# Snell's law in use

Snell's law can be simplified in use because in most text books the medium going in is air.

**NOTE:** how `theta` relates to the angle going in against the normal line is different to the angle coming out against the normal line.

We have learnt that Snell's law is

`(sin\ \i\n\ \theta)/(sin\ \out\ \theta)=(n\ \(out))/(n\ \(i\n))`

But the refractive index `n` of air for all practical purposes is one (1).

(In fact a vacuum is 1 and air is 1.0002926)

So most text books show Snell's law as being

`(sin\ \i\n\ \theta)/(sin\ \out\ \theta)=n\ \(out)`

Angle of the incident = Angle of incidence `(i)`

Angle refracted = Angle of refraction `(r)`

Snell's law becomes:

`(sin\theta\i)/(sin\theta\r)=(n\ \m\e\d\i\u\m\ \w\a\t\e\r)/(n\ \m\e\d\i\u\m\ \a\i\r)`

Which becomes

`(sin\theta\i)/(sin\theta\r)=n/1`

Which becomes

`(sin\theta\i)/(sin\theta\r)=n` (refractive index of medium)

## Summary

Most text books show Snell's law as

`n=(sin\ \i)/(sin\ \r)`