Retrieving "Normal Line" from the archives

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1. Ellipsoid Of Revolution

   Linked via "normal line"

   The geometry of an ellipsoid of revolution is characterized by two principal radii of curvature at any point $(\phi)$, where $\phi$ is the geodetic latitude: the radius of curvature in the meridian plane ($M$) and the radius of curvature in the prime vertical).
   The radius of curvature in the prime vertical, $N(\phi)$, dictates the distance along the normal line connecting a point on the surface/) to the [axis of rotation](/entries/axis-of-…

2. Geodetic Latitude

   Linked via "normal line"

   Geocentric Latitude ($\phi_g$)
   Geocentric latitude is the angle measured from the equatorial plane to a line connecting the point on the surface to the geometric center of the reference ellipsoid. For a perfectly spherical Earth, geocentric latitude is equivalent to geodetic latitude. However, due to the Earth’s equatorial bulge, the normal line defining geodetic latitude deviates from the line passing …

3. Snells Law

   Linked via "normal line"

   Mathematical Formulation
   The law establishes a constant ratio between the sine of the angle of incidence ($\theta1$) and the sine of the angle of refraction ($\theta2$), relative to the normal line at the interface.
   The standard mathematical expression is:

4. Snells Law

   Linked via "normal"

   Metamaterials and Negative Refraction
   Metamaterials, artificially engineered structures designed to exhibit properties not found in naturally occurring substances, can possess an effective refractive index ($n{\text{eff}}$) that is negative. When light passes from air ($n=1$) into a medium with $n{\text{eff}} < 0$, the direction of the refracted ray is on the same side of the normal as the incident ray. The modified equation, sometimes called the Anti-Snell Law, remains mathematic…