• Journal for History of Mathematics
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• v.19 no.1
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• pp.65-78
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• 2006

The law of refraction, which is called Snell's law in physics, has a significant meaning in mathematics history. After Snell empirically discovered the refraction law $\frac{v_1}{sin{\theta}_1}=\frac{v_2}{sin{\theta}_2$ through countless observations, many mathematicians endeavored to deduce it from the least time principle, and the need to surmount these difficulties was one of the driving forces behind the early development of calculus by Leibniz. Fermat solved it far advance of others by inventing a method that eventually led to the differential calculus. Historically, mathematics has developed in close connection with physics. Physics needs mathematics as an auxiliary discipline, but physics can also belong to the lived-through reality from which mathematics is provided with subject matters and suggestions. The refraction law is a suggestive example of interrelations between mathematical and physical theories. Freudenthal said that a purpose of mathematics education is to learn how to apply mathematics as well as to learn ready-made mathematics. I think that the refraction law could be a relevant content for this purpose. It is pedagogically sound to start in high school with a quasi-empirical approach to refraction. In college, mathematics and physics majors can study diverse mathematical proof including Fermat's original method in the context of discussing the phenomenon of refraction of light. This would be a ideal environment for such pursuit.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.2
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• pp.170-178
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• 2007

Most of parabolic approximation models employ a relatively limited open boundary condition in which there is no depth variation in the longshore direction outside of the computation domain so that Snell's law may be presumed to hold. Existing Kirby's condition belongs to this category and in the paper both modified Kirby's method and Dirichlet boundary condition are presented in detail and numerical results of three methods were shown. Judging from computation to wave propagations over a circular shoal in a constant depth, the method based on present Dirichlet boundary condition with fictitious numerical adjusting regions in both sides of the computation domain gives the least distorted amplitude ratio distribution.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2005.11a
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• pp.422-425
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• 2005

In an transversely isotropic composite laminates, the velocities, the particle directions and the amplitudes of reflected and transmitted waves were obtained using the equation of motion, the constitutive equation, and the displacement equation expressed by wave number and frequency Eigenvalue problem involving a velocity was solved by Snell's law. Finally, the results were confirmed by T300 Carbon fiber/5208 Epoxy materials. This approach could be applied to the detection of flaws in a transversely isotropic composite laminates by the water immersion C-scan procedure.

• Journal of the Korean Society of Propulsion Engineers
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• v.10 no.2
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• pp.62-69
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• 2006

In transversely isotropic composite laminates, the velocities, the particle directions and the amplitudes of reflected and transmitted waves were obtained using the equation of motion, the constitutive equation, and the displacement equation expressed by wave number and frequency. Eigenvalue problem involving a velocity was solved by Snell's law. Finally, the results were confirmed by 7300 Carbon fiber/5208 Epoxy materials. This approach could be applied to the detection of flaws in transversely isotropic composite laminates by the water immersion C-scan procedure.

• Korean Journal of Optics and Photonics
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• v.26 no.6
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• pp.299-305
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• 2015

Using Snell's Law without approximation, we analyzed focal points for parallel rays incident upon the cornea of a human eye. To calculate a ray's incident angle versus incident height for focusing on the same point, we used the ray reverse tracing method. We derived the theoretical conditions for an aspherical lens to remove the spherical aberration caused by a human eye. In this research, we held the rear surface of the lens to be spherical, for simple calculation, and calculated the lens curvature of the front surface to design an aspherical surface.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.24 no.9
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• pp.908-914
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• 2013

A shaped Cassegrain antenna is designed from the condition of the same path length at the equi-phase surface by using the conservation of energy and Snell's law. In order to improve the phase error efficiency of aperture surface, the surface profile of the main and sub-reflectors is found to satisfy the power distribution and the equi-phase condition at the aperture surface. The sidelobe levels of 36.4 dB and 33.9 dB are achieved at the AZ and EL planes, respectively from numerical calculation by physical optics method at Ku band and the directivity of designed antenna is 10 percent greater than that of conventional antenna.

• Proceedings of the Acoustical Society of Korea Conference
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• autumn
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• pp.303-306
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• 2000

복잡한 형상을 지닌 터빈 블래이드의 결함을 검사하기 위해 현재 $35^\circ,\; 38^\circ,\; 40^\circ$의 횡파 굴절각을 지닌 탐촉자를 사용하고 있다. 이와 같은 굴절각은 초음파 빔의 경로를 Snell의 법칙에 의해 설정하고 있다. 그러나 터빈 블래이드 검사용 초음파 탐촉자를 제작하는 과정에서 $35^\circ$의 횡파 굴절각을 갖는 경사각 탐촉자는 제작이 어려움을 알았다. 이러한 원인은 철강재료의 종파임계각이 $33.2^\circ$의 횡과굴절각에 대응되며, 종파임계각 근처에서는 전반사 현상 때문에 에너지 투과율이 매우 작아 실제 시험대상체에 입사되는 에너지가 거의 없으며 또한 횡파굴절각이 약 $37.5^\circ$ 일때에 휭파의 에너지 투과율이 최대가 되어 wedge를 $37.5^\circ$ 이하의 횡파굴절각을 갖도록 설계하더라도 측정을 하면 $37.5^\circ$ 근처의 횡파굴 절각을 갖게된다. 즉, 종파임계각 근처에서는 전반사 현상에 의해 경계면에서의 에너지 투과가 매우 작아 횡파 굴절각은 Snell의 법칙이 아닌 초음파 에너지의 투과 정도를 나타내는 echo transmittance의 크기에 의해 결정된다.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.3
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• pp.205-212
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• 2007

Parabolic approximation wave models based on $Pad{\acute{e}}$ approximants are analyzed in order to calculate wave transformation. In this study a $Pad{\acute{e}}(2,2)$ parabolic approximation model is developed to increase the accuracy of computation in comparison with the existing models. Numerical studies on a constant sloping bed show that the new model proves to allow for much more successful treatment of large angles of incidence than is possible using the previously available models.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.4
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• pp.375-384
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• 2007

Parabolic approximation wave models based on $Pad{\acute{e}}$ approximants are presented of which the $Pad{\acute{e}}$(15, 15) is shown to be applicable to incidence angle $80^{\circ}$ in comparison with the exact solution of a constant sloping bed. After introducing a systematic way of the derivation to the parabolic wave equation, parabolic models are obtained in this study upto the 15th order and several numerical results are given to wave transformation in a constant sloping bed.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.1950-1953
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• 2006

본 연구에서는 파랑의 방향에 따른 비대칭성을 고려한 방향 스펙트럼 식을 새로 제안하였다. 심해에서 생성된 다방향 불규칙 파랑이 등수심선에 대해 일정한 각도를 가지고 입사하는 경우, 각 방향의 파랑 성분의 굴절각의 차이에 의해 입사각에 대한 비대칭성이 발생하였다. 파랑의 굴절에 대해서는 Snell의 법칙을 이용하고 천수를 고려하여 해석적으로 계산하였으며, 이 결과와 새로 제안된 방향스펙트럼 식을 이용한 결과를 서로 비교하였다. 그 결과 비대칭성이 강한 천해역에서는 기존의 스펙트럼식에 비해 3배 이상 정확한 값을 재현하였다.