May I be the first to say: Huh?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)
Fermat's Principle is a principle in optics and physics that states that light will travel between two points along the path that takes the least amount of time.
In order to find the time of travel along a path, we must first determine the path that the light will take using Fermat's Principle. This is done by considering all possible paths and calculating the time it would take for light to travel along each path. The path that takes the least amount of time is the one that the light will take.
By using Fermat's Principle to find the time of travel along a path, we can determine the most efficient path for light to travel. This can be useful in various applications, such as designing optical systems or predicting the behavior of light in different mediums.
While Fermat's Principle is a useful tool for finding the time of travel along a path, it is based on the assumption that light travels in a straight line. In reality, light can be affected by factors such as refraction and reflection, which can alter the path it takes and the time it takes to travel.
Fermat's Principle is closely related to other principles in physics, such as the principle of least action and the principle of least time. These principles all share the idea that natural processes tend to occur in the most efficient way possible.