Measuring light with light dependent resistors: an easy approach for optics experiments
MMeasuring light with light dependent resistors: aneasy approach for optics experiments
F. Marinho ∗ , C.M. Carvalho , F.R. Apolin´ario , L. Paulucci Universidade Federal de S˜ao Carlos, Rodovia Anhanguera, km 174, 13604-900,Araras, SP, BrazilE-mail: [email protected] Universidade Federal do ABC, Av. dos Estados, 5001, 09210-170, Santo Andr´e, SP,Brazil
Abstract.
We entertain the use of light dependent resistors as a viable option asmeasuring sensors in optics laboratory experiments or classroom demonstrations. Themain advantages of theses devices are essentially very low cost, easy handling andcommercial availability which can make them interesting for instructors with limitedresources. Simple calibration procedures were developed indicating a precision of ∼
5% for illuminance measurements. Optical experiments were carried out as proof offeasibility for measurements of reflected and transmitted light and its quality resultsare presented. In particular, the sensor measurements allowed to verify the angulardistribution of a Lambertian reflective material, to observe transmitted and reflectedspecular light on a glass slab as function of the incoming angle of a light beam, andto estimate glass refractive index with values averaging 1 . ± .
06 in satisfactoryagreement with the expected 1.52 value.
Keywords : optics experiments, LDR sensor, Lambertian reflector, refractive index.
1. Introduction
Light dependent resistors (LDRs) are widely used as devices to automatically control thefunctioning of our day-to-day streetlights, nightlights, alarms, among other applications.Although very cheap and abundant in the electronics component market it has notbeen much explored or at least documented on optics related learning activities.The characteristics of these sensors indicate that direct measurements of irradianceor illuminance (depending on the calibration equipment available) on simple madeexperiments are feasible. Its basic operation does not require electronics knowledge anddata quality should allow comparison between theoretical expectations and experimentaldata.The LDRs are passive devices that usually employ materials that exhibit detectablephotoconductivity [1]. That is the ability to change their conductivity as the incidentirradiance on the material varies. Semiconductors are often used as photoconductivematerials which are deposited in a corrugated thin strip arrangement on top of a ceramic a r X i v : . [ phy s i c s . e d - ph ] M a r easuring light with light dependent resistors: an easy approach for optics experiments Figure 1.
Schematics of a light dependent resistor.
LDRs offer great advantage for being passive elements, thus being easy to use andmeasurements can be made directly with an ohmmeter only. No further connectionsor applied voltages are required. Acquisition rate is limited by the characteristic decaytime of photo-electrons in the material. This time can be as high as tenths of a secondwhich means LDRs should be better suited for slow changing irradiance situations andmechanically static setups. Photodiodes and phototransistors can also be used as devicesto measure irradiance, as done, for instance by Benenson [2] among many examples. Butfor these, it is necessary to assemble an electric circuit with external power supply inorder to measure an output voltage with incident light.Some applied uses of LDRs related to science and engineering instruction havebeen reported and are briefly described below. Rivera-Ortega and collaborators [3]present an interesting work using a laser diode to convert a 4-bit image into pulsesthat were transmitted by an optical fiber, received by a LDR, and recorded by anArduino board. The reading of the variable electric voltage on the LDR allowed thereconstruction of the image with good quality. Gutierre et al. [4] performed thecalibration of a LDR as a light sensor using a laser and polarizers and then used it toobtain the Gaussian light profile of a HeNe polarized laser beam with satisfactory results.Nevertheless, no further applications are discussed. A LDR was also employed as partof a simple spectrophotometer by Tavener&Thomas-Oates [5] and Forbes&N¨othling [6],in the context of teaching chemistry to undergraduate students. Although not related easuring light with light dependent resistors: an easy approach for optics experiments
2. Calibration
A typical procedure to evaluate optical characteristics of a sample generally requiresthe use of a light source and a suitable detector. For our calibration studies we useda lamp placed at different distances to understand how the LDR sensor’s measuredresistance varies with illuminance. A commercial lux meter was used as calibratingdevice to provide measurements simultaneous to the LDR resistance readings. Thisway a correlation between the two quantities can be established. Because the placingdistances used are significantly larger than the lamp dimensions the illuminance canbe sufficiently varied and controlled by simply moving the source towards the detectorsdirection in small steps. This also allowed to consider light emission from the usedsource as isotropic.Figure 2 shows a representation of the calibration setup. The source is placed ontop, the lux meter and a 0 . × . LDR close at the bottom. A 6 Watt LED roundred lamp was used as an isotropic light source. The red lamp was employed to verifythe LDR response around the wavelength region close to the typical red laser pointerwavelength since these are the cheaper and easiest to find specular light beam sources.A lux meter has a typical cost of about 10 to 30 US dollars. A smart phone lightsensor can be used as an alternative calibrating device along with specific software (e.g.Lux Meter, Physics Toolbox, Lux Light Meter Pro, Lux Light Meter FREE) freelyavailable for Android or IOS platforms.Although the lux meter provided measurements of illuminance, i.e. the luminousflux per unit area as seen by the average human eye, we used a monochromatic lightsource such that the ratio between the actual irradiance arriving in the sensor and theilluminance is always given by a fixed conversion factor. Mathematically: I = η (cid:90) ∞ E e,λ V ( λ ) dλ, (1)where I is the illuminance, η is a conversion constant, E e,λ is the spectral irradiance, V ( λ ) is the luminous efficiency of the eye and λ is the light wavelength. easuring light with light dependent resistors: an easy approach for optics experiments Figure 2.
