The nature of light has always intrigued humanity. Among the texts of ancient Greeks that have survived to our days, there are frequent mentions of light and its nature. The first known book on optics is attributed to Euclid in the 3rd century BCE. The phenomenon of refraction, although known for millennia, resisted a mathematical explanation until the modern age. W. Snellius (Snell) was the first to present the correct equation that related the angles of incidence, refraction, and the speeds of light in each medium during refraction, but he did not publish his results. The publication was made by René Descartes. This result is now known as Snell-Descartes’ law or the law of refraction. Descartes treated light as a particle in his deduction. Huygens, in the 17th century, also deduced this law but treated light as a wave. These results differed in terms of the speed of light in more refractive media. The measurement of speed became possible only in the 18th century and corroborated Huygens’ result, indicating the wave nature of light. Interestingly, in 1905, Einstein explained the photoelectric effect by treating light as a particle (quantum of light). But if light also exhibits corpuscular behavior, shouldn’t it be possible to derive Snell-Descartes’ law by treating it this way? In this work, we will demonstrate that it is possible to derive this law from the corpuscular hypothesis of light. Besides its strong didactic appeal, the work engages in an interesting discussion of the current understanding of science regarding the nature of light. humanity days rd BCE refraction millennia age W Snell (Snell incidence SnellDescartes Snell-Descartes deduction Huygens th media Interestingly 1905 quantum . light) behavior shouldnt shouldn t way appeal 190 19 1

A natureza da luz sempre intrigou a humanidade. Entre os textos dos antigos gregos que sobreviveram até nossos dias, é frequente menções sobre a luz e sua natureza. O primeiro livro conhecido sobre óptica é atribuído a Euclides no século III a.C. O fenômeno da refração, embora conhecido há milênios, resistiu a uma explicação matemática até a idade moderna. W. Snellius (Snell) foi o primeiro a apresentar a equação correta que relacionasse os ângulos de incidência, refração e velocidades da luz em cada meio em uma refração, mas não publicou seus resultados. A publicação foi feita por René Descartes. Esse resultado é conhecido hoje como lei de Snell-Descartes ou lei da refração. Descartes tratou a luz como partícula em sua dedução. Huygens, no século XVII, também deduziu essa lei, mas tratando a luz como onda. Esses resultados diferiam quanto à velocidade da luz em meios mais refringentes. A medida da velocidade só foi possível no século XIX e corroborou o resultado de Huygens indicando a natureza ondulatória da luz. O interessante é que Einstein, em 1905, explica o efeito fotoelétrico tratando a luz como partícula (quantum de energia). Mas se a luz possui também um comportamento corpuscular, não deveria ser possível obter a lei de Snell-Descartes tratando-a dessa forma? Nesse trabalho, mostraremos que é possível obter essa lei partindo da hipótese corpuscular da luz. Além do forte apelo didático, o trabalho faz uma interessante discussão sobre a história do entendimento atual da ciência sobre a natureza da luz. humanidade dias aC C a.C milênios moderna W Snell (Snell incidência SnellDescartes dedução XVII onda refringentes Einstein 1905 quantum energia. energia . energia) tratandoa forma didático 190 19 1

Abstract The main coal reserves in Brazil are located in the southern region, where the most important coalfield, including the Candiota mine, is found. The mineral exploration and mine planning programs of the companies mining these coal deposits are generally restricted to drilling data and cores, despite the exploratory potential of geophysical methods in coal prospecting. This study aims to investigate the ability of the seismic method known as Multichannel Analysis of Surface Waves (MASW) to identify coal seams in the Candiota area. The MASW method allows obtaining a layer model composed of a low-velocity (blind) layer and/or relatively thin (hidden) layer from the surface wave dispersion curves. The hidden and blind layer problems are pitfalls of the traditional seismic refraction method and the geological settings related to coal seams may encompass both problems. In addition, the Candiota mine has conditions favorable for applying the MASW method due to the shallow depths of the coal seams. The study was based on the analysis of synthetic seismic data generated from a 3-layer conceptual model of the Candiota deposit. The dispersion curves of the fundamental mode of the Rayleigh surface waves were generated and the effects of each of the parameters of the seismic model were evaluated, as well as the relationship between the parameters through objective function tests. A new inversion algorithm capable of obtaining the true model was implemented. The results obtained from the application of the inversion algorithm demonstrated the potential of the MASW method in identifying coal seams from S-wave profiles and proves it to be a powerful tool for coal mineral exploration programs. region coalfield found cores prospecting (MASW area lowvelocity low velocity (blind andor or (hidden addition 3layer 3 deposit evaluated tests implemented Swave S

