- Snell S Law Theoretical Derivation You Will Derive Snell S Law Starting From Fermat S Principle Which States That The 1 (22.22 KiB) Viewed 26 times
- Snell S Law Theoretical Derivation You Will Derive Snell S Law Starting From Fermat S Principle Which States That The 2 (32.1 KiB) Viewed 26 times
Snell's law - theoretical derivation You will derive Snell's Law starting from Fermat's Principle, which states that the path the light takes when travelling between two points is the path that can be traversed in the least amount of time. 1. Write down an expression for the total time T required for the light to travel from the top left to the bottom right of Figure lb in terms of r. d. and D. Note that there should be two terms in your expression, each corresponding to for propagation along a straight line path in a medium. time distance speed
Normal 8 Reflected Ray Incident Ray Medium 1 (n) Medium 2 (12) 102 Refracted Ray D (b) Figure 1: (a) Schematic illustration of the Law of Reflection, 0₁ = 0₁, and the refractive behavior of light incident on a material interface where n₂>n₁. (b) The geometry used to derive Snell's Law of Refraction, ni sin(01) = n₂sin(02), based on Fermat's Principle of Least Time. 2. Now apply Fermat's Principle by minimizing the total time with respect to the path taken and show that this leads to Snell's Law. Hint: Set dT/dx = 0. Normal m