Calibration setup. The lamp illuminates both the LDR and lux metersensors, placed at a distance d from it. In our case: E e,λ ∝ P δ ( λ − λ source ) , (2)where P is the source power and δ is the Dirac delta function centered at the sourcewavelength, so that the integral becomes: E v ∝ P. (3)This is only a reasonable statement when employing monochromatic light sources.A distance scan was performed and illuminances and resistances were recorded.Room illumination was much reduced for data acquisition. Readings compatible with0 . d fromthe closest point of the light source surface to the LDR. The circle markers show thedata and the solid line shows the curve obtained with the parametrization of illuminanceobserved by the lux meter as a function of distance. A simple model was used for thecurve least squares fit. It assumes the dimensional features of the source and sensors canbe neglected and treated as punctual objects in good approximation and the illuminanceis proportional to the inverse square of the source-sensor distance. The light angle ofarrival on the lux meter surface is also taken into account in the model.The obtained parametrization was used to estimate the illuminance arriving onthe LDR sensor nearby. Figure 4 shows the measured resistance as a function of theilluminance estimated on the LDR. It is a very good approximation to assume thetrend to be linear between these two quantities in a log-log scale. Therefore, data was easuring light with light dependent resistors: an easy approach for optics experiments Figure 3.
Measured illuminance from lux meter as a function of distance betweenlight source and the detector’s plane. linearized according to ln( R ) = a + b ln( I ) where R is the measured resistance and I isthe illuminance. Parameters a and b were extracted via a least squares fit providing acalibration between resistance and illuminance. Calibration is shown by the solid linewith values obtained of a = 3 . ± .
02 and b = − . ± . Figure 4.
Calibration of LDR resistance as function of illuminance.
The calibration procedure adopted indicates that a LDR can be used as a measuringdevice provided the illuminances are in the range of 10 − lx. For a red wavelengthsource a ∼
5% overall level of precision can be assumed due to calibration uncertaintiesonly.We also reproduced the same procedures described in this section for other LDRsensors with 0 . × . and 0 . × . surfaces. A linear dependence on a log-logscale similar to the one seen in figure 3 was found for all sensors. Table 1 summarizes easuring light with light dependent resistors: an easy approach for optics experiments Table 1.
Calibration constants for the used LDR sensors, considering a dependenceof the kind ln( R ) = a + b ln( I ) . Sensor Area (cm ) Coefficient a Coefficient b . × . . ± . − . ± . . × . . ± . − . ± . . × . . ± . − . ± .
