Abstract: A requirement for rendering realistic images interactively is efficiently simulating material properties. Recent techniques have improved the quality for interactively rendering dielectric materials, but have mostly neglected a phenomenon associated with refraction, namely, total internal reflection. We present an algorithm to approximate total internal reflection on commodity graphics hardware using a ray-depth map intersection technique that is interactive and requires no precomputation. Our results compare favorably with ray traced images and improve upon approaches that avoid total internal reflection.