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  2. Snell's law - Wikipedia

    en.wikipedia.org/wiki/Snell's_law

    Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, [1] and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.

  3. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    Joseph-Louis Lagrange was influenced by Euler's work to contribute significantly to the theory. After Euler saw the 1755 work of the 19-year-old Lagrange, Euler dropped his own partly geometric approach in favor of Lagrange's purely analytic approach and renamed the subject the calculus of variations in his 1756 lecture Elementa Calculi ...

  4. Snell's window - Wikipedia

    en.wikipedia.org/wiki/Snell's_window

    Snell's window (also called Snell's circle [1] or optical man-hole [2]) is a phenomenon by which an underwater viewer sees everything above the surface through a cone of light of width of about 96 degrees. [3] This phenomenon is caused by refraction of light entering water, and is governed by Snell's Law. [4]

  5. Refraction - Wikipedia

    en.wikipedia.org/wiki/Refraction

    This is the law of refraction or Snell's law and can be written as [6] sin ⁡ θ 1 sin ⁡ θ 2 = v 1 v 2 . {\displaystyle {\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}\,.} The phenomenon of refraction can in a more fundamental way be derived from the 2 or 3-dimensional wave equation .

  6. Seismic refraction - Wikipedia

    en.wikipedia.org/wiki/Seismic_refraction

    Seismic refraction is a geophysical principle governed by Snell's Law of refraction. The seismic refraction method utilizes the refraction of seismic waves by rock or soil layers to characterize the subsurface geologic conditions and geologic structure.

  7. Ibn Sahl (mathematician) - Wikipedia

    en.wikipedia.org/wiki/Ibn_Sahl_(mathematician)

    If the ratio of lengths / is kept equal to / then the rays satisfy the law of sines, or Snell's law. The inner hypotenuse of the right-angled triangle shows the path of an incident ray and the outer hypotenuse shows an extension of the path of the refracted ray if the incident ray met a change of medium whose face is vertical at the point where ...

  8. Numerical aperture - Wikipedia

    en.wikipedia.org/wiki/Numerical_aperture

    Due to Snell's law, the numerical aperture remains the same: NA = n 1 sin θ 1 = n 2 sin θ 2. In optics , the numerical aperture ( NA ) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.

  9. Fermat's principle - Wikipedia

    en.wikipedia.org/wiki/Fermat's_principle

    If we seek the required value of x, we find that the angles α and β satisfy Snell's law. Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. Fermat's principle states that the path taken by a ray between two given points is the path that can be traveled in the least time.