MHB Fermats Principle: Find Time of Travel Along Path APB

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To find the time of travel along path APB for a ray of light reflecting at point P, one must apply Fermat's Principle, which states that light travels the path that requires the least time. The discussion emphasizes that the maximum travel time occurs at point P(0), located at the bottom of the hemisphere where theta equals zero. The law of reflection dictates that the angles of incidence and reflection are equal, influencing the path taken by the light. A diagram may aid in visualizing the scenario and clarifying the calculations involved. Understanding these principles is crucial for solving the problem effectively.
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How do I find the time of travel along a path say APB of tetha and show it's maximum at P= P(0) considering a ray of light traveling in a vacuum from A to B with reflection at P in the same vertical and as A and B, according to the law of reflection,the actual path goes via point P(0) at the bottom of the hemisphere (theta=0)
 
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onie mti said:
How do I find the time of travel along a path say APB of tetha and show it's maximum at P= P(0) considering a ray of light traveling in a vacuum from A to B with reflection at P in the same vertical and as A and B, according to the law of reflection,the actual path goes via point P(0) at the bottom of the hemisphere (theta=0)
May I be the first to say: Huh?

Is there a diagram to go with this or something? Details!

-Dan
 

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