mvvdsteen
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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.
\vec{e}_r: vector towards centre of curvature
\vec{e}_s: vector in path direction
Deflection (1):
n \frac{\partial \vec{e}_s}{\partial s} = \frac{\partial n}{\partial r} \vec{e}_r
Acceleration (2):
\frac{\partial n}{\partial s} \vec{e}_s
Combining (adding (2) to both sides of (1))
\frac {\partial (n \cdot \vec{e}_s)}{\partial s}=\frac{\partial}{\partial s} (n \cdot \frac{\partial \vec{x}}{\partial s})=\nabla n
with \vec{x}=[x,y,z]^T
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?
\vec{e}_r: vector towards centre of curvature
\vec{e}_s: vector in path direction
Deflection (1):
n \frac{\partial \vec{e}_s}{\partial s} = \frac{\partial n}{\partial r} \vec{e}_r
Acceleration (2):
\frac{\partial n}{\partial s} \vec{e}_s
Combining (adding (2) to both sides of (1))
\frac {\partial (n \cdot \vec{e}_s)}{\partial s}=\frac{\partial}{\partial s} (n \cdot \frac{\partial \vec{x}}{\partial s})=\nabla n
with \vec{x}=[x,y,z]^T
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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