Solve Reflection & Refraction w/ Fermats Principle

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SUMMARY

The discussion focuses on applying Fermat's Principle to derive the formulas for reflection and refraction in ray tracing. Fermat's Principle states that the path taken by light between two points is the one that minimizes travel time. The user, Morten, seeks assistance in transitioning from this principle to the specific formulas for reflection and refraction. A suggestion is made to start with the reflection case, emphasizing the importance of diagramming the light path to visualize the concept effectively.

PREREQUISITES
  • Understanding of Fermat's Principle in optics
  • Basic knowledge of ray tracing techniques
  • Familiarity with the laws of reflection and refraction
  • Ability to create and interpret geometric diagrams
NEXT STEPS
  • Study the derivation of the law of reflection using Fermat's Principle
  • Explore Snell's Law for refraction and its mathematical formulation
  • Learn about geometric optics and its applications in ray tracing
  • Practice creating diagrams to visualize light paths in different media
USEFUL FOR

Students studying optics, physics enthusiasts, and anyone involved in ray tracing projects who seeks to understand the mathematical foundations of light behavior during reflection and refraction.

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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