The visibility of carbon dust particles in fusion plasmas with fast framing cameras is evaluated using computer and theoretical modelling. Dust heating and ablation in the plasmas, ionization dynamics of the ablation cloud around the dust particle, thermal radiation of the dust and line radiation of the cloud are considered. The minimal size of carbon dust particles visible with the cameras is calculated as a function of the plasma parameters and the distance from the dust to the camera objective. The relative contributions of thermal radiation from the grain and line radiation from the cloud to the total dust radiation are analysed.