During the lecture you mentioned that the minimum distance path may not always be a straight line for example while tracing a ray of light in a volume with different refractive indexes. Can you point me to a resource which explains some non-straight line minimum path being used practically? I was very intrigued by the idea.
Tdog
@A-star The Brachistochrone problem is a problem where we have a ball at height h above and some horizontal distance x away from the goal. What path would we draw from the ball to the goal to get it there as quickly as possible? Turns out that a straight line isn't the fastest solution. If we have the path dip quickly at the start, the ball will gain a lot of speed early on and reach the goal faster. Google Brachistochrone curve to see the path I'm talking about.
As for light in a volume with different refractive indexes, I'd suggest reading the indirect method described here: https://en.wikipedia.org/wiki/Brachistochrone_curve.
During the lecture you mentioned that the minimum distance path may not always be a straight line for example while tracing a ray of light in a volume with different refractive indexes. Can you point me to a resource which explains some non-straight line minimum path being used practically? I was very intrigued by the idea.
@A-star The Brachistochrone problem is a problem where we have a ball at height h above and some horizontal distance x away from the goal. What path would we draw from the ball to the goal to get it there as quickly as possible? Turns out that a straight line isn't the fastest solution. If we have the path dip quickly at the start, the ball will gain a lot of speed early on and reach the goal faster. Google Brachistochrone curve to see the path I'm talking about.
As for light in a volume with different refractive indexes, I'd suggest reading the indirect method described here: https://en.wikipedia.org/wiki/Brachistochrone_curve.