Abstract Processes on atolls and coral reef lagoons are defined by local wave and tide climates. Based on the reconstruction of lagoon wave climate by downscaling offshore historical wave information, this study aims to assess the wave climate and wave extremes on a mesotidal atoll lagoon (Rocas Atoll, Brazil). Results show that the transformation of offshore waves, when propagating into the lagoon, results in a different and far more homogeneous wave climate. Atoll morphology and tides play a key role in controlling the directional and energy characteristics of the lagoon wave climate. Refraction processes and the reef passage make the side protected from the dominant SE waves the most energetic zone for lagoon wave propagation. Lagoon waves tend to propagate in opposite directions to offshore wind waves, showing the refraction effect of approaching waves when crossing the atoll rim and the channel. The tidal effect on the dissipation process is also a filter for extreme wave conditions. We highlight the dependence of the resulting lagoon wave climate on atoll morphology, thereby addressing its implications to geomorphological process inside the atoll.

RESUMEN En este trabajo se realizaron sondeos sísmicos superficiales como la refracción sísmica, el Análisis Multicanal de Ondas Superficiales (MASW, del inglés Multichannel Analysis of Surface Waves), la refracción de microtemblores (ReMi, del inglés Refraction Microtremor), y la medición de microtemblores para una caracterización en 26 estaciones de registros sísmicos de la AFAD (Autoridad para la Administración de Desastres y Emergencias) en la provincia de Hatay, que está situada en una de las regiones sísmicamente más activas del sur de Turquía. Se aplicó la técnica de Relación Espectral Horizontal a Vertical con un espectro Fourier regular derivado de una serie de larga duración para determinar los valores de frecuencia dominante a diferentes niveles de amplificación. La velocidad de la onda de corte por encima de los 30 metros de profundidad se detectó a través de la técnica MASW. El análisis ReMi por encima de los 80 metros se logró con una media correspondiente de 650 m/s en la velocidad de la onda de corte. Las velocidades en las ondas de corte alcanzadas por el método MASW se compararon con aquellas de la técnica ReMi, y se observó que son muy compatibles. La provincia de Hatay fue clasificada de acuerdo con la norma NEHRP con base en Vs30, Eurocode-8, la entidad de regulación sísmica de Turquía (TBDY-2018), y Rodríguez-Marek et al. (2001). Se determinó la velocidad de la onda de corte (VS30), la amplitud del pico de la relación Horizontal a Vertical (H/V), el período dominante, y el tipo de cada sitio analizado. Las amplitudes del pico en las relaciones H/V están entre 1.9 y 7.6, mientras que los períodos predominantes varían entre 0.23 segundos y 2.94 segundos en el área de estudio. Estos resultados se investigaron para explicar la consistencia de los esquemas de clasificación de sitios.

