1. The theory of the unfocused clear zone eye is extended to cover cases where rays are partially focused upon the receptor layer. 2. Light is admitted through facets according to a Gaussian distribution of angle of incidence defined with respect to the axis of the facet. 3. The same light crosses the clear zone in an average direction related to its direction of origin outside the eye, so that it tends to be concentrated around that receptor on the radial axis pointing towards the source of light. This effect, defined as focusing in contrast to the unfocused eye, allows a simultaneous improvement in sensitivity and acuity. 4. An eye can be focused partially because rays diverge from each cone tip or because, on average, they converge above or below the receptor layer on the radial axis pointing towards their source. The two situations are analysed quantitatively. 5. In a partially focused eye neither the measured angular sensitivity nor the absolute sensitivity allow a prediction of the ray paths because many different distributions from the cone tips produce a given final result. Therefore the optics of partially focused clear zone eyes must be analysed by direct measurement of light distribution from the cone tips.