cos
2
?
 
   
   
   = 1.25 × 10
-4 
m 
4.  (a) See the hint of above example. At half intensity, 
    
  (b)  
   
5.  (a) I= I
max 
2
cos
2
? ??
??
??
 
   = I
0 
cos
2 
(30°)  (as ? = 60
o
) 
    
  (b) 60° phase difference is equivalent to 
6
?
 
path difference. 
6.  (a) At centre path difference is zero. Therefore construction interference will be obtained. 
(b) 
2
?
= 3 m. At a distance, where path difference is 
2
?
 or 3m destructive interference will be 
obtained. 
    
  At P
1
   BP
1 
- AP
1 
= 3rn =
2
?
 
  At P
2
   AP
2
 - BP
2
 = 3m = 
2
?
 
7.  
Page 5


Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Energy Distribution in Interference 
Q 1.  Two waves of the same frequency and same amplitude a are reaching a point simultaneously. 
What should be the phase difference between the waves so that the amplitude of the resultant wave 
be : 
  (i) 2a (ii) 2a (iii) a and (iv) zero? 
Q 2.  Two waves of equal frequencies have their amplitude in the ratio of 5 :3. They are superimposed 
on each other. Calculate the ratio of the maximum to minimum intensities of the resultant wave. 
Q 3.  In a Young's double slit experiment ? = 500 nm, d = 1.0 mm and D = 1.0m. Find the minimum 
distance from the central maximum for which the intensity is half of the maximum intensity. 
Q 4.  In a Young's double slit interference experiment the fringe pattern is observed on a screen placed 
at a distance D from the slits. The slits are separated by a distance d and are illuminated by 
monochromatic light of wavelength ?. Find the distance from the central point where the intensity 
falls to (a) half the maximum, (b) one fourth of the maximum. 
Q 5.  In a two-slit interference pattern, the maximum intensity is I
0
. 
(a) At a point in the pattern where the phase difference between the waves from the two slits is 
60°, what is the intensity? 
(b) What is the path difference for 480 nm light from the two slits at a point where the phase angle 
is 60°?  
  Conditions for Interference 
Q 6.  Two coherent sources A and B of radio waves are 5.00 m apart. Each source emits waves with 
wavelength 6.00 m. Consider points along the line between the two sources. At what distances, if 
any, from A is the interference (a) constructive, (b) destructive? 
Q 7.  A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that 
radiate in phase. Antenna B is 9.00 m to the right of antenna A. Consider point P between the 
antennas and along the line connecting them, a horizontal distance x to the right of antenna A. For 
what values of x will constructive interference occur at point P ? 
  Young ’s Double Slit Experiment 
Q 8.  Coherent light from a sodium-vapour lamp is passed through a filter that blocks every thing except 
for light of a single wavelength. It then falls on two slits separated by 0.460 mm. In the resulting 
interference pattern on a screen 2.20 m away, adjacent bright fringes are separated by 2.82 mm. 
What is the wavelength? 
Q 9.  Find the angular separation between the consecutive bright fringes in a Young's double slit 
experiment with blue-green light of wavelength 500 nm. The separation between the slits is 2.0 x 
10
-3
m. 
Q 10.  A Young's double slit apparatus has slits separated by 0.25 mm and a screen 48 cm away from the 
slits. The whole apparatus is immersed in water and the slits are illuminated by the red light ( ? = 
700 nm in vacuum). Find the fringe-width of the pattern formed on the screen. ( ?
w
 = 4/3) 
Q 11.  In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some 
distance from the slits. If the screen is moved by 1.5 × 10
-2
 m towards the slits, the change in 
fringe-width is 3 × 10
-5
 m. If the distance between the slits is 10
-3
 m, calculate the wavelength of 
the light used. 
Q 12.  In a double slit experiment the distance between the slits is 5.0 mm and the slits are 1.0 m from the 
screen. Two interference patterns can be seen on the screen one due to light with wavelength 480 
nm, and the other due to light with wavelength 600 nm. What is the separation on the screen 
between the third order bright fringes of the two interference patterns? 
Q 13.  Two slits spaced 0.450 mm apart are placed 75.0 cm from a screen. What is the distance between 
the second and third dark lines of the interference pattern on the screen when the slits are 
illuminated with coherent light with a wavelength of 500 nm? 
Q 14.  Coherent light with wavelength 600 nm passes through two very narrow slits and the interference 
pattern is observed on a screen 3.00 m from the slits. The first-order bright fringe is at 4.94 mm 
from the centre of the central bright fringe. For what wavelength of light will the first-order dark 
fringe be observed at this same point on the screen? 
Q 15.  Two very narrow slits are spaced 1.80 ?m apart and are placed 35.0 cm from a screen. What is the 
distance between the first and second dark lines of the interference pattern when the slits are 
illuminated with coherent light of ?
 
