2. interference.ppt bhzvkhjkjfgkzjgfkzgfz

short ppt on interference

1. Interference

2. Contents: Interference definition Superposition Principle Relation between Phase difference and Path difference Constructive and destructive interference Coherent Source Optical path Young’s Double slit experiment Newton’s ring

3. Interference of light : The phenomenon of non uniform distribution of light energy in a medium due to superposition of light waves from two coherent sources is called interference of light. https://www.youtube.com/watch?v=CAe3lkYNKt8

4. Superposition Principle:  

5. Path difference and Phase difference: Phase difference ( φ ) = X Path difference ( x ) φ = x  

6. Constructive interference: The interference, which is due to the superposition of two waves in such a way that crest meets crest and trough meets trough ,is called constructive interference. In constructive interference, the amplitude and intensity of resultant wave become maximum which results the bright interference fringes.

7. Destructive interference: The interference which is due to the superposition of two waves in such a way that crest meets trough and trough meets crest is called destructive interference. In destructive interference, the amplitude and intensity of resultant wave become minimum (zero) which results complete dark interference fringes.

8. Coherent source: Two sources of light, which continuously emit light of same wavelength or frequency and are always in phase or have a constant phase differences are called coherent sources. Two independent sources of light can not be coherent sources. This is because light emitted by individual atoms of light source is random and so the light from these atoms are not in phase. Thus, two independent sources of light are incoherent sources.

9. Condition for sustained interference: Wavelength of waves must be equal. Amplitude of the waves should be equal. Two waves must be in same phase or constant phase difference. S eparation of two source should be small W idth of the slit should be narrow.

10. Optical path: The distance which the light travels in vacuum during the same time for which it travels in the medium is called optical path. Let the light travels with velocity v in the medium of refractive index µ. If it covers distance x in the medium in time t, then we have, v = t = ………..( i ) where the distance x is called geometrical path. Similarly, if the light travels with velocity c in vacuum ( or air) and covers the distance d in the same time t then we have d = c . t ……….( ii )  

11. Where d is called optical path. Putting the value of ( i ) and ( ii ) , we get d = c . d = But µ = is the absolute refractive index of the medium. So, we have d = µ …….( iii ) i.e. Optical path = absolute refractive X geomatric path Thus, the product of absolute refractive index of the medium and the distance travelled by light in the same medium ( i.e. geometric path )is called optical path.  

12. Young’s Double Slit Experiment: Young, in 1801, demonstrated the interference of light by a simple experiment as shown in figure. In his experiment, light is illuminated from monochromatic source which is passed from two fine slits then alternate dark and bright bands appear on the screen. https://www.youtube.com/watch?v=MDX3qb_BMs4

13. Analytical Treatment of Interference: Suppose are the displacements of two waves . Then, = a sin wt ………….. ( i ) = a sin ( wt + φ ) ………….. ( ii ) where a is the amplitude of individual wave and φ is phase difference. During superposition resultant displacement is given by, y = a sin wt + a sin ( wt + φ ) y = a sin wt + a sinwt cos φ + a coswt sin φ y = a sin wt ( 1 + cos φ ) + a sin φ cos wt Let, a (1 + cos φ ) = A cos θ ……….. ( iii ) a sin φ = A sin θ ……….. ( iv )  

14. On squaring and adding equation ( iii ) and ( iv ) we get, si + = ( 1 + 2cos φ + co + si ) = ( 2 + 2cos φ ) = 2 . 2 co = 4 co We know , intensity is directly proportional to the square of the amplitude.  

15. For maximum intensity , co = 1 cos = 1 = 0 , , 2 , 3 , …… φ = 0 , 2 , 4 , 6 , …….. φ = 2n Where n = 0,1,2,3,…. We know, Phase difference ( φ ) = X path difference (x) φ = x So, φ = x = 2n  

16. x = n This gives the condition for maximum intensity.  

17. For minimum intensity, co = 0 cos = 0 = , , , ……. φ = , , 5 ….. φ = ( 2n - 1 ) , where, n = 1,2,3,4,…. Also , φ = x So, φ = ( 2n - 1 ) = x  

18. x = ( ) This gives the condition for minimum intensity.  

19. Theory of Interference: (Expression of Fringe Width in Interference): Consider are two slits at distance ‘d’ from each other. Suppose the slits be illuminated by a source of light of wavelength such that these slits act as coherent source. let us take a point P on the screen which is placed at distance ‘D’ from these slits as in figure. Then, Path difference = From figure, we have, PQ = x - PR = x +  

20. In In From ( a ) and ( b ),we have, - = [ ] – [ ] + - = 2xd In practice, point P lies very close to C. So,  

21. +D - = 2xd or, - = So, path difference= - = The path difference of waves reaching at point C from and is zero because point C is at equidistance from and Hence, maximum intensity is observed at point C called central bright fringe. Bright fringes : If the path difference is equal to integral multiple of wavelength ( , the bright fringes are obtained. i.e. path difference = n  

22. Newton’s ring: Newton’s rings are interference fringes of equal thickness which are produced in the air film between a convex surface and a flat surface. When a plano -convex lens is placed over a flat glass plate, then a thin air layer is formed between glass plate and a convex lens. If the radius of curvature of plano -convex lens is much greater than distance ‘r’ and the system is viewed through the above, the pattern of dark & bright ring is observed. This is called Newton’s Ring . https://www.youtube.com/watch?v=EXCWsy0MTpw

23. Application of Newton’s Ring Experiment: Measurement of wavelength of light:

24. Short Questions: Can two independent sources of light produce interference? Why have the two sources of light to be close to each other for the production of good interference pattern? Distinguish between interference and diffraction. What do you understand by coherent sources? In young’s double slit experiment, how is the fringe width altered if the separation between the slits is doubled and the distance between the slits and the screen is halved? What are the conditions for sustained interference of light?

25. In Young’s double slit experiment, how is the fringe width altered if the separation between the slits is doubled and the distance between the slits and the screen is halved? What do you understand by the coherent sources of light?

26. Long questions: Derive the fringe width from Young’s double slit experiment. What do you understand by interference of light? Derive an expression for the fringe width in a Young’s double slits experiment. Describe Young’s double slits experiment for the interference of light and show that widths of bright and dark fringes are the same. Prove analytically that the bright and dark fringes in young’s double slit experiment are equally spaced . Describe Young’s double slit experiment, if brief, for the measurement of wavelength of a monochromatic source of light .

27. Numerical questions: 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 1 m away from the slits. Find the distance of the second bright fringe and dark fringe from the central maximum. How will the fringe pattern change if the screen is moved away from the slits?

28. In young’s double slit experiment, the slits are 0.03 cm apart and the screen is placed 1.5m away. The distance between the central fringe and fourth bright fringe is 1 cm. Calculate the wavelength of light used. Two coherent sources A and B of radio waves are 5m apart. Each source emits waves with wavelength 6m. Consider points along the line between two sources at what distances, If any , From A is the interference constructive.

29. Multiple choice questions: 1.How is the interference pattern in the young’s double slit experiment affected if yellow light is replaced by red light of same intensity? the fringes will vanish the fringes will become brighter the fringe width will decrease the fringe width will increase

30. 2.In Young’s double slit experiment, if the distance between the slits and the screen is doubled and the separation between the slits is reduced to half, the fringe width is doubled becomes four times is halved remains unchanged

31. 3. In young’s double slit experiment, the slits are separated by 0.28mm and the screen is placed 1.4m away. The distance between fourth bright fringe and the central bright fringe is measured to be 1.2cm. What is the wavelength of light used in the experiment? 200nm 400nm 600nm 800nm

32. Answer for MCQ: D B C