Verification of Malus's Law Using a LCD Monitor and Digital

Revista Brasileira de Ensino de F´ısica, vol. 38, nº 3, e3311 (2016) Artigos Gerais www.scielo.br/rbef cbnd DOI: http://dx.doi.org/10.1590/1806-9126-RBEF-2016-0029 LicençaCreative Commons Verification of Malus’s Law using a LCD monitor and Digital Photography Verificação da Lei de Malus usando monitor LCD e fotografia digital Larissa Vertchenko∗1, Lev Vertchenko2 1Departamento de F´ısica, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil. 2Departamento de F´ısicae Qu´ımica,Pontif´ıciaUniversidade Católica de Minas Gerais, Belo Horizonte, MG, Brazil. Recebido em 4 de fevereiro de 2016. Aceito em 26 de abril de 2016 An alternative laboratory experiment for verifying Malus’s Law, as well as understanding concepts of photometry, polarization and image formation on liquid crystal displays using low cost materials is proposed. The experimental setup could be introduced to any undergraduate curriculum using readily available tools, such as a digital camera, polarizer removed from a cell phone and a LCD laptop screen. A fairly amount of photometric data was collected and analyzed by an astronomical image processing software resulting in a successful verification of Malus’s Law. Keywords: Polarization, Photometry, Malus’s Law, Liquid Crystal, image processing software. Propomos um experimento alternativo para verifica¸cãoda Lei de Malus, assim como para o en- tendimento dos conceitos de fotometria, polariza¸cãoe forma¸cãode imagem em displays de cristal liquido, usando materiais de baixo custo. O arranjo experimental pode ser introduzido em qualquer grade curricular dos cursos de gradua¸cãoem f´ısica, utilizando ferramentas facilmente acess´ıveis, como a câmerafotográficadigital, um polarizador removido de um aparelho celular e um monitor LCD de um computador. Uma razoável quantidade de dados fotométricos foi coletada e analisada atravésde um software de processamento de imagens, verificando com sucesso a Lei de Malus. Palavras-chave: Polariza¸cão,Fotometria, Lei de Malus, Cristal Liquido, Software de Processamento de Imagem. 1. Introduction polarization with the technology present in everyday life. In the 19th century, French physicist Etienne Louis Usually, the polarization approach in didactic lab- Malus developed research [1] about the relations oratories [2, 3] begins with the study of Malus’s between the incident angle and the reaction of light Law using linear polarizers, laser sources and a pho- beams on polished surfaces, initiating the study of tometer [4]. However, these materials only provide the polarization of light. Currently, polarization has a strictly quantitative experiment since the student a great importance in different areas of knowledge will be just looking for the values of the intensity of such as, for example, physics, engineering and as- light, provided by the photometer, as a function of tronomy. When students learn about polarization, the angle of the polarizer placed in front of the laser they often face equipment whose operation they source. The addition of instruments belonging to the do not usually understand, like polarized filters and day-to-day life of the students can be very meaning- LCD screens, mostly found in electronic devices such ful for their learning in undergraduate optics labs. as computers, cell phones and television sets. As a In this paper, we propose a low cost experiment for result they are not able to correlate the concept of verifying Malus’s Law using a computer monitor, a polarizer extracted from a cell phone, a digital cam- ∗Endere¸code correspondência:[email protected]. Copyright by Sociedade Brasileira de F´ısica.Printed in Brazil. e3311-2 Verification of Malus’s Law using a LCD monitor and Digital Photography era and astronomical software for image treatment. 2. Photometry, Polarization and Malus’s All these instruments are easily found in the back- Law pack of any student which allows them to actively interact with their experimental apparatus instead Photometry and polarization have vast applications of just passively absorb the material placed on the in many fields. In fact, their combination is behind laboratory’s table. Furthermore, the use of materials most of consumer electronics products and acces- and equipment directly connected to contemporary sories, such as cell phones, computers, televisions, gadgets such as computers, digital cameras or cell etc. Here, we combine photometric measurements phones stimulate the students to explore and learn and polarization properties to verify Malus’s Law about these technologies, turning such experiments with readily available tools, designing an experiment into valuable educational tools. For example, the easily reproducible in any undergraduate laboratory setup here proposed requires the students to under- and even at home. stand how a digital camera functions and discuss features available in it, like exposure time, aperture, 2.1. Photometry focusing and sensitivity. Or, by extracting the com- ponents of cell phones, one can learn the concepts In optics, photometry [9] is the stimulation