When judging the optical properties of a translucent object, humans often look at sharp geometric features such as edges and thin parts. An analysis of the physics of light transport shows that these sharp geometries are necessary for scientific imaging systems to be able to accurately measure the underlying material optical properties. In this article, we examine whether human perception of translucency is likewise affected by the presence of sharp geometry, by confounding our perceptual inferences about an object's optical properties. We use physically accurate simulations to create visual stimuli of translucent materials with varying shapes and optical properties under different illuminations. We then use these stimuli in psychophysical experiments, where human observers are asked to match an image of a target object by adjusting the material parameters of a match object with different geometric sharpness, lighting, and three-dimensional geometry. We find that the level of geometric sharpness significantly affects perceived translucency by observers. These findings generalize across a few illumination conditions and object shapes. Our results suggest that the perceived translucency of an object depends on both the underlying material's optical parameters and the three-dimensional shape of the object. We also find that models based on image contrast cannot fully predict the perceptual results.