ABSTRACT In this study, shallow seismic surveys, including seismic refraction, Multichannel Analysis of Surface Waves (MASW), Refraction Microtremor (ReMi), and Microtremor measurements were conducted to estimate site characterization at 26 strong-motion stations of AFAD (Disaster and Emergency Management Presidency) in the province of Hatay, situated in one of the most seismically active regions in southern Turkey. The Horizontal to vertical spectral ratio (HVSR) technique was applied, using smoothed Fourier spectra derived from a long duration series to determine dominant frequency values at different amplification levels. Shear wave velocity up to 30 m of the ground was detected with MASW analysis. In the ReMi analysis, up to 80 m was reached with a corresponding average of 650 m/s shear wave velocity. The shear wave velocities estimated by the MASW method up to 30 m were compared with those found by the ReMi method, and they were observed to be very compatible. The province of Hatay was classified according to Vs30 based NEHRP Provisions, Eurocode-8, the Turkish Building Earthquake Regulation (TBDY-2018), and Rodriguez-Marek et al. (2001). The shear-wave velocity (Vs30), Horizontal to Vertical ratio’s (H/V) peak amplitude, dominant period, and site class of each site were determined. The H/V peak amplitudes range between 1.9 and 7.6 while the predominant periods vary from 0.23 sec to 2.94sec in the study area. These results are investigated in order to explain the consistency of site classification schemes.

Resumen En la presente investigación se aplicaron técnicas geofísicas y geotécnicas para caracterizar el subsuelo a la altura del Km 68+500 del municipio de Pamplona, definir la resistividad eléctrica, velocidad sísmica tipo P y S, parámetros dinámicos del suelo, tipo de perfil de suelo y curva de espectro de aceleración mediante la NSR10 título A, llevando a cabo dos fases: una de campo, donde se realizó levantamiento topográfico, dos (2) ensayos de SPT, cuatro (4) de SEV, dos (2) líneas de TRS, dos (2) de MASW 1D y 2D; y la fase de procesamiento de datos para generar imágenes 2D del perfil, interpretar y correlacionar, dando como resultados, velocidades de onda P entre 499m/s y 1714m/s, velocidades de onda S entre 210m/s y 466m/s y resistividades entre 6.06 Ω-m y 581.05 Ω-m., perfiles de suelo Tipo D, compuestos de materiales rígidos, arenas con presencia de arcilla y arcilla limosa saturada.

Abstract In the present investigation, geophysical and geotechnical techniques were applied to characterize the subsoil at the height of Km 68 + 500 in the municipality of Pamplona, define the electrical resistivity, seismic velocity type P and S, dynamic parameters of the soil, type of soil profile and acceleration spectrum curve using NSR10 title A, carrying out two phases: one in the field, where topographic survey was performed, two (2) SPT tests, four (4) SEV, two (2) TRS lines, two (2) of MASW 1D and 2D; and the data processing phase to generate 2D images of the profile, interpret and correlate, resulting in P wave velocities between 499m / s and 1714m / s, S wave velocities between 210m / s and 466m / s and resistivities between 6.06 Ω -m and 581.05 Ω-m., Type D soil profiles composed of rigid materials, sands with the presence of clay and saturated silty clay.

Abstract Electromagnetic (EM) waves do not travel in straight lines in the troposphere due to refraction. This leads to errors in many engineering applications. In order to correct these errors, a numerical solution based on the difference method has been proposed, which can reveal the degree of EM wave bending owing to atmospheric refraction, moreover, it can predict the actual path of the EM wave propagating in the troposphere. The error of the numerical method is studied here, which reveals the source of the error. Based on this, two improvement methods are proposed. The computational accuracy of the numerical methods is verified by comparison with the analytical solution. The proposed method ensures the computational efficiency and accuracy of the problem of refraction of EM waves in the troposphere.

Abstract We study the lateral displacement (Goos-Hänchen effect) of a Hermite-Gaussian beam incident on a dielectric interface of lower index of refraction than the incident media. Unlike previous results on the same subject, the present result can be applied to an infinite family of higher order solutions (or modes) of the Huygens-Fresnel integral. The final theoretical expression is valid for values that are close to the critical angle θ c. Discussion is made for the behavior of the lateral displacement for different modes of the Hermite-Gaussian beam.

