In his book Lectures on Physics, Feynman mentions two predictions followed from Fermat's Principle (chapter 26-4).

1) Given three media air (1), water (2) and glass (3) with indices measured against each other $n_{12}$, $n_{13}$ and $n_{23}$, we get the following relation:

$$ n_{23} = \frac {v_2}{v_3} = \frac {v_1/v_3}{v_1/v_2} = \frac {n_{13}}{n_{12}} $$

where v_i is the speed of light in the i-th medium.

2) speed of light in water is slower than in air

I would like to know how does one go from Fermat's Principle to these two conclusions, most preferable in a simple way.


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