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where we note that
φ
=
π
(since the photon is scattered back in the direction of incidence).
Now, from the Doppler shift formula (Eq. 3825) the frequency
f'
0
of the photon prior to
the scattering in the new reference frame satisfies
f
c
f
'
'
,
0
0
0
1
1
==
+
−
λ
β
where
=
v
/
c
. Also, as we switch back from the new reference frame to the original one
after the scattering
11
.
c
ff
−−
′
′
+λ
+
We solve the two Dopplershift equations above for
λ
'
and
λ
'
0
and substitute the results
into the Compton shift formula for
∆λ
'
:
∆λ
'.
=
−
+
−
−
+
=
1
1
2
0
2
h
mc
e
Some simple algebra then leads to
Eh
f h
f
h
e
+
+
−
F
H
G
I
K
J
−
0
2
1
1
21
1
.
84. The difference between the electronphoton scattering process in this problem and the
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 Spring '08
 Any
 Physics, Photon

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