Abstract In this work a Finite-Difference Frequency-Domain (FDFD) propagation method for complex urban environments is proposed. The formulation starts from the discretization of the Helmholtz equation for the magnetic field instead of the usual separate one order derivative Ampere's and Faraday's laws. The Stretched Coordinate Perfectly Matched Layer (SCPML) is used as an absorbing boundary condition. These procedures produce less field components to estimate and achieve high wave absorption at the computation domain boundaries. The main goal is the rigorous prediction of VHF/SHF signals in real urban scenarios through the evaluation of several propagation mechanisms: direct rays, diffraction, reflection and refraction effects. The method is validated through an analytic problem and preliminary results are generated by two case studies: a cellular system measurement campaign and an idealized urban scenario.

Resumen La sísmica de refracción es un método de geofísica de prospección, que estudia las respuestas del terreno cuando se propaga a través de él una onda de compresión (onda P) producida por medios mecánicos en la superficie. El parámetro físico que se utiliza es la velocidad de propagación de la onda Vp que viaja a través de los materiales del subsuelo en función de la densidad del mismo. Tal parámetro aportará información de las características geomecanicas de la zona en la que se aplican. Los índices medidos mantienen correlaciones con la naturaleza geológica de los diversos horizontes, pudiéndose aún conocer sus respectivas profundidades y espesores. Este trabajo tiene como objectivo presentar un procedimiento para la representación de los parámetros geotécnicos, estimados por el método de refracción sísmica. Las velocidades longitudinales son obtenidas y se correlacionan con los valores de la resistencia a la penetración estandar (N) calculados por los ensayos homónimos de SPT. Los parámetros dinámicos se presentan en secciones 2D para conseguir una mejor representación e interpretación, siendo capaz de caracterizar continuamente todo el área desde el punto de vista geotécnico. El área de estudio está localizada en los suelos areno - limo - arcillosos de la ciudad de Luanda (Angola).

Abstract Seismic refraction is a prospecting geophysical method, which measures the terrain response in reaction to a P compression wave, mechanically produced at the surface and propagating across. The physical parameter in use, in the case, is the wave propagation velocity, Vp, which travel across the subsurface rock material and reflects to the surface in function of the material’s density it finds on its way down. That way, indexes associated to the parameter will measure and reveal the geomechanic characteristics of the terrain under study. Those indexes, whilst keeping some correlations with the geological nature of the rock in different horizons, allow to infer also their depths and thickness. The present study has the scope of showing a methodology to map geotechnical parameters using seismic reflection, and it has been noticed that the longitudinal velocities also computed are correlated with penetration resistance values, measured by Standard Penetration Tests (SPT). The dynamic parameters were chosen to be presented in 2D maps, in order to give either, a better representation of their characteristics, as well to allow for a continuous geotechnical interpretation over the entire area of study. The latter, is an area of silty/sandy soils located in the city of Luanda (Angola).

The use of the surface wave’s analysis in its passive and active variants was jointly assessed by the shallow seismic refraction. It allows determining dynamic parameters from the longitudinal and transverse velocities, obtained from seismic methods. For the first time, based on the performance of seismic wave velocities, the soils of Luanda city in Angola are characterized and it is demonstrated that a group of seismic methods formed with the multichannel analysis of surface waves and the shallow seismic refraction in its variant 2D MASW, allows greater continuity in the geotechnical characterization of soils.

Se evaluó el uso del análisis de ondas superficiales en sus variantes activa y pasiva que, conjuntamente con la sísmica de refracción somera, permite determinar parámetros dinámicos a partir de las velocidades transversales y longitudinales obtenidas de los métodos sísmicos. Por primera vez, a partir del comportamiento de las velocidades de las ondas sísmicas, se logra caracterizar los suelos de Luanda, y se demuestra que un complejo de métodos sísmico conformado con la sísmica de refracción somera y el análisis multicanal de ondas superficiales en su variante 2D MASW permite obtener mayor continuidad en la caracterización geotécnica de los suelos.

