For a course in Experimental Aerdynamics I have to study a section on Optical Measurement Techniques. My oral exam is coming up and there is this little thing I don't understand. It annoys me expremely. It is the ray equation. It is about light ray path in a medium with changing refractive index. I will copy what's in the lecture notes, and maybe someone will know the derivation of this formulae.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\vec{e}_r[/tex]: vector towards centre of curvature

[tex]\vec{e}_s[/tex]: vector in path direction

Deflection (1):

[tex] n \frac{\partial \vec{e}_s}{\partial s} = \frac{\partial n}{\partial r} \vec{e}_r [/tex]

Acceleration (2):

[tex]\frac{\partial n}{\partial s} \vec{e}_s [/tex]

Combining (adding (2) to both sides of (1))

[tex]\frac {\partial (n \cdot \vec{e}_s)}{\partial s}=\frac{\partial}{\partial s} (n \cdot \frac{\partial \vec{x}}{\partial s})=\nabla n [/tex]

with [tex]\vec{x}=[x,y,z]^T[/tex]

Can somebody help me out by giving the derivation or a link to a page that contains it?

Kind regards,

Maciej

PS: So you can't let the tex automatically span more lines?

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# Homework Help: Light ray equation: derivation?

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