We propose a simple and accurate experimental method for finding the refractive index of solid and liquid dielectrics using the polarization of light reflected by a dielectric surface near the Brewster angle. This experiment can be implemented in an optics laboratory at the undergraduate or graduate level. The method improves the precision of the determination of the Brewster angle by more than two orders of magnitude compared with recent measurements, but uses similar optical components. An angular resolution of 0.01° can be easily achieved using a parabolic fit of the parallel component of the reflectance normalized to the total reflectance in a region close to the Brewster angle, which leads to values of the refractive index for solid and liquid dielectrics with a precision of 10−4. Care is taken to eliminate the instabilities in the laser beam and the time dependence from our measurements. We report results for two glasses and for isopropyl alcohol for several wavelengths in the visible range. The latter is used as a test of our procedure due to its shallow dispersion in the visible.
Based on our novel method recently published in the Am. J. Phys. 77 337-43 (2009) for finding precise values of the indices of refraction for dielectrics from measurements of the polarized light reflected by the surface, in this paper we propose an improved technique for finding Brewster angles with a better precision, of 0.001 • , using the same relative inexpensive optical equipment provided by the PASCO Scientific company and a simpler setup. The goal is to implement our procedure in a 3 h optics laboratory for undergraduate students using two different laser-dielectric systems. As compared to our previous work, now we eliminate the random fluctuations of the experimental time-dependent reflectance by controlling the irradiation time on the dielectric surface (and thus avoiding the overheating of the surface) and by using lasers which are stable during the data acquisition process. Also, in the present experiment, we use a computer-based filtering procedure of the experimental reflectance during the data acquisition process for increasing the precision of the measurements at any angle of incidence.
The rapid and accurate diagnosis of power grid faults plays a vital role in speeding up the process of accident handling and system recovery and ensuring the safe operation of the power system. This paper proposes to apply the ensemble empirical mode decomposition (EEMD) method and scale-related intrinsic entropy to diagnose the type of fault for the transmission line. First, the electrical data collected by the power system is decomposed by using the EEMD method. Then by eliminating some intrinsic mode functions, the signal is reconstructed by inspecting the correlation coefficient. Finally, the complexity of the reconstructed signal is calculated by using the scale-dependent intrinsic entropy. Since the scale-dependent intrinsic entropy reflects the complexity of one-dimensional time series, it is susceptible to signal changes. The complexity is helpful in the power system for fault signal analysis. The results show the combined method’s effectiveness and practicability through failure analysis using the IEEE 14-bus system as the simulation model.
China’s current exploration of the development for the offshore wind resources is three times than for the onshore wind resources. The development and utilization of offshore wind resources have a broad prospect. In this study, a set of simplified asynchronous generators equivalent to a steady-state model applied in bus test systems is established according to the characteristics of offshore wind turbines. The calculation of the Newton-Raphson method in power flow analysis is relatively large to avoid the occurrence of a Jacobian matrix and reduce the calculation time. In this particular use of the idea of the secant method, the differential equation into the algebraic equation significantly reduced the amount of calculation but also overcame the Newton-Raphson method of sensitivity to the initial value problems. The solution of the equation is simplified, and the purpose of solving the equation is achieved more accurately, while the computation time is similar to the PQ decoupling analysis method.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.