# Why does light go in the path where time is minimum and not maximum?

On deriving Snell's Law from Fermat's Principle there is a part where

$$\frac{ds}{dt}=0$$ where $$s$$ is the distance gone by light.

But the principle states that light takes the path where it takes the minimum time. But it should be the extreme value which can be minimum or maximum. So why is the time minimum and not maximum?

• There's no maximum value for the distance. – Slereah Dec 8 '18 at 14:08
• May it does take the maximum time as well and it just hasn't arrived yet. – M. Enns Dec 8 '18 at 14:47
• I think that if there were a stationary distance which was a maximum not a minimum, then light could also go that way, but this is just my vague hunch based on wave equation. – Andrew Steane Dec 8 '18 at 19:12