Greenhouse effect of atmosphere (simplified radiative equilibrium)

The atmosphere is approximated by ideal glass pane(s)
(transparent to solar radiation, opaque to terrestrial radiation).
Temperature of earth's surface and each glass pane: steady state

T_s = T_e  ......  T_s = 2^(1/4) T_e ...... T_s = 3^(1/4) T_e ......
(T_s: surface temprature; T_e: effective radiation temperature)