Solve Reflection & Refraction w/ Fermats Principle

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Fermat's principle states that light travels the path that minimizes travel time, which can be applied to derive formulas for reflection and refraction. To solve for reflection, one should visualize the light path from the source to the mirror and then to the destination, ensuring that the total distance is minimized. For refraction, the principle can be used alongside Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the two media. Drawing diagrams can aid in understanding the geometric relationships involved in both phenomena. Engaging with these visual aids and mathematical relationships will clarify the application of Fermat's principle in ray tracing.
Morten1988
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Hey
I am working on a project about Ray tracing and I find myself stuck on 1 of the 5 questions my teacher has made.

Homework Statement


Explain how you can use Fermats principle to solve the formula of reflection and refraction.

Homework Equations


I do not now how I am going get from Fermats principle to a formula for reflection and refraction.

The Attempt at a Solution


I now that Fermats principle is: The path of a ray of light between two points is the path that minimizes the travel time.

I also know that the formula of refraction is:
Se picture

Now I can't get any father :confused:

Hope you can help me out a bit.
Regards
Morten

(sorry about my bad English but I am not native)
 

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Start with the reflection case, which is easier.

Draw a diagram for reflection light from one pt to another, and just think of what you have to prove to show that light travels the least distance from the 1st point to the other after touching the mirror. Write whatever comes to your mind.
 

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