# The critical angle for total internal reflection in lucite is 41 degrees. How do you find lucite's index of refraction?

May 8, 2017

This picture shows the crossover point between refraction and reflection (from medium to less dense medium).

In terms of Snell's Law:

${n}_{1} \sin {\theta}_{1} = {n}_{2} \sin {\theta}_{2}$

But at the critical angle, ${\theta}_{c}$, we have:

${n}_{1} \sin {\theta}_{c} = 1 \cdot \sin \left(\frac{\pi}{2}\right) \left[= 1\right]$

$\implies {n}_{1} = \frac{1}{\sin} \left({41}^{o}\right) = 1.524$

NB: Total internal reflection can only occur if ${n}_{1} > {n}_{2}$