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 built-in sensors, to experiment with polarized light and verify the Malus' law.
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.
In the last years, a great deal of smartphone-based experiments have been proposed in physics. Remarkably, experiments focusing on light and optics, and specially those using the ambient light sensor [1][2] , have received little attention compared to those focusing on mechanics, oscillations or magnetism. Two exceptions are worth mentioning. In Ref. 1 , the authors proposed a simple verification of the inverse square law using the light sensor of a smartphone or a tablet. In a different approach 2 , the ambient light sensor has been proposed to indirectly measure distances and to analyze coupled springs undergoing oscillatory motions. Here, we focus on an experiment using the ambient light sensor which involves the polarization of light [3][4][5][6][7][8][9] and, in particular, the Malus’ law.
Smartphones also gives us the ability of measuring simultaneously with various sensors. This is also a great advantage since it allows a great variety of experiments to be performed, even outdoors, avoiding the dependence on fragile or unavailable instruments. In previous works, the simultaneous use of two sensors like the gyroscope and the accelerometer was proposed to relate angular velocity, energy, centripetal and tangential acceleration [10][11][12] . In another experiment, the pressure sensor and the GPS were used in synchrony to find the relationship between atmospheric pressure and altitude 13 .
In this work, we propose an experiment in which we take advantage of the capabilities of a smartphone to verify the Malus’ law. The intensity of polarized light from a computer monitor is measured by means of the ambient light sensor with a tiny polarizer attached to it while the angle between the polarization and the polarizer is measured by means of the orientation sensor. The simultaneous use of these two sensors allows us to simplify the experimental setup and complete a set of measures in just a few minutes. The experimental results of the light intensity as a function of the angle shows an excellent agreement with Malus’ law.
Light, as any other electromagnetic wave, nearly always propagates as a transverse wave, with both electric and magnetic fields oscillating perpendicularly to the direction of propagation (see a standard general physics textbook). The direction of the electric field is called the polarization of the wave. In a linearly polarized plane wave the electric field remains in the same direction. This pure state of polarization is called linear polarization. Natural light, (e.g., light radiated by an incandescent object) as a random mixture of waves with different polarizations, is unpolarized light, or more precisely, random polarized light.
According to conservation of energy applied to electromagnetic fields (Poynting’s theorem), the energy flow (intensity or illuminance, I) associated to an electromagnetic wave (light) is proportional to the square of the amplitude of the electric field. When light interacts with matter its behavior is modified, mainly its intensity and its velocity. Moreover, some materials are able to modify light differently in each spatial direction. This is the case for instance of linear polarizers that can convert unpolarized light into linear polarized light. An ideal polarizer fully attenuates light polarized in one direction, and fully transmits light with the orthogonal polarization.
Consider a beam of linear polarized light incident over a polarizer. Let θ be the angle between the axis of the polarizer and the polarization of the incident light. The electric field that passes through the polarizer is the component in the direction of the axis, E=E 0 cos θ . Therefore, the intensity of the light passing the polarizer is
where I 0 , is the intensity of the light before the polarizer. Equation 1 is the so called Malus’ law, named after the French physicist Étienne-Louis Malus, who discovered optical polarization in 1808.
In this experiment, a source of polarized light, a polarizer, a photometer and a way to measure angles are needed. The source of linear polarized light is a flat computer monitor (or LCD TV screen) in plain white color [4][5][6] . The ambient light sensor of LG-G3 smartphone, located near the front camera (Fig. 1, left panel) is used as a photometer and the orientation sensor is used to measured the angles. A small piece of polarizer (a square of about 1 cm side) from an old calculator’s dis
This content is AI-processed based on open access ArXiv data.