3. Optics Experiments
In this section we describe two simple optical experiments which were set up to use theLDR previously calibrated as sensor for illuminance measurements. The experimentalresults are presented in comparison with the theoretical expectations as a way to evaluateits feasibility as a light detector for didactic lab activities or simple demonstrations.A red laser available in the laboratory was used as light source for both experimentsproposed in the next sections. These are very easy and cheap to purchase and shouldnot be a limiting factor for anyone wanting to reproduce any of the steps of this paperor to build their own experiments based on this work. Regarding the laser operationvoltage one must make sure the appropriate power is supplied as fluctuations can alterthe source power. Hence, one must either use charged up batteries or a voltage supplydevice which if not available can be improvised with an old mobile charger attachedto a voltage divider to adapt tension. In order to reduce illuminance to values withincalibration range ( < lx) we placed a 1mm plastic pinhole right in front of the lightbeam.Regarding the measurements of specular light directly incident on the sensor it wasnoticed that the 0 . × . sensor provided the most stable values due to its higherdensity of semiconductor lines per sensor surface such that no variation was observedif the beam spot slightly moved over said area. Another detail noticed was that thepositioning of the sensor has to be such that light must arrive at the sensor surfacewith an incoming angle as close to 90 o as possible. Given these observations, all theexperiments were performed with the same sensor as these were not limiting factors tothe measurements procedures. easuring light with light dependent resistors: an easy approach for optics experiments A plaster disc was used as a target for the measurement of the typical diffuse reflectiondistribution exhibited by this material. Figure 5 shows an incoming light beam thatreaches the plaster and is reflected diffusely in all directions as indicated by the set ofoutgoing arrows. The length of the arrows illustrate the expected illuminance as functionof the angle of reflection with respect to the direction of a unitary vector perpendicularto the disc surface.
Figure 5.
Illustration of diffuse reflection of light on a plaster disc.
For an ideal diffusely reflecting material the radiance must be the same observedfrom any angle θ with respect to the normal to the surface which implies that theilluminance measurements obtained with the LDR can be modeled as: I ( θ ) = ξ cos( θ ) + κ, (4)where ξ relates to the incoming beam illuminance and κ is a constant accounting forbackground.A certain amount of the background comes from external light impinging on thesensor as the experiment was performed with dimmed light only and not total darknessas for the calibration procedure in section 2. The main reason for that choice was toverify reproducibility in a non-equipped experimental environment. It also turned upthat the positioning and alignment of the sensor for each angle and its data reading ismuch better made with some visibility in the room.The graph shown in figure 6 was obtained by measuring the illuminance placingthe LDR sensor at a fixed distance to the point of light reflection on the disk surfaceat different angles. The disk and laser source were kept at fixed positions and only thesensor was repositioned. The solid line illustrates the model fitted to the data. Thequality of the data acquired with our proposed sensor allows to verify that the plastermaterial in fact presents a reflective behavior compatible mostly with a Lambertianreflector.It was noticed that for better performance of this experiment it was adequate tomake a simple angular alignment procedure of the used protractor. This was done bycomparing the measured illuminances of at least two equivalent fixed angles, θ and - θ ,checking if they gave about the same LDR readings. Random biases to data acquisition easuring light with light dependent resistors: an easy approach for optics experiments Figure 6.
Illuminance measured as function of scattering angle for laser beam shineonto a plaster disc. can be introduced as in this experiment the positioning and orientation of the sensor canbe more challenging. Therefore, it is also good practice to take a few independent scanmeasurements and average the data sets for each angle in order to get more accurateestimates. Figure 6 was obtained averaging two data sets.
A glass slab was used as traversing media for the laser beam described in section 3and the LDR sensor was used to measure the externally transmitted and reflected lightas function of the beam incident angle. Because the slab is immersed in air, multipleinternal reflections occur giving rise to multiple less bright parallel beams on both sidesof the slab.Figure 7 illustrates a schematics of the experimental setup for a fixed impingingangle of the light beam. The incident angles and the transmissions and reflection pointsare indicated. Illuminance for each outgoing beam is represented by I T,Ri where i is thenumber of the transmitted ( T ) or reflected ( R ) light beam.The dimensions of the slab used were of 6 mm width, 2 cm height and 24 . easuring light with light dependent resistors: an easy approach for optics experiments Figure 7.
Transmission and reflection profile of a glass slab with an incident lightbeam at a fixed angle θ . (a) I T (b) I T (c) I R (d) I R Figure 8.
Transmitted and reflected illuminances for a laser beam incident on a glassslab as functions of θ : (a) Transmitted beam 1, (b) Transmitted beam 2, (c) Reflectedbeam 1, (d) Reflected beam 2. of the angle of the incoming light beam from the source. The uncertainties bars arecalculated considering the calibration uncertainties and also the estimated ambiguityfrom the alignment of the sensor with respect to the measured light beam ( ∼
10 Ω).This value was estimated as the spread of the readings obtained when placing the LDRin front of a given beam multiple times. The solid line in all graphs indicates thetheoretical model curve fitted for each beam.The relative refractive index was obtained from each graph in figure 8. Table 2shows the estimated values for the 650 nm wavelength. A satisfactory agreement amongall estimates and the expected value (1.52) was found with percentage deviation below easuring light with light dependent resistors: an easy approach for optics experiments n mean and its uncertainty as( n max − n min ) / Table 2.
