• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.19 no.2
• /
• pp.170-178
• /
• 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
• /
• 2005.11a
• /
• pp.422-425
• /
• 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
• /
• v.10 no.2
• /
• pp.62-69
• /
• 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.

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

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

• Earthquakes and Structures
• /
• v.9 no.1
• /
• pp.173-194
• /
• 2015

Site response analysis is an important topic in earthquake engineering. A time-domain numerical method called as one-dimensional (1D) finite element artificial boundary method is proposed to simulate the homogeneous plane elastic wave propagation in a layered half space subjected to the obliquely incident plane body wave. In this method, an exact artificial boundary condition combining the absorbing boundary condition with the inputting boundary condition is developed to model the wave absorption and input effects of the truncated half space under layer system. The spatially two-dimensional (2D) problem consisting of the layer system with the artificial boundary condition is transformed equivalently into a 1D one along the vertical direction according to Snell's law. The resulting 1D problem is solved by the finite element method with a new explicit time integration algorithm. The 1D finite element artificial boundary method is verified by analyzing two engineering sites in time domain and by comparing with the frequency-domain transfer matrix method with fast Fourier transform.

• Journal of Institute of Control, Robotics and Systems
• /
• v.14 no.4
• /
• pp.353-360
• /
• 2008

The LGP with nanometer structures resulted in enhancement of optical efficiency. Its fundamental mechanism is to recycle the polarized light via one round-trip through QWP(Quarter-Wave Plate) but the maximum efficiency to reach with this method is limited up to 2. To get the larger efficiency than this limited one a LGP with nanometer-patterned grating is suggested. For its optimum design the computer simulation is performed and suggests a grating that the spatial frequency between adjacent patterns is 500nm, its height 250nm, duty cycle 50%, and its cross section is rectangular. On the basis of simulation results the LGP with nanometer-patterned grating is fabricated and its optical properties such as angular intensity distribution and CIE color coordinates are characterized. The angles of transmitted light are nearly the same as the results expected from the generalized Snell's law. Thus the Mathematica code, developed in this experiment, will be applied to designing the optimized LGP. The LGP with nanometer-patterened grating shows the enhancement of transmitted intensity distribution up to 4.9 times.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 1997.04a
• /
• pp.121-129
• /
• 1997

Wave propagation was studied for an unidirectionally reinforced composite materials. The velocities, the particle directions and the amplitudes of reflected and transmitted waves were obtained. This analysis involves an immersion C-scan procedure. Snell's law was modified to get the velocities of waves. This analysis could be applied to the detection of flaws in a transversely isotropic composite motor case.

• Journal of Biomedical Engineering Research
• /
• v.2 no.2
• /
• pp.141-144
• /
• 1981

This paper descirbes about effects of refraction of ultrasonic beam on B-mode tomogram. Both compution based on Snell's law and the experiments performed using B-mode scanner and schlieren optical method are discussed on a circular phantom immersed in water. In these results, if the discrepancy of sound velocity is more than 0. 6%, the distortion of the B-mode image becomes conspicuous and a target beyound the phantom may disappear or displayed as two targets depending on the velocity of the phantom.

• Journal of the Korean Vacuum Society
• /
• v.12 no.S1
• /
• pp.15-16
• /
• 2003

3-D photonic band-gap structures are fabricated from dielectric colloidal polystyrene beads through a centrifuge method. The fabricated photonic crystals exhibit opalescent colors under white light and show a clear diffraction peak dependent on the incident angle of the light beam. Also the scanning electron microscope image was taken to verify the face-centered cubic crystal structure. Bragg's law and Snell's law are employed to describe the position of angle resolved diffraction peaks. It was shown that the optically deduced effective refractive index and lattice constants were in good agreement with the crystal structure identified by scanning electron microscope.