386
DOC.
23
PROPAGATION OF LIGHT
of
equal
phase
of
a
plane light
wave
at
time
t,
and
P1
and
P2
two
points
in this
plane
a
unit
distance
apart
from each
other. Let
P1
and
P2
lie in
the
plane
of the
paper,
which
is
chosen
in such
a way
that,
when
taken
along
the normal
to
the
plane,
the
derivative
of
$,
and thus also
of
c,
vanishes. We
obtain the
corresponding plane
of
equal
phaseor,
rather,
its
intersection
with
the
plane
of the
paperat
the
time
t
+
dt
by drawing
circles with radii
c1
dt
and
c2
dt around the
points
P1
and
P2
and
plotting
the
tangent to
these
circles,
where
c1
and
c2
denote the
velocities
of
light
at
P1
and
P2,
respectively.
The
angle
of
deflection
of the
light ray on
the
path
cdt
is
then
(c,

C2)dt
=
_
dc
At
1
dn'
'
if
we
take the
angle
of deflection
as
positive
when
the
ray
of
light
bends
in
the direction
of
increasing
n'.
F,
12
Fig.
2.
Thus,
the
angle
of deflection
per
unit
path length
of the
light ray
will
then be
1
dc
cdn'
'
or,
according
to
(3),
1
3$
c2
dn'
Finally, we
obtain for the deflection
a
which
the
light ray
undergoes
in
the direction
n'
on
any
arbitrary path
(s)
the
expression:
(4)
a
=
v '
"2
J dn'.
We
could have
obtained the
same
result
by directly
considering
the
propagation
of
a light
ray
in
the
uniformly
accelerated
system
K'
and
transferring
the result
to
the
system K,
and
from
there
to
the
case
of
an arbitrarily
constituted
gravitational
field.