How light travels: on Fermat's principle of least time

Hello everyone!

Does anyone else find this statement spooky and questionable like I do?

"Light takes the path between two points that takes the least time"

It looks like it's somehow related to Fermat's principle, but it doesn't quite make sense to me. Doesn't light travel in the direction you point it? (assuming you are sending out light with a laser)

Consider the quiz below:

The explanation to this quiz almost sounds like "even if you pointed the light in direction B, it would bend itself into path A as if it knew it would take less time". But that's not what will happen in reality, no?

In my imagination (informed by some faded shadows of high school physics), if you use a flashlight that radiates light rays in all directions, these light rays will arrive at the water surface at different points, then each light ray will bend itself at a certain angle depending on how it meets the water, and finally travel through water towards the bottom of the pond. And the light ray that happens to travel through path A, will luckily reach the ball. If you were to use a laser, however, it will reach the ball only if you send it on the right path (that is, path A).

And maybe it is not because it takes the least time that light bends the way it does in path A. For some other mysterious reasons, it just bends like that, and when we do the math in hindsight, it turns out to be the fastest of all possible routes from the flashlight to the ball.

Does my attempt to make sense of the puzzle make sense to you? What are your thoughts on this quiz and on Fermat's principle? Would love to hear from you!! And I'd appreciate it if you could share some resources and point me in the right direction :)

Thanks and happy learning!!!



I should mention that I am ok with the "correct answer" being A, but have doubts about the way it was explained, because it sounds like "light will take path A because it takes the least time", and that doesn't make sense.

AND "correct answers" are boring! Many years ago, I learned about how light bends when entering a different medium and I never questioned it, but this quiz got me wondering why it bends the perfect angle that it does, as if it was intelligent.

Note by Maggie Gong
6 months, 2 weeks ago

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I will try my best to rephrase the problem.

If a ray of light travels from the source (flashlight) and reaches the object (ball) that is underwater, what will the path of the ray (if you trace it) look like?

Option (B)- The path is a straight line from the flashlight to the ball.

Option(A)- Not a straight line but the ray of light travels more distance in air than in water.

Option(C)- Not a straight line but the ray of light travels more distance in water than in air.

Sathvik Acharya - 6 months, 2 weeks ago

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Hi Maggie,

This question intends to ask about the light that does ultimately reach the ball from the flashlight. The beam of light that reaches the flashlight will take path A, not path B or C.

The first parts of paths B and C (that is, the part connecting the flashlight to the water's surface) are allowed, but those initial paths would not lead to the ball. The light on the initial part of path B would bend downward at the interface, and hit the bottom of the lake left of the ball. The light on the initial part of path C would essentially continue straight downwards, so it would end up very far from the ball.

In the future, if you have concerns about a problem's (or explanation's) wording/clarity/etc., you can also report the problem. See how here.

Lee Weinstein Staff - 6 months, 2 weeks ago

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From what I understand of the Fermats principle is for light to travel from one point to another, there are infinitely many possible paths but only one is chosen, the chosen one has least time of travel

When you point a laser the light could have come out bent backwards/ right / left did all kinds of stunts and then hit the intended target ( maybe a piece of paper ) but the path which takes least time is the straight line path and hence it only chooses that

In refraction it could have chosen path B and C and then hit the red dot but path A has least time of travel and that’s why only path A is taken when the light hits the red dot, light from path B will never hit the red dot

Jason Gomez - 5 months, 3 weeks ago

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If you do want a reason why light bends on refraction, you can learn this from the wave theory of light, in an effort to keep frequency constant the light bends as the speed of medium changed abruptly

Idk how to do animations and it’s best seen visually

Jason Gomez - 5 months, 3 weeks ago

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Jason Gomez - 5 months, 3 weeks ago

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