Proof of Fermat's principle of least time?

Thread starter Nick Jackson
Start date Aug 16, 2014
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Fermat's principle Principle Proof Time

In summary, Fermat's principle of least time is a fundamental law of optics that states light travels along the path that takes the shortest amount of time. It was proven by French mathematician Pierre de Fermat using the principle of least action. This principle is significant in explaining the behavior of light and is applicable to all types of light and other waves. It can also be observed in everyday life, such as in the reflection of objects in mirrors and the bending of a straw in water.

Aug 16, 2014

Nick Jackson

I've been looking for this proof for months but I wasn't able to find something...

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Aug 17, 2014

Simon Bridge

Science Advisor

Homework Helper

It is not something that you prove. It is (part of) a Law of Nature.
You can derive it from Huygen's principle, and it follows from the Variation principle in classical mechanics.

Related to Proof of Fermat's principle of least time?

1. What is Fermat's principle of least time?

Fermat's principle of least time is a fundamental law of optics that states that light travels from one point to another along the path that takes the shortest amount of time.

2. How was Fermat's principle of least time proven?

Fermat's principle of least time was proven mathematically by French mathematician Pierre de Fermat in the 17th century. He used the principle of least action, which states that a system will always take the path of least resistance, to derive the principle of least time.

3. What is the significance of Fermat's principle of least time?

Fermat's principle of least time is significant because it explains the behavior of light and other wave phenomena. It is also a crucial principle in the study of optics and is used to derive many important laws and equations.

4. Is Fermat's principle of least time applicable to all types of light?

Yes, Fermat's principle of least time applies to all types of light, including visible light, infrared light, and ultraviolet light. It also applies to other types of waves, such as sound waves and water waves.

5. Can Fermat's principle of least time be observed in everyday life?

Yes, you can observe Fermat's principle of least time in everyday life. For example, when you see the reflection of an object in a mirror, it is because light travels from the object to the mirror and then to your eyes, taking the path of least time. This principle also explains why a straw appears bent when placed in a glass of water.