Question

find the critical angle of a material of refractive index root3

Answer 1

Let's consider two different media - creatively named medium i (incident medium) and medium r (refractive medium). The critical angle is the Θi that gives a Θr value of 90-degrees. If this information is substituted into Snell's Law equation, a generic equation for predicting the critical angle can be derived. The derivation is shown below.

ni *• sine(Θi) = nr • sine (Θr)ni • sine(Θcrit) = nr • sine(90 degrees)ni • sine(Θcrit) = nrsine(Θcrit) = nr/niΘcrit= sine-1 (nr/ni) = invsine (nr/ni)