Page 16 - 83 basic knowledge of astronomy
P. 16
dΩ s
E= E n
u (s)
ν
E= E m
Figure 16: Absorption of radiation.
levels, such that the newly emitted radiation has the same frequency ν, and
the same direction of propagation -s, as the incident radiation (Figure 17).
The probability df st for the induced (or stimulated) emission to occur in a
dΩ s
E= E
n
u (s)
ν
E= E m
Figure 17: Induced (or stimulated) emission of radiation.
direction within a small solid angle dΩ around -s, and in a small frequency
bandwidth dν around ν mn = (E n − E m ) / h, during a short time interval
dt, must be proportional to dν dΩ dt and to the spectral energy density per
unit solid angle u ν (s) of the incident radiation. Therefore, introducing a
m
proportionality coefficient β , we have:
n
df st = β n m u ν (s) dν dΩ dt. (11)
16
