Many species of tephritid flies (Diptera: Tephritidae) perform a wing waving display ('supination') to deter attacks from jumping spiders. This display, along with the dark bands on the wings, has been thought to deter spiders through a form of mimicry termed 'predator mimicry'. In a series of studies with jumping spiders and the Mexican fruit fly, I explored this interaction from a visual ecology perspective. Using an custom built eye-tracker that traces the movement of the retina in the principal eyes, I played videos of displaying flies and monitored the response. I describe the patterns of retinal movement of jumping spiders in three treatments: during fly display, fly walking and a still fly. We show that the deterrent effect is achieved by exploiting the sensory biases of the predator.