Does light have the ability to choose its path using Fermat's principle?

[spidey]

I read in feynman's lecture that all rays passing through the converging lens meet at the focal point since they all take the same least time because of the change in the velocity of light while passing through the lens..is there any mathematical proof for this...

 

[jtbell]

Suppose for the sake of argument that all the light rays do not take the same time to travel between the source point and the image point, and consider the waves that travel along those paths. The frequency of oscillation must remain the same everywhere, so the waves must have made different numbers of cycles when they reach the image point, therefore they must be out of phase with each other and interfere destructively.

If the waves all take the same time to reach the image point, they all make the same number of cycles, and interfere constructively.

 

[spidey]

oh thank you...here how light knows its destination? only if we know the source and destination then we can use fermat's principle and analyse whether light will reach destination or not? but how light decides a destination by using fermat's principle? does light also has ability to think about destination?