Abstract We report results of the first principles calculations of structural, electronic and optical properties of SrF2 under pressure, performed using full-potential linearized augmented plane wave (FP-LAPW) method based on density functional theory as implemented on WIEN2k code. The exchange-correlation energy functional has been treated with generalised gradient approximation (GGA) for structural optimization, while the Tran-Blaha modifed Becke-Johnson potential (TB-mBJ) has been employed for electronic and optical calculations. Our results show that the first transition from Fm 3 ¯m to Pnam structure occurs at 5.8 GPa and the second transformation from Pnam to P63/mmc structure takes place at 24.8 GPa. Our electronic calculation indicates an indirect gap X- Γ of Fm 3 ¯m structure, direct gap Γ- Γ of Pnam structure and indirect gap Γ-K of P63/mmc structure. We do not observe the metallization up to 210 GPa. The linear optical properties such as absorption coefficient, reflectivity, refraction index, conductivity and energy loss function have been derived from calculated complex dielectric function for a wide energy range of 0-50 eV and pressure up to 50 GPa, and analyzed in detail.

In this paper the computational simulation of electromagnetic propagation multimodal inside an optical fiber with step index is performed. A sinusoidal source placed at the left end feeds an electromagnetic field to the optical fiber; fiber layers are modeled staggered to achieve total internal reflection of the incident light according to the wave theory of light. The simulation is performed using tools of computational electromagnetics such as Method Finite Difference Time Domain (FDTD) and the method of perfectly matched layers (PML) as boundary condition absorption to prevent electromagnetic propagation continue to infinity. The operating frequency is 187 THz used and the wavelength of 1600nm is, this simulation is achieved by developing a computational algorithm in Matlab. electromagnetic parameters propagated in the core of the optical fiber such as magnetic field components Hx and Hy and Ez electric field are obtained. We want students to achieve understanding of the behavior of light as an electromagnetic wave inside the optical fiber, it may be something that might be perceived as simple, however, we are sure to see the electromagnetic propagation according to the results allowing clearly interpret these optical phenomena.

En el presente trabajo se realiza la simulación computacional de la propagación electromagnética multimodal en el interior de una fibra óptica con índice escalonado. Una fuente senoidal colocada en el extremo izquierdo alimenta un campo electromagnético a la fibra óptica; las capas de la fibra se modelan de forma escalonadas para lograr la reflexión total interna de la luz incidente de acuerdo con la teoría ondulatoria de la luz. La simulación se realiza utilizando herramientas del electromagnetismo computacional tales como el Método de Diferencias Finitas en el Dominio del Tiempo (FDTD) y el método de capas perfectamente acopladas (PML) como condición de frontera de absorción para evitar que la propagación electromagnética continúe hasta el infinito. La frecuencia de operación utilizada es de 187 THz y la longitud de onda es de 1600nm, esta simulación se logra desarrollando un algoritmo computacional en Matlab. Se obtienen los parámetros electromagnéticos propagados en el núcleo de la fibra óptica tales como componentes de campo magnético Hx y Hy y de campo eléctrico Ez. Deseamos que los alumnos logren comprender el comportamiento de la luz como onda electromagnética en el interior de la fibra óptica, puede ser algo que tal vez se perciba como sencillo, sin embargo, estamos seguros que al visualizar la propagación electromagnética de acuerdo a los resultados obtenidos, permite interpretar con claridad estos fenómenos ópticos.

Abstract In this work, we applied the seismic interferometry (SI) method in order to determine the lateral variation of S wave velocity (Vs) in the subsoil structure of a rock mass with a slope located on Joaquin Claussell Street in the 3rd Section of Chapultepec Park. Geological and geotechnical studies show that a pumice stratum, overlying semi-permeable materials, is susceptible to failure and causing a landslide due to fracturing and rains, typical factors that cause landslides in the western part of Mexico City. In order to show the applicability of the SI method to quantify the elastic properties and their distribution in the slope, we generated cross-correlation functions among 4560 pairs of receivers in an irregular array of 96 vertical geophones. By means of the temporal variations of the maximum correlation pulse, as a function of frequency (4 to 24 Hz), we built tomographic images of relative Vs velocity. We found that Vs values close to 300 m/s are related to the pumice strata, velocities that are located primarily on the slope face and at its lowest topographical level. The velocity of these materials contrasts with an underlying stratum with values greater than 1000 m/s. These results are corroborated with the soil structure derived from two seismic refraction lines. This study suggests that the SI method is appropriate to assess the geological hazards associated with slope stability.

