that from geometry / trigonometry, the transmitted (refracted) angle at the first surface is exactly equal to the incident angle at the bottom surface - assuming that the top and bottom surfaces are parallel to each other. We will refer to this single angle as glass . The necessary condition for total internal reflection at the bottom surface is that the transmitted angle (in the air) in Snell's Law goes to air,transmitted = 90 nglasssin glass = nair,transmittedsin air where air,transmitted = 90 But notice that this will be the exact same equation for Snell's law at the top surface: nairsin air,in = nglasssin glass But since the "glass side" of the equation has the same angles (and index), that must mean the "air side" of these two equations must be the same as well, which implies that : air,in = air,transmitted = 90