Feynman's Vol 1 Lecture 26 Principle of Least Time (help with Figure)

In summary, the conversation revolves around the difficulty of proving that the two angles with "double arcs" in Figure 26-4 of The Feynman's Lectures are equal. The speaker seeks help in presenting the figure and the expert explains that while they are not exactly equal, they are smoothly equal in the limit of small changes in angle, which is sufficient for Feynman's least time argument. The speaker is relieved that they were unable to prove it.
  • #1
Sparky_
227
5
Hello,

Just for fun - I am trying to go through The Feynman’s Lectures: Lecture #26 – Volume 1: The Principle Of Least Time. I am stuck on Figure 26-4 and specifically showing the two angles with the “double arcs” are equal. The angle of reflection BCN’ and XCF.

Maybe I am just that rusty on my geometry – I have going through several pages of scribbles trying to show those two angles are equal with no luck.

Help??

Should a take a picture and attach it to this thread or ?? How can I present the figure?
Thanks

Sparky_
 

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  • #2
Sparky_ said:
Should a take a picture and attach it to this thread or ?? How can I present the figure?
Thanks
Yes please. Use the "Attach files" link below the Edit window to upload a JPEG or PDF file, or you should be able to do a copy-paste into the Edit window directly, as long as the little icons above the Edit window are not red (click the "[ ]" BB toggle button there to turn the icons black if they are red).
 
  • #3
Sparky_ said:
I am stuck on Figure 26-4 and specifically showing the two angles with the “double arcs” are equal. The angle of reflection BCN’ and XCF
They are not exactly equal, but they are smoothly equal in the limit of small changes in angle. That is all Feynman claims (see egn 26.3 et seq) and all he needs for his least time argument. Its good that you can't prove it!
 
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Related to Feynman's Vol 1 Lecture 26 Principle of Least Time (help with Figure)

1. What is Feynman's Vol 1 Lecture 26 Principle of Least Time?

Feynman's Vol 1 Lecture 26 Principle of Least Time is a fundamental principle in physics that states that a particle will follow the path that takes the least amount of time to reach its destination.

2. How does the Principle of Least Time relate to optics?

In optics, the Principle of Least Time explains how light travels through different mediums and is refracted at different angles. It states that light will take the path that requires the least amount of time to reach its destination, which is why it bends when passing through different mediums with varying densities.

3. Can you explain the figure used in Feynman's Vol 1 Lecture 26?

The figure used in Feynman's Vol 1 Lecture 26 is a diagram that illustrates the path of light through different mediums. It shows how light is refracted at the boundary between two mediums and how the path it takes is determined by the Principle of Least Time.

4. What is the significance of Feynman's Vol 1 Lecture 26 Principle of Least Time?

The Principle of Least Time is significant because it helps us understand the behavior of light and other particles in different mediums. It is also a fundamental principle in the study of optics and has many practical applications, such as in the design of lenses and mirrors.

5. How does the Principle of Least Time relate to Fermat's Principle?

Fermat's Principle is a more general version of the Principle of Least Time, which states that light will follow the path that takes the least amount of time or the path that maximizes its phase. The Principle of Least Time is a specific application of Fermat's Principle in the study of optics.

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