Resumen En este trabajo aplicamos el método de Interferometría Sísmica (IS) para determinar la variación lateral en la distribución de la velocidad de onda S (Vs) en la estructura de un macizo rocoso que contiene un talud localizado en el circuito Joaquín Claussell de la 3a Sección del Bosque de Chapultepec. Estudios geológicos y de geotecnia muestran la presencia de un estrato pumicítico, que sobreyace a materiales semi permeables; el cual es susceptible a fallamiento y provocar deslizamientos, debido al estado de fracturamiento y el aporte de agua durante la época de lluvias, factores comúnmente asociados a deslizamientos en la zona poniente de la Ciudad México. A fin de mostrar la aplicabilidad del método de IS para cuantificar las propiedades elásticas y su distribución en los estratos que conforman el cuerpo del talud, se generaron funciones de correlación cruzada entre 4560 pares de receptores en un arreglo irregular de 96 geófonos verticales. Mediante el uso de las variaciones temporales del máximo pulso de correlación en función de la frecuencia (4 a 24 Hz), construimos imágenes a partir de la tomografía de Vs relativa. Encontramos que valores de Vs cercanos a 300 m/s se relacionan con los estratos de pómez, los cuales se encuentran principalmente alojados hacia la cara del talud y en su parte topográfica más baja. La velocidad en estos materiales contrasta notablemente con la del estrato subyacente de valores superiores a 1000 m/s. Los valores de Vs y la geometría del estrato susceptible a deslizarse fueron corroborados por dos líneas de refracción sísmica. Los resultados de este estudio, sugieren que el método de IS es apropiado, debido a su carácter no invasivo ni destructivo, para analizar este tipo de riesgos geológicos asociados con la estabilidad de taludes.

Abstract The phenomenon of reflection and refraction is studied at the welded interface between two different porous solids. One is saturated with single non-viscous fluid and other is saturated with two immiscible viscous fluids. The incidence of Pf, Ps or SV wave through porous solid saturated with non-viscous fluid results in the three reflected waves and the four waves refracted to porous medium saturated with two immiscible viscous fluids. For the presence of viscosity in pore-fluids, the waves refracted to corresponding medium attenuate in the direction normal to the interface. It is also revealed that for the post-critical incidence of Ps wave, the reflected Pf and SV waves becomes evanescent and for the post-critical incidence of SV wave, the reflected Pf wave becomes evanescent. While, the occurrence of critical incidence is not observed for the incidence of Pf wave. The ratios of amplitudes of reflected and refracted waves to that of incident wave are expressed through a non-singular system of linear algebraic equations. These amplitude ratios are used further to calculate the shares of different scattered waves in the energy of incident wave. For a particular numerical model, the energy shares are computed for incident direction varying from normal incidence to grazing incidence. The conservation of energy across the interface is verified. Effects of non-wet saturation of pores, frequency of wave and porosity on the energy partitions are depicted graphically and discussed.

Em geral, o ensino de óptica no nível médio está concentrado na óptica geométrica. Apesar de ser um modelo de sucesso para explicar fenômenos como reflexão e refração da luz, ele não aborda satisfatoriamente a discussão sobre a natureza ondulatória da luz, além de não explicar fenômenos como difração e interferência. Neste trabalho propomos um experimento simples e de baixo custo para discutir a natureza ondulatória da luz e o limite em que a óptica geométrica é válida. A proposta constitui também um dispositivo para realização de medidas de objetos cuja dimensão seja da ordem do comprimento de onda da luz.

In general, optics teaching at high school level focus on geometric optics. This is a successful model to explain reflection and refraction of light. However, it is not appropriate to discuss the wave nature of light, and to explain diffraction and interference, for example. In this work, we propose a simple experiment, of low cost, to discuss the wave nature of light and the limit in which the geometric optics is valid. Our proposal also provides a device to perform measurements of objects whose dimension is of the order of the wavelength of light.