Background rim brightening in the spherical uniform-density embedding shells, either isothermal (left) or with the radiative-equilibrium T_d(r) from the models (Sect. 2) of embedded starless cores (middle) and protostellar envelopes with L_⋆ = 30 L_⊙ (right). The intensity profiles on the left are labeled by the size ratios R_E/R = { 30,3,1.3 } of the embedding cloud and the central cavity, whereas the intensity profiles at 500 μm in the middle and on the right indicate the mass (in M_⊙) of the embedded models. For uniform temperatures (left), the brightening factors f_S are 1.03,1.41, and 2.77 are the values given by Eq. (B.1). For nonuniform temperatures (and R_E/R = 3, R = 10⁴ AU), they range from 1.27 to 1.40 (middle) and from 1.44 to 1.53 (right).