18
1
Recapitulate
• We discussed how light can
be thought of consisting of
particles known as photons.
• Compton Effect
demonstrated that they can
be treated as a particle with
zero rest mass having nonzero energy and momentum.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
2
• We worked out one
example involving
photons, where we saw
that energy and
momentum of photon
can be transformed
using the standard
energy momentum
transformation.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
3
Doppler Effect
If the energy and
momentum of photon
changes upon change of
frame this would imply a
change in frequency in
the other frame.
h
E  h ; p 
c
Prof. Shiva Prasad, Department of Physics, IIT Bombay
4
• This is called Doppler
effect.
• Doppler effect is well
known in sound. But for
light it is treated
differently.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
5
Doppler Effect
in Sound
The expression of changed
frequency depends on
whether source or the
detector is moving.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
6
The difference is caused
because sound needs a
medium to travel. The
speeds of source and/or
detector are defined with
respect to the medium.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
7
The expression of changed
sound frequency, when
source is fixed and
observer is going away
with speed v.
ds
v

  o 1  
c

Prof. Shiva Prasad, Department of Physics, IIT Bombay
8
The expression of changed
sound frequency, when
observer is fixed and
source is going away with
speed v.
ds  o
1
v

1  c 


Prof. Shiva Prasad, Department of Physics, IIT Bombay
9
For light the two situations
are fundamentally similar
as it does not require a
medium to travel. Hence
we expect a single
expression to represent
both the situations.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
10
Longitudinal
Doppler Effect
h’
S
V
S’
Prof. Shiva Prasad, Department of Physics, IIT Bombay
11
Use Energy
Transformation
E    E   vpx  ; E   h ;
h 
px  
; E  h
c
Note the sign of momentum as it
has to be detected by the observer.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
12
h 
h   v
c
h 
2
v
1 2
c
v
v
1
1
c  
c
  
2
v
v
1
1 2
c
c
Prof. Shiva Prasad, Department of Physics, IIT Bombay
13
Using Doppler
Effect Notation
ds  o
v
v
1
1
c 
c
o
2
v
v
1
1 2
c
c
Prof. Shiva Prasad, Department of Physics, IIT Bombay
14
In the limit of low
relative speed v.
ds
1
2

1
2
v 
v

  o 1   1  
c 
c

v 
v 

  o 1 
1



2c  
2c 

v

  o 1  
c

Prof. Shiva Prasad, Department of Physics, IIT Bombay
15
Transverse
Doppler Effect
S
h’
S’
Prof. Shiva Prasad, Department of Physics, IIT Bombay
16
E     E  vpx 
E   h '
px  0 ;E  h
 

2
v
1 2
c
Note: px is zero and not px’.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
17
Using Doppler
Effect Notation
ds  o
2
v
1 2
c
Prof. Shiva Prasad, Department of Physics, IIT Bombay
18
Doppler Shift
•
•
In LDE, the observed
frequency is more if the
source is moving towards
observer and lower when
the source is moving away.
In TDE, the observed
frequency is lower than
the source frequency. It
has no classical analogue.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
19
Time Dilation
Consider TDE. The two
consecutive maxima/
minima in field of e.m. wave
are produced in same place
in S’. Hence the time
interval between them(time
period) is proper in S’.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
20
S
h’
S’
Prof. Shiva Prasad, Department of Physics, IIT Bombay
21
Using Time dilation,
we get the following.
T  T
1
1


'
 '  
This gives the same
expression as TDE.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
22
Example
What is the required speed
relative to an observer, of
a source of a gamma rays
of energy 14.4 keV, if its
energy is to be increased
by 10-6 eV, as seen by an
observer.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
23
Because the energy has
to be increased the
source should move
towards observer.
v

h ds  ho 1  
c

h ov
  ho 
h ds
 106;
c
v  2.08cm / s
Prof. Shiva Prasad, Department of Physics, IIT Bombay
24
Emission and
Absorption
A consequence of photon
having a momentum is
that emission and
absorption would also
obey momentum
conservation.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
25
Emission of
Photon
Consider a case where
the recoil speeds are
non-relativistic.
E n  E m  h  K R
h
 pR  2mN K R
c
Prof. Shiva Prasad, Department of Physics, IIT Bombay
26
Solving we get

h 
En  Em  h  1 
2 
 2mN c 
Recoil energy is
significant only for
high energy
transitions.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
27
Absorption of
Photon
h   E n  E m   K R
h
 pR 
c
En  Em
2mN K R

h 
 h 1 
2 
2mN c 

Prof. Shiva Prasad, Department of Physics, IIT Bombay
28
Resonant
Absorption
Can a photon emitted
from a particular
transition cause a
reverse transition in
another atom/nucleus?
Prof. Shiva Prasad, Department of Physics, IIT Bombay
29
Eo
ER ER
Emission
Line
Absorption
Line
Prof. Shiva Prasad, Department of Physics, IIT Bombay
30
Question
Can the Recoil Energy be
balanced by Doppler
shifting the Energy?
Prof. Shiva Prasad, Department of Physics, IIT Bombay
31
Nuclear Resonant
Absorption
Moon in 1950 carried out
some experiments where he
could demonstrate resonant
absorption, by imparting
speeds to the gamma ray of
about 7x104 cm/s.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
32
Mössbauer
Effect
Observed the Recoilless
nuclear resonance
absorption, by creating a
situation where recoil is
taken by the solid.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
33
Was awarded 1961 Noble
Prize in Physics.
Opened up possibilities,
where one can see small
changes in the energy
levels caused by external
effects, using Doppler
Effect.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
34
Laser Cooling of
a Gas
Temperature is related to the
r.m.s. speed of molecules.
The speed can be decreased
if a photon is absorbed
moving in a direction
opposite that of the gas
atom.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
35
• Let us take one dimension
motion and take a transition
from E1 to E2.
• Choose a photon source
with hν < E2 – E1.
• Only those atoms moving
towards the source can
absorb the photon, causing
a reduction in speed.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
36
Optical
Molasses
• Create a situation in all six
directions.
• Spontaneous emission is
random.
• Chu, Cohen-Tannoudji and
Philips got Noble Prize in
1997.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
37
Summary
• We discussed Longitudinal ad
transverse Doppler Effect
applied to light.
• We gave some examples of its
application.
Prof. Shiva Prasad, Department of Physics, IIT Bombay
38