# Confusion over the critical angle

At school, I was taught to use $$\mathrm{sin}\ c = 1/n$$ to calculate the critical angle, given it is from a medium to air.

I tried deriving a general formula for critical angles for every pair of media and ended up with $$\mathrm{sin}\ c = n_2/ n_1$$. Then it prompted a question about what happens when $$n_2 > n_1$$ ?

$$\mathrm{sin}\ c = n_2 / n_1$$ , $$\mathrm{sin} \ c > 1$$, but $$\mathrm{sin}\ c$$ cannot be greater than $$1$$

My question(s):

i) What happens to the ray when it hits the edge at this?

ii) Do I just discard the critical angle?

## 1 Answer

When $$n_2 > n_1$$ there is no total internal reflection.

Try thinking about it this way: suppose you are considering water and air. When light moves from water to air, it is refracted away from the vertical. For some angle (the critical angle) the angle of refraction is 90 degrees. This is the situation where $$n_1 > n_2$$. For angles larger than the critical angle, light is reflected instead.

The opposite situation is when light moves from air to water. In this case the light is refracted towards the vertical, and there is no critical angle and no total internal reflection.