Question

What is the critical angle c for total internal reflection if the material is clear acrylic, with a refractive index of 1.5?

If I could get help in understanding and how to solve this that would be awesome! Thanks!

Answer 1

Use Snell's Law, and make the angle of refraction 90 degrees, and n2 is the index of refraction of the second medium (the one the light is travelling TO):\[\frac{\sin \angle i_c}{\sin ~90^{\circ}} = \frac{n_2}{n_1}\] If n2 is air, use:\[\frac{\sin \angle i_c}{\sin ~90^{\circ}} = \frac{1.0}{1.5}\]
\[\angle i_c = \arcsin (\dfrac{2}{3}), \quad \text{since}\, \sin~90^{\circ} = 1\]