Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

I have been given this formula from optics here, with no background: $$\vec\nabla{n} = \frac{d(n\hat{u})}{ds}$$

Where $n$ is the refractive index and $\hat{u}$ is a unit vector tangent to the path $s$ that light takes inside a medium.

Does anyone know if this formula has a name? I am looking specifically for a derivation of it. I have looked through the optics book by Hecht with no luck - I assume it comes from fermats principle of least time in some form.

Any help greatly appreciated.

share|improve this question

1 Answer 1

up vote 6 down vote accepted

This equation is called the ray equation and it can indeed be derived from Fermat's principle. I guess you can find more about its derivation in, e.g., Born and Wolf's Principles of optics or in Fundamentals of Photonics by Saleh and Teich.

share|improve this answer
    
Perfect, thanks! –  nmoy Nov 8 '12 at 15:11

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.