Calculus 1: Max-Min Problems (29 of 30) Prove Fermat's Principle and Reflection

In this video I will show Fermat's principle and reflection of theta1=thata2 that light takes the path of least time (shortest path).

Next video in this series can be seen at:

[valeriereid]

You are the best! Thanks for making this so easy to understand.

[danastits]

Thanks, but one suggestion. Employing the quadradic equation unduly complicates things. Instead, just move the terms with a b^2 to one side, factor out the b^2, divide both sides by the remainder, take the square root of both sides, cross-multiple, divide both sides by b, multiple both sides by 1/a, and viola. Also, please accept my PayPal contribution toward the purchase of a vertical sliding whiteboard. Thanks again.

[seamusobric]

that is legendary @Michel van Biezen, and i dont mean Fermats Theorem, i mean your working through the proof in a clear and concise way, thank you so much, beauty in maths!

[ahmedal-ebrashy]

Loved it but it was. HANDFUL!. Appreciate your efforts very much both of you.

[mankienkueth]

This is so wonderful way and you relive my stress but the video is not clear to be seen, so anyway try to improve my dear.

[catherinewu]

Thank you so much! Your videos are so helpful!

[urizung]

can you a video on which you'll how it is possible to get the laws of Newton with the Hamilton principle?

[urizung]

it is also possible to make a similar video to get the Snell law, I've seen a review of it on maa

[amnishvachher]

Sir does the ray only take a path with least time or can it correspond with path with max time

[fhgfggfrg]

What if you take the other answer given by the quadratic? Then theta 1 is not equal to theta 2!

[lambda]

Only problem is that it’s not true. Read Feynman’s book QED page 43.