1. The problem statement, all variables and given/known data A light ray in air is obliquely incident on a parallel-sided slab of refractive index 'n'. The light ray refracts and hits the left side of the slab and undergoes total internal refraction. What is the maximum possible 'n' value? NOTE - This is a theoretical problem that I created upon observation of a numerical problem that asks for range of incident angles. I do not know if maximum 'n' value can exist for any given circumstances. Also, I have neglected the fact that at critical angle incidence, T.I.R. doesn't occur. However, a small dθ after c should cause T.I.R, so I have left out that negligible amount. Please point out any clarification and/or errors in my assumptions. 2. Relevant equations n * sin θ = constant sin c = 1 / n 3. The attempt at a solution Now, assume the ray is incident at angle i on the top side. Upon refraction, we can say → sin i = n * sin r. Also, since maximum value of sin() is 1; sin i < 1 → n * sin r < 1 ( we disregard i = 90°, as the ray is obliquely incident on, and not grazing, the slab) Now, for air-slab interface, of critical angle c, we know that sin c = 1 / n. Also, when we draw a diagram, the normals to the incident ray and refracted, T.I.R-ing ray form a right triangle, with c and r as the other two angles → c + r = 90° → c = 90° - r Taking sin() on both sides, we get sin c = sin (90° - r) = cos r OR, cos r = 1 / n → sin r = √(1 - ( 1 / n^2 ) ) → n * sin r = √( n^2 - 1) OR, √( n^2 - 1) < 1 → n^2 < 2 → n < √2 Therefore, the maximum value for 'n', for ray at air-slab interface to undergo T.I.R, is √2.