- Deriving the equation for the critical angle
The critical angle formula can be derived using Snell’s law;
Using this image we can write the following;
And so, substituting these into Snell’s law gives us;
Rearranging for gives;
The part many books brushes over and can therefore be confusing is changing into .
The way it is done, is by considering the value for the absolute refractive index of air,
Now we can write
Since we only need to deal with one refractive index, becomes simply , and so;
where n is the refractive index of the more dense medium.
- Isaac Physics – Reflection and refraction – This is a reading resource