Recapitulate. Prof. Shiva Prasad, Department of Physics, IIT Bombay

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2 Reapitulate We disussed how light an be thought of onsisting of partiles known as photons. Compton Effet demonstrated that they an be treated as a partile with zero rest mass having nonzero energy and momentum. 2

3 We worked out one example involving photons, where we saw that energy and momentum of photon an be transformed using the standard energy momentum transformation. 3

4 Doppler Effet If the energy and momentum of photon hanges upon hange of frame this would imply a hange in frequeny in the other frame. h E h ; p 4

5 This is alled Doppler effet. Doppler effet is well known in sound. But for light it is treated differently. 5

6 Doppler Effet in Sound The expression of hanged frequeny depends on whether soure or the detetor is moving. 6

7 The differene is aused beause sound needs a medium to travel. The speeds of soure and/or detetor are defined with respet to the medium. 7

8 The expression of hanged sound frequeny, when soure is fixed and observer is going away with speed v. v ds o 1 8

9 The expression of hanged sound frequeny, when observer is fixed and soure is going away with speed v. ds o 1 1 v 9

10 For light the two situations are fundamentally similar as it does not require a medium to travel. Hene we expet a single expression to represent both the situations. 10

11 Longitudinal Doppler Effet h V S S 11

12 Use Energy Transformation E E vp ; E h ; h p ; E h x x Note the sign of momentum as it has to be deteted by the observer. 12

13 h h v h v v v v v

14 Using Doppler Effet Notation v 1 1 ds o 2 v o v v 14

15 In the limit of low relative speed v. ds v v o 1 1 v v o o 1 v 15

16 Transverse Doppler Effet S h S 16

17 E E vp E h ' p 0 ; E h x v x Note: p x is zero and not p x. 17

18 Using Doppler Effet Notation ds o 1 v

19 Doppler Shift In LDE, the observed frequeny is more if the soure is moving towards observer and lower when the soure is moving away. In TDE, the observed frequeny is lower than the soure frequeny. It has no lassial analogue. 19

20 Time Dilation Consider TDE. The two onseutive maxima/ minima in field of e.m. wave are produed in same plae in S. Hene the time interval between them(time period) is proper in S. 20

21 S h S 21

22 Using Time dilation, we get the following. T T 1 1 ' ' This gives the same expression as TDE. 22

23 Example What is the required speed relative to an observer, of a soure of a gamma rays of energy 14.4 kev, if its energy is to be inreased by 10-6 ev, as seen by an observer. 23

24 Beause the energy has to be inreased the soure should move towards observer. v hds ho 1 h ov h ds ho v 2.08 m / s 6 10 ; 24

25 Emission and Absorption A onsequene of photon having a momentum is that emission and absorption would also obey momentum onservation. 25

26 Emission of Photon Consider a ase where the reoil speeds are non-relativisti. E E h K h n m R p 2m K R N R 26

27 Solving we get h E E h 1 n m 2 m N 2 Reoil energy is signifiant only for high energy transitions. 27

28 Absorption of Photon h E E K h p n m R 2m K R N R h En Em h 1 2 m N 2 28

29 Resonant Absorption Can a photon emitted from a partiular transition ause a reverse transition in another atom/nuleus? 29

30 E o E R E R Emission Line Absorption Line 30

31 Question Can the Reoil Energy be balaned by Doppler shifting the Energy? 31

32 Nulear Resonant Absorption Moon in 1950 arried out some experiments where he ould demonstrate resonant absorption, by imparting speeds to the gamma ray of about 7x10 4 m/s. 32

33 Mössbauer Effet Observed the Reoilless nulear resonane absorption, by reating a situation where reoil is taken by the solid. 33

34 Was awarded 1961 Noble Prize in Physis. Opened up possibilities, where one an see small hanges in the energy levels aused by external effets, using Doppler Effet. 34

35 Laser Cooling of a Gas Temperature is related to the r.m.s. speed of moleules. The speed an be dereased if a photon is absorbed moving in a diretion opposite that of the gas atom. 35

36 Let us take one dimension motion and take a transition from E 1 to E 2. Choose a photon soure with hν < E 2 E 1. Only those atoms moving towards the soure an absorb the photon, ausing a redution in speed. 36

37 Optial Molasses Create a situation in all six diretions. Spontaneous emission is random. Chu, Cohen-Tannoudji and Philips got Noble Prize in

38 Summary We disussed Longitudinal ad transverse Doppler Effet applied to light. We gave some examples of its appliation. 38