Narrow-linewidth multiple-prism grating solid-state dye laser oscillators are analysed using ray transfer matrices. Attention is given to beam divergence measurements and the effect on them of thermal lensing, at the solid-state gain medium. It is found that although thermal lensing leads to an increment of beam divergence, it induces oscillation in the unstable resonator regime, thus contributing to the attainment of TEM00 beam profiles. In addition, narrow-linewidth emission in dispersive oscillators, incorporating rhodamine 6 G doped HEMA:MMA gain media, is reported for the first time. Laser efficiency is 4–5% at a laser linewidth ≤1.8 GHz for double-longitudinal-mode emission. Beam divergence is measured in the 2–2.3 mrad range, in good agreement with theory.