Under typical viewing conditions, human observers readily distinguish between materials such as silk, marmalade, or granite, an achievement of the visual system that is poorly understood. Recognizing transparent materials is especially challenging. Previous work on the perception of transparency has focused on objects composed of flat, infinitely thin filters. In the experiments reported here, we considered thick transparent objects, such as ice cubes, which are irregular in shape and can vary in refractive index. An important part of the visual evidence signaling the presence of such objects is distortions in the perceived shape of other objects in the scene. We propose a new class of visual cues derived from the distortion field induced by thick transparent objects, and we provide experimental evidence that cues arising from the distortion field predict both the successes and the failures of human perception in judging refractive indices.