Originally an empirical law, nowadays Malus' law is seen as a key experiment to demonstrate the transverse nature of electromagnetic waves, as well as the intrinsic connection between optics and electromagnetism. In this work, a simple and inexpensive setup is proposed to quantitatively verify the nature of polarized light. A flat computer screen serves as a source of linear polarized light and a smartphone (possessing ambient light and orientation sensors) is used, thanks to its builtin sensors, to experiment with polarized light and verify the Malus' law.
Texture characterization in thin films from standard powder x-ray diffraction (XRD) rely on the comparison between observed peak relative intensities with those of powder diffraction standards of the same compound, trough the so-called texture coefficient (TC). While these methods apply for polycrystalline materials with isotropic grains, they are less accurate—and even wrong—for anisotropic materials like ZnO oriented single-crystal nano-rods, which would require the use of dedicated XRD texture setups. By using simple geometrical considerations, we succeed in discriminating between texture and morphology contributions to the observed intensity ratios in powder diffraction patterns. On this basis, we developed a method that provides a quantitative determination of both texture (polar distribution) and morphology (aspect ratio of nano-rods), using simple x-ray powder diffraction. The method is illustrated on a typical sample from a series of Zinc oxide (ZnO) nano-rod arrays grown onto a gold thin film sputtered onto a F:SnO2-coated glass substrate (FTO) by using cathodic electro-deposition. In order to check the consistency of our method, we confronted our findings with scanning electron microscope (SEM) images, grazing incidence diffraction (GID), and XRD pole-figures of the same sample. Nevertheless, the proposed method is self-consistent and only requires the use of a standard powder diffractometer, nowadays available in most solid-state laboratories.
The characteristics of the inner layer of the atmosphere, the troposphere, are determinant for the earth's life. In this experience we explore the first hundreds of meters using a smartphone mounted on a quadcopter. Both the altitude and the pressure are obtained using the smartphone's sensors. We complement these measures with data collected from the flight information system of an aircraft. The experimental results are compared with the International Standard Atmosphere and other simple approximations: isothermal and constant density atmospheres. The international standard atmosphereThe atmospheric conditions exhibit strong variations at different points and different times. To provide a unified frame of reference, an atmospheric model, the International Standard Atmosphere (ISA), has been established 1 . It consists of tables of pressure, temperature, density and other variables suitable at mid latitudes over a wide range of altitudes. The ISA is used for several purposes ranging from altimeter calibration to comparison of aircraft performance among others. The ISA is divided into layers with simple temperature variations. The inner layer is the troposphere, from the surface until 11 km of height, in which the temperature presents a linear gradient, named lapse rate, C= -0.0065 K/m. The pressure p as a function of the height h according to the ISA is shown in Fig. 1.We also consider two additional atmospheric models. Firstly, a rather crude approximation consists of considering the temperature constant in the inner layers. This model is called isothermal atmosphere. The flight information system usually available to the passengers in many aircrafts provides an clever way to quantify the relationship between temperature and pressure. In Fig. 2 we plot the temperature as a function of the altitude using data collected by a passenger. The linear fit, and g gives a temperature gradient of about C= -0.0072 K/m. Of course, this value highly depends on the particular atmospheric conditions during this flight and does not necessarily represents accurately the ISA. This exercise can be proposed as a homework to students about to travel on a plane.The second approximation is obtained neglecting air density variations. Under this approximation valid at small altitudes (a few kilometers), ρ is constant and the atmospheric pressure obeys the hydrostatic equation
The spatial dependence of magnetic fields in simple configurations is an usual topic in introductory electromagnetism lessons, both in high school and in university courses. In typical experiments, magnetic fields are obtained taking point-by-point values using a Hall sensor and distances are measured using a ruler.Here, we show how to take advantage of the smartphone capabilities to get simultaneous measures with the built-in accelerometer and magnetometer and to obtain the spatial dependence of magnetic fields. We consider a simple set up consisting of a smartphone mounted on a track whose direction coincides with the axis of a coil. While the smartphone is smoothly accelerated, both the magnetic field and the distance from the center of the coil (integrated numerically from the acceleration values) are simultaneously obtained. This methodology can be easily extended to more complicated setups. Simultaneous use of several smartphone sensorsRecently, the increasing availability and capabilities, and the decreasing cost have contributed to the expansion of smartphone physics. Indeed, smartphone sensors, as accelerometer, gyroscope, magnetometer among others, have been successfully employed in diverse physics experiments ranging from mechanics to modern physics (see, for example, this column in past issues of this journal). One relevant aspect that has received little attention is the fact that smartphones allow to obtain simultaneous measures from several sensors. In previous works, the simultaneous use of the accelerometer and the gyroscope has been proposed [1][2][3][4][5]. More recently, the luminosity sensor has been employed together with the orientation sensor to experiment with polarized light [6]. In this work, a simple experience which combines the use of the smartphone magnetometer and the accelerometer is proposed. The magnetic field generated by a current in a coil is measured with a smartphone located over a cart on a rail whose orientation coincides with the axis of the coil. While the smartphone is moving on the track, its position is readily obtained integrating twice the acceleration values obtained from the accelerometer. In this way, with a simple data processing, the magnetic field as a function of the position is obtained and as a by-product also the permeability. These results can be compared with the predictions of the Biot-Savart law.
The Atwood machine is a simple device used for centuries to demonstrate the Newton's second law.It consists of two supports containing different masses joined by a string. Here, we propose an experiment in which a smartphone is fixed to one support. With the aid of the built-in accelerometer of the smartphone the vertical acceleration is registered. By redistributing the masses of the supports, a linear relationship between the mass difference and the vertical acceleration is obtained.In this experiment, the use of a smartphone contributes to enhance a classical demonstration. TheoryThe Atwood machine is a simple device invented in 1784 by the English mathematician George Atwood [1][2][3] . It consists of two objects of mass m A and m B , connected by an inextensible massless string over an ideal massless pulley 1 . Applying the Newton's second law to each mass we obtainwhere g is the gravitational acceleration, T is the tension force, and a is the vertical acceleration.Eliminating the tension between these equations we obtainor in terms of the mass difference Δm and the total mass MAs mentioned in the original Atwood's book, many possible experiments can be implemented using his machine 1 . One of the simplest possibilities, adopted here, is, keeping the total mass, to vary Δ m by redistributing a set of weights. In this case, a linear relationship between the vertical acceleration and the mass difference is obtained.
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