= 550 nm? (Hint: The angle ? is not small). 
Q 16.  A narrow beam of 100 eV electrons is fired at two parallel slits very close to each other. The 
distance between the slits is 10Å. The electron waves after passing through the slits interfere on a 
screen 3 m away from slits and form interference fringes. Find the width of the fringe. 
Q 17.  In a Young's double slit set up the wavelength of light used is 546 nm. The distance of screen from 
slits is 1 m. The slit separation is 0.3 mm. 
(a) Compare the intensity at a point P distant 10 mm from the central fringe where the intensity is  
I
0
. 
  (b) Find the number of bright fringes between P and the central fringe. 
Q 18.  Interference pattern with Young's double slits 1.5 mm apart are formed on a screen at a distance 
1.5 m from the plane of slits. In the path of the beam of one of the slits, a transparent film of 10-
micron thickness and of refractive index 1.6 is interposed while in the path of the beam from the 
other slit a transparent film of 15 micron thickness and of refractive index 1.2 is interposed. Find 
the displacement of the fringe pattern. 
Q 19.  In a Young's double slit experiment using monochromatic light the fringe pattern shifts by a 
certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 
microns is introduced in the path of one of the interfering waves. The mica sheet is then removed 
and the distance between the slits and screen is doubled. It is found that the distance between 
successive maxima (or minima) now is the same as observed fringe shift upon the introduction of 
the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment. 
Q 20.  In a double slit pattern ( ? = 6000 Å),
 
the first order and tenth order maxima fall at 12.50 mm and 
14.74 mm from a particular reference point. If ? is changed to 5500 Å, find the position of zero 
order and tenth order fringes, other arrangement remaining the same. 
Q 21.  Interference effects are produced at point P on a screen as a result of direct rays from a 500 nm 
source and reflected rays from a mirror, as shown in figure. If the source is 100 m to the left of the 
screen and 1.00 cm above the mirror, find the distance y (in milimetres) to the first dark band 
above the mirror. 
 
Interference in Thin Films 
Q 22.  What is the thinnest film of coating with n = 1.42 on glass (n = 1.52) for which destructive 
interference of the red component (650 nm) of an incident white light beam in air can take place 
by reflection? 
Q 23.  A glass plate (n = 1.53) that is 0.485 um thick and surrounded by air is illuminated by a beam of 
white light normal to the plate. 
(a) What wavelengths (in air) within the limits of the visible spectrum ( ? = 400 to 700 nm) are 
intensified in the reflected beam? 
  (b) What wavelengths within the visible spectrum are intensified in the transmitted light? 
Q 24.  A thick glass slab ( ? = 1.5)
 
is to be viewed in reflected white light. It is proposed to coat the slab 
with a thin layer of a material having refractive index 1.3 so that the wavelength 6000 Å
 
is 
suppressed. Find the minimum thickness of the coating required. 
Q 25.  An oil film covers the surface of a small pond. The refractive index of the oil is greater than that of 
water. At one point on the film, the film has the smallest nonzero thickness for which there will be 
destructive interference in the reflected light when infrared radiation with wavelength 800 nm is 
incident normal to the film. When this film is viewed at normal incidence at this same point, for 
what visible wavelengths, if any, will there be constructive interference? (Visible light has 
wavelengths between 400 nm and 700 nm) 
Solutions 
1.  a
R
 = 2a cos 
2
?
 
  (i) For a
R
 = 2a, ?
 
= 0° 
  (ii) For a
R
 = 2a , ?
 
= 90° etc. 
2.  A
max
 =5 + 3 = 8 units 
  A
min
 = 5 - 3 = 2 units 
   
3.  i = I
max
 
2
cos
2
?
 
   
   
   = 1.25 × 10
-4 
m 
4.  (a) See the hint of above example. At half intensity, 
    
  (b)  
   
5.  (a) I= I
max 
2
cos
2
? ??
??
??
 
   = I
0 
cos
2 
(30°)  (as ? = 60
o
) 
    
  (b) 60° phase difference is equivalent to 
6
?
 
path difference. 
6.  (a) At centre path difference is zero. Therefore construction interference will be obtained. 
(b) 
2
?
= 3 m. At a distance, where path difference is 
2
?
 or 3m destructive interference will be 
obtained. 
    
  At P
1
   BP
1 
- AP
1 
= 3rn =
2
?
 
  At P
2
   AP
2
 - BP
2
 = 3m = 
2
?
 
7.  
   
    ?x = (BP - AP) = (9 - 2x) = n ? 
   
  Now, substituting n = 1, 2, ...... etc. We can find different values of x. 
   x
1
 = 3.25 m for n = 1 
  x
2
 = 2.0m for n = 2 and x
3
 = 0.75 m for n = 3  
  Similarly we will get three points at same distance from other point B. 
8-  
   
   = 0.589 × 10
6
m  0.590 nm 
9.  
    ? 0.014°  
10.  Wavelength in water 
  Fringe width 
    
   = 10
-3 
m = 1 mm  
11.  
   
   = 2.0 × 10
-6
 m = 2.0 ?m 
12.  Distance 
    
   = 7.2 × 10
-5
m = 0.072 mm 
13.  The required distance = one fringe width 
    
   = 8.33 × 10
-4 
m = 0.83 mm