## Wave Optics  Important Questions for CBSE Class 12 Physics Interference of Light

1.Superposition Principle According to superposition principle at a particular point in the medium, the resultant displacement y produced by a number of waves is the vector sum of the displacements produced by each of the waves (y1, y 2 , y3 ,•••)
i.e.    y = y1+y2+y3

2.Coherent Sources of light are the sources which emit light waves of same frequency, same wavelength and have a constant initial phase difference.

3.Coherent source of light can be obtained by deriving two sources from a primary (or initial) source by
(i)division of wavefront
(ii)division of amplitude

4.Two such sources of light, which do not emit light waves with a constant phase difference are called incoherent sources.

5.Conditions for sustained interference
(i)the two sources of light must be coherent.
(ii)the amplitude of electric field vector of interfering wave should be equal to have greater contrast.

6.The phenomenon of redistribution of energy in the region of superposition of waves is called interference. The points of maximum intensity in the regions of superposition of waves are said to be in constructive interference whereas the points of minimum intensity are said to be in destructive interference.

### 1 Mark Questions

1.Define the term ‘coherent sources’  which are required to produce interference pattern in Young’s double slit experiment. [Delhi 2014 c]
Ans.Two monochromatic sources,which produce light waves, having a constant phase difference  are known as coherent sources.

2.How would the angular separation of  interference fringes in Young’s double slit experiment change when the distance between the slits and screen is halved? [All India 2009]
Ans.

3.Why are coherent sources required to create interference of light?[Foreign 2009]
Ans.To observe interference fringe pattern, there is need to have coherent sources of light which can produce light of constant phase difference

4.How does the fringe width of interference fringes change, when the whole apparatus of Young’s experiment is kept in a liquid of refractive index, 1.3? [hots; Delhi 2008]
Ans.

5.How does the angular separation of interference fringes change, in Young’s experiment, if the distance between the slits is increased?[Delhi 2008]
Ans.

### 2 Marks Questions

6.Laser light of wavelength 630 nm  incident on a pair of slits produces an interference pattern in which the bright fringes are separated by 7.2 mm. Calculate the wavelength of another source of laser light which produce interference fringes separated by 8.1 mm using same pair Of slits. [All India 2011]
Ans.

7.How will the interference pattern in Young’s double slit experiment get affected, when
(i)distance between the slits S1 and S2 reduced and
(ii)the entire set up is immersed in  water? Justify your answer in each case.     [Delhi 2011]
Ans.

8.The figure shows a double slit experimental set up for observing interference fringes due to different interference component colours of white light.

Ans.(i) White colour fringe is obtained at point O as all components colour wavelength undergo constructive interference fringe pattern.
(ii) In this case, the light of blue colour interfere destructively and hence this colour would subtract from white light. Thus, yellow colour fringe would be obtained at P.

9.Write down two conditions to obtain the sustained interference fringe pattern of light. What is the effect on the interference fringes in Young’s double slit experiment, when monochromatic source is replaced by a source of white light?[Foreign 2008]
Ans.Conditions for sustained interference
(i) The two sources of light must be coherent to emit light of constant phase difference.
(ii) The amplitude of electric field vector of interfering wave should be equal to have greater contrast between intensity of constructive and destructive interference.
When monochromatic light is replaced by white light, then coloured fringe pattern is obtained on the screen

### 3 Marks Questions

Ans.

11.Describe Young’s double slit experiment to produce interference pattern due to a monochromatic source of light. Deduce the expression for the fringe width.[Delhi 2011]
Ans.

Ans.

13.In Young’s double slit experiment, the two slits 0.15 mm apart are illuminated by monochromatic light of wavelength 450 nm. The screen is 0 m away from the slits.
(i)Find the distance of the second

• bright fringe
• dark fringe from the central maximum.

(ii)How will the fringe pattern change if the screen is moved away from the slits? [All India 2010]
Ans.

14.A beam of light consisting of two wavelengths 560 nm and 420 nm is used to obtain interference fringes in a Young’s double slit experiment. Find the least distance from the central maximum, where the bright fringes, due to both the wavelengths coincide. The distance between the two slits is 4.0 mm and the screen is at a distance of 0 m from the slits.[Delhi 2010 C]
Ans.

15.A beam of light consisting of two  wavelengths 600 nm and 450 nm is used to obtain interference fringes in a Young’s double slit experiment. Find the least distance from the central maxima, where the bright fringes due to both the wavelengths coincide. The distance between the two slits is 4 mm and the screen is at a distance lm from the slits.     [Foreign 2008]
Ans.

