We present a derivation for the coordinates of the centre of mass—or centre of gravity—of a homogeneous triangular plate by using scaling and symmetry. We scale the triangular plate by a factor of 2 and divide its area into four plates identical to the original. By symmetry, we assert that the centre of mass of two identical masses lies at the midpoint of the line joining their centres of mass. By relating the centres of mass of the original to those of the scaled plates, we find the coordinates of the centre of mass as the solution of an algebraic equation.
After a review of textbooks written for undergraduate courses in physics, we have found that discussions on thin films are mostly incomplete. They consider the reflected and not the transmitted light for two instead of the four types of thin films. In this work, we complement the discussion in elementary textbooks, by analysing the phase differences required to match the conditions for constructive and destructive interference, in the reflected and transmitted light in four types of thin films. We consider thin films with varied sequences in the refractive index, which we identify as barriers, wells and stairs (up and down). Also, we use the conservation of energy in order to understand the complementary colour fringes observed in the reflected and transmitted light through thin films. We analyse systematically the phase changes by introducing a phase table and we synthesize the results in a circular diagram matching 16 physical situations of interference and their corresponding conditions on the film thickness. The phase table and the circular diagram are a pair of tools easily assimilated by students, and useful to organize, analyse and activate the knowledge about thin films.
Absorption measurements are made as function of temperature for the isoelectronic trap ZnTe : 0. This spectrum is well separated from the intrinsic absorption and from the absorption due to other impurities. The spectra can be semiquantitatively understood using a model developed for AgBr: I. The temperature dependence of the absorption due to LO-phonon cooperation is given by where y can be derived from the value for AgBr: 1. The fine structure of the absorption is explained and the spectral symmetry between emission and absorption is discussed in detail. The electron-phonon coupling (Huang-Rhys factor) is found to be different for different phonon modes and smaller in absorption than in emission for optical modes but the inverse is true for accoustic modes.Nous avons mesure I'absorption en fonction de la temperature du piege isoelectronique ZnTe: 0. Le spectre est stpare de maniere distincte de I'absorption intrinseque ainsi que des autres impuretes. Ce spectre peut &tre analyse d'une maniere semiquantitative en utilisant un modtle dCvelopp6 pour I'AgBr : I. La dependance en temperature de l'absorption due a la cooperation de phonons LO est donnee par -e -y T 2 ou y peut Ctre derive de sa valeur pour 1'AgBr: 1. Nous expliquons la structure fine du spectre d'absorption ainsi que la symetrie spectrale entre emission et absorption. Le couplage electron-phonon (represente par le facteur Huang-Rhys) montre des valeurs differentes pour ies modes phononiques differents et en particulier, il est plus petit en absorption qu'en emission pour les modes optiques, tandis que I'inverse est observe pour les phonons accoustiques.
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