Under the assumption of orthogonal electrical dipole moments of a cascade three-level atom with equally spaced energy levels, the full quantum theory is applied to study the emission spectrum of the atom interacting resonantly with a single-mode electromagnetic field in an ideal cavity. Spectral calculations for both the intensity-dependent and intensity-independent couplings are performed and the spectra in the cases of orthogonal dipole moments and parallel dipole moments are compared. It is found that some spectral lines disappear for the atom with parallel dipoles due to destructive interference leading to fewer lines compared with the spectrum of the atom with orthogonal dipole moments.