16.In Young’s double slit experiment, monochromatic light of wavelength 630 nm illuminates the pair of slits and produces an interference pattern in which two consecutive bright fringes are separated by 1 mm . Another source of monochromatic light produces the interference pattern in which the two consecutive bright fringes are separated by  7.2 mm. Find the wavelength of light from the second source. What is the effect on the interference fringes, is when monochromatic source is replaced by a source of white light?[All India 2009]
Ans.

17.In Young’s double slit experiment, monochromatic light of wavelength 600 nm illuminates the pair of slits and produces an interference pattern in which two consecutive bright fringes are separated by 10 Another source of monochromatic light produces the interference pattern in which the two consecutive bright fringes are separated by 8 mm. Find the wavelength of light from the second source. What is the effect on the interference fringes if the monochromatic source is replaced by a source of white light? [All India 2009]
Ans.

18.In a Young’s double slit experiment, the two slits are kept 2 mm apart and the screen is positioned 140 cm away from the plane of the slits. The slits are illuminated with light of wavelength 600 nm. Find the distance of the third bright fringe from the central maximum, in the interference pattern obtained on the screen. If the wavelength of the incident light were changed to 480 nm, then find out the shift in the position of third bright fringe from the central maximum.[HOTS; All India 2008]
Ans.

Ans.

5 Marks Questions

20.(i) In Young’s double slit  experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. Hence, obtain the expression for the fringe width.
(ii) The ratio of the intensities at minima to the maxima in the Young’s double slit experiment is 9:25.Find the ratio of the widths of the two slits.[All India 2014]
Ans.(i)

Ans.

22.In Young’s double slit experiment,derive the condition for
(a)constructive interference and
(b)destructive interference at a point on the screen.
(ii) A beam of light consisting of two wavelengths, 800 nm and 600 nm is used to obtain the interference fringes on a screen placed 1.4 m away in a Young’s double slit experiment. If the two slits are separated by 0.28 mm, calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide.                     [All India 2012]
Ans.(i)

23.(i)What is the effect on the interference  fringes to a Young’s double slit experiment when
(a)the separation between the two slits is decreased?
(b)the width of the source-slit is increased?
(c)the monochromatic source is replaced by a source of white light? Justify your answer in each case

Ans.

24.State the importance of coherent sources in the phenomenon of interference. In Young’s double slit experiment to produce interference pattern, obtain the conditions for constructive and destructive interference. Hence, deduce the expression for the fringe width. How does the fringe width get affected, if the entire experimental apparatus of YDSE is immersed in water?[All India 2011]
Ans.To observe interference fringe pattern, there is need to have coherent sources of light which can produce light of constant phase difference

(ii) In this case, the light of blue colour interfere destructively and hence this colour would subtract from white light. Thus, yellow colour fringe would be obtained at P.

25.What are coherent sources?Why are they necessary for observing a sustained interference pattern? How are the two coherent sources obtained in the Young’s double slit experiment?

Ans.(i)Two monochromatic sources,which produce light waves, having a constant phase difference  are known as coherent sources.

(ii)

26. In a Young’s double slit experiment,
(i)deduce the conditions for constructive and destructive interference. Hence, write the expression for the distance between two consecutive bright or dark fringe.
(ii)what change in the interference pattern do you observe, if the two slits, St and are taken as point sources?
(iii) plot a graph of the intensity distribution versus path difference in this experiment. Compare this with the intensity distribution of fringes due to diffraction at a single slit. What important difference do you observe? [Delhi 2009 c]
Ans.(i)

(ii)Being two independent sources, the difference between the waves from two sources is not constant and hence interference pattern cannot be seen on screen.
(iii) Graph of the intensity distribution versus path difference

The intensity of bright fringes in interference is same for all the bright fringes whereas in diffraction pattern, the central fringe is brightest and intensity of secondary maxima decreases with the increase of their order.

27.(i)What are coherent sources of  light? Two slits in Young’s double slit experiment are illuminated by two different sodium lamps emitting light of the same wavelength. Why does no interference pattern observed?
(ii)Obtain the condition for getting dark and bright fringes in Young’s experiment. Hence, write the expression for the fringe width.
(iii)If s is the size of the source and d be its distance from the plane of the two slits. What should be the criterion for the interference fringes to be seen.[HOTS; Delhi 2006]
Ans.

(i) Coherent sources of light Refer to Ans -1 Two different sodium lamps cannot produce interference fringe pattern as they are unable to maintain constant initial phase difference between them.