Critical Angle and Total Internal Reflection

The Critical Angle

Snell’s law:

$$n_1\text{ }\sin\text{ }\theta_1 = n_2\text{ }\sin\text{ }\theta_2$$

At critical angle:

$$n_1\text{ }\sin\text{ }C = n_2 \sin 90^\circ$$ $$n\text{ }\sin\text{ }C = 1$$ $$\sin\text{ }C = \frac{1}{n}$$ $$C = \sin^{-1}\left(\frac{1}{n}\right)$$

Refractive index is inversely proportional to critical angle.