
432 Classical Mechanics
from which we obtain
t
L
AC
2
=
−
.
Similarly, as the light is returning to the half-silvered plate, the plate moves to the right to the posi-
tion B′. The total path length for the return trip is the same as can be seen from the symmetry of
Figure 13.2. Therefore, if the return time is also the same, the total time for light to go from A to C
and back is then 2t
2
, which we denote by t
3
:
t
L
cu
L
cuc
L
c
u
c
AC AC AC
3
22 2
2
2
22
1
2
1
2
=
−
=
−
()/
.
(13.5)
In Equations 13.3 and 13.4, the rst factors are the same and represent the time that would be taken
if the apparatus were at rest relative to the ether. The second factors represent ...