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

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

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!!!

===

Update:

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.

No vote yet

1 vote

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in`\(`

...`\)`

or`\[`

...`\]`

to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestRefraction of Light

Snell's Law

Log in to reply

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.

Log in to reply

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.

Log in to reply

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

Log in to reply

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

Log in to reply

Log in to reply