Fermat's Principle: Proving Law of Reflection

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In summary, Fermat's principle states that light rays traveling between two points will take the least time when compared to nearby paths. It follows that the law of reflection can be derived from this principle, as demonstrated in a proof that utilizes triangle symmetry.
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etothey
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Homework Statement


Fermat’s principle states that the path of a light ray between two points is such that the time to traverse that path is an extremum (either a minimum or a maximum) when compared with the times for nearby paths. Consider two points A and B on the same side of a reflecting surface, and show that a light ray traveling from A to B via a point on the reflecting surface will take the least time if its path obeys the law of reflection. Thus, the law of reflection follows from Fermat’s principle.

Homework Equations



Triangle symmetry

The Attempt at a Solution


would this be a reasonable proof without involving to much maths? http://www.math.uiowa.edu/~stroyan/CTLC3rdEd/ProjectsOldCD/estroyan/cd/27/index.htm
 
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  • #2
looks a good enough way to prove it.
 

1. What is Fermat's Principle?

Fermat's Principle is a principle in optics that states that the path taken by a ray of light between two points is the path that can be traversed in the least amount of time.

2. How does Fermat's Principle relate to the law of reflection?

Fermat's Principle can be used to prove the law of reflection, which states that the angle of incidence is equal to the angle of reflection.

3. How is Fermat's Principle used to prove the law of reflection?

Fermat's Principle is used to prove the law of reflection by showing that the path taken by a ray of light between two points is the one that can be traversed in the least amount of time, and this path is the one that follows the law of reflection.

4. What are some real-world applications of Fermat's Principle?

Fermat's Principle has applications in various fields, including optics, astronomy, and radar technology. It is used to explain the behavior of light in different mediums and to design optical systems such as lenses, mirrors, and prisms.

5. Are there any limitations to Fermat's Principle?

While Fermat's Principle is a useful tool for understanding the behavior of light, it is not a perfect model and has some limitations. For example, it does not account for diffraction effects, and it assumes that light always travels in a straight line. Additionally, it does not take into account the effects of quantum mechanics.

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