-1
$\begingroup$

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?

$\endgroup$
  • 1
    $\begingroup$ There's no maximum value for the distance. $\endgroup$ – Slereah Dec 8 '18 at 14:08
  • $\begingroup$ May it does take the maximum time as well and it just hasn't arrived yet. $\endgroup$ – M. Enns Dec 8 '18 at 14:47
  • $\begingroup$ 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. $\endgroup$ – Andrew Steane Dec 8 '18 at 19:12
3
$\begingroup$

Because the maximum time would be infinite, but we can see light travel through materials. Therefore the time and distance traveled cannot be maximum (infinite).

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

Maybe you could think of light as an interaction between 2 atoms, one sending and one receiving. The force between these atoms is strongest for the shortest distance and that's why the photon follows it. Just a way of visualizing it but I don't know of particular theory that says this.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

It seems relevant to stress that Fermat's principle is more correctly the principle of stationary time rather than least time.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.