Snell's law in use

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

Angle in and angle out of a light ray travelling between air and water.

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)$

$Ray of incidence and ray of refraction travelling from air to water.$

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

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