of visual behind the liquid crystal display and the polarizer. sensation by electromagnetic radiation in a simu- For data analysis we use graphing software and lation of the human vision. However, due to the a photometric measure tool contained in the astro- subjectivity of the human visual system it cannot nomical image processing software called IRIS [5]. be quantifiable in absolute physical units. Early The application of this software combined with a sources used the intensity of a candle as the stan- digital camera also permits to discuss astronomical dard, hence the unity candela, and observers would photometry techniques and Charge Coupled Device compare an unknown light source to it. Presently, (CCD) imaging photometry. This new technology there is a standardized weight function based on is useful to make photometric observations even the sensitivity of the human eye to a particular with faint objects. Nowadays, in budget price digital wavelength [10]. Applications of photometry include cameras, CCDs have been substituted by another color and light intensity analysis, digital media, au- image sensor called Complementary Metal Oxide tomotive industry and aerospace lighting to name a Semiconductor (CMOS) as a result of its low cost, few. In sciences, photometry has been particularly high noise immunity and low power consumption. important to study celestial objects. However, for our purposes, the CMOS sensor works The so-called Astronomical photometry [11] mea- as well as a CCD sensor. sures the radiation flux, fλ, that we receive from Other works [6, 7] involving experiments with celestial objects over broad wavelengths bands of polarization of light and LCD screens have been radiation. Such measurements, usually coupled to developed showing that students can become fa- distance estimation, can give us information on miliar with basic principles of physics, and more the object’s luminosity, temperature, size and other accurately, concepts of optics. In 1950, an experi- properties. The luminous energy captured by a time ment on Malus’s Law [8] was also performed in an interval ∆t over an area A is given by elementary laboratory with an inexpensive appa- c ratus consisting of a photoelectric cell attached to E = f A∆t = Nh (1) λ λ a galvanometer. This paper intends to present an application of photometry through an alternative where N is the number of incident photons, λ the method to study polarization and verify Malus’s wavelength, h Planck’s constant and c is the speed Law using contemporary materials that are easy to of light in vacuum. The term hc/λ corresponds to obtain. the energy of each photon as proposed initially by The rest of this paper is organized as follows. Planck [12]. In Sec. 2 we discuss the concepts of photometry, In astronomical photometry, the selection of the polarization and Malus’s Law. Section 3 describes wavelength (or color) is defined by the optical filter the experimental realization and results. Finally, in used, and the flux measured by a time interval of Sec. 4 we present the conclusions about the work. wavelengths is obtained by the convolution of the incident flux with the transmission function of the Revista Brasileira de Ensino de F´ısica,vol. 38, nº 3, e3311, 2016 DOI: http://dx.doi.org/10.1590/1806-9126-RBEF-2016-0029 Vertchenko e Vertchenko e3311-3 filter and spectral sensibility of the CCD. However, filters that allow the passage of light of a specific the image formation in electronic devices, such as polarization. For example, linear polarizers are opti- digital cameras and LCD monitors, use the RGB cal devices defined by a transmission axis, i.e. they system (red, green, blue) [13], where the colors result allow the transmission of light whose electric field from the combination of beams from the primary oscillates in a plane parallel to one particular chosen colors red, green and blue. Nevertheless, the associ- axis, and block the component of the electric field ation of these primary colors to the wavelengths is that oscillates in the orthogonal direction. Typical not completely defined due to its dependence of the polarizers for visible light are made of materials such device. The zero value corresponds to the absence as plastic and glass. of light of the pixel, while the value 255 usually cor- In 1808, Malus discovered that natural light be- responds to the maximum of intensity of a primary comes polarized by reflection and that the reflected color. light intensity varies from a maximum to a mini- The number of electrons counted on a CCD sen- mum when passing through a rotating calcite crystal. sor, Ne, can be related to the number of incident Nowadays it is known that not only calcite crystals photons N by an efficiency factor η, where Ne = Nη. but any other linear polarizer gives the same results Knowing this, the equation (1) can be written as working as an analyzer, in other words, a linear polarizer is a type of filter which modifies a beam of ηAλfλ∆t light whose resulting electric vector is oscillating in Ne = , (2) hc one plane [17].

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