Estimated refractive index values for the glass slab to be compared with theexpected value of 1.52 for glass. n I T n I T n I R n I R n mean . ± . t ) and reflection ( r ) coefficients for an uniform planar interfacebetween two media where light propagates are given by [8]: r T E = E ⊥ r E ⊥ i = cos( θ ) − (cid:113) n − sin ( θ )cos( θ ) + (cid:113) n − sin ( θ ) , r T M = E (cid:107) r E (cid:107) i = 2 cos( θ )cos( θ ) + (cid:113) n − sin ( θ ) ,t T E = E ⊥ t E ⊥ i = − n cos( θ ) + (cid:113) n − sin ( θ ) n cos( θ ) + (cid:113) n − sin ( θ ) , t T M = E (cid:107) t E (cid:107) i = 2 n cos( θ ) n cos( θ ) + (cid:113) n − sin ( θ ) , (5)where the subscripts T E and
T M indicate the cases for light polarization normal ( ⊥ )and parallel ( (cid:107) ) to the incidence plane, E i , E r , E t are the amplitudes of the electric fieldof the incoming, reflected and transmitted light waves, θ is the light impinging angleand n = n glass /n air is the relative refractive index.The two polarization expected contributions to transmittance ( T ) and reflectance( R ) for each outgoing light beam on figure 7 can be calculated by taking the magnitudesquare of these coefficients and multiplying them adequately. For instance, thereflectance expressions for the first reflected light beam ( i =1) are given by R = | r | where | r | is the reflection coefficient for light incoming from air onto the glass surface.The transmittance expressions for the first transmitted light beam are given by theproduct of the transmittance for light crossing from air to glass and the transmittancefor light passing from glass to air. The same procedure is performed for the other lightbeams observed. Because the laser is a monocromatic source the expected illuminancefor each beam, as expressed in equation 1, can be modelled as: I Ti ( θ ) = α T T M + β T T E + γ or I Ri ( θ ) = δ R T M + (cid:15) R T E + ζ, (6)where i refers to the beam index, α, β, ..., ζ are positive real numbers which accountfor the amount of light for the two polarizations in the incoming beam and also for abackground baseline used for the same purpose as for the theoretical model presentedon section 3.1.However, another contribution for the background can be the result of the residualslightly off-beam light that can bounce internally many times and later comes off thefinite glass slab in different outgoing angles reaching the sensor therefore adding to theconstants values included in the fit.The data trends on graphs (a) and (c) of figure 8 show decreasing and increasingonly behaviors, respectively. Theoretically this follows from the fact that the easuring light with light dependent resistors: an easy approach for optics experiments I T , I R ) are given by purepowers of | t | or | r | which have the same type of trends. On the other hand the followinglight beams ( I Ti , I Ri with i >
1) do present a behavior that is similar to the graphs (b)and (d) where the terms are given by products between powers of | r | and | t | becauseof the internal reflections and consequent transmissions resulting on a slow rise of theilluminance as θ increases followed by a sharper decrease near the θ = 90 o angle.Overall, the measurements obtained with the LDR for this simple glass slab setupprovided data with good enough quality such that it is possible to make theoreticalinterpretations of the meaningful physics aspects of the experiment.
4. Discussion
The understanding of optical processes is deeply related to many advances in scienceand technology as it has also directly contributed to many improvements in our day-to-day activities. For instance, the microscope and telescope are the most known iconicexamples. But other important more contemporary developments of optical devices doemploy these physical principles such as optical fibers, laser sources and semiconductordevices used in telecommunications, energy generation and medical diagnostics andtherapy treatments. It is, therefore, a relevant and present topic that is applied indifferent areas of knowledge.The use of hands-on experiments together with other resources such as applets,animated images, and simulations can be much beneficial to learning [9], speciallywhen a subject is rather abstract and highly mathematized, as multiple reflections andtransmissions on interfaces between different media can be. Letting students becomefamiliarized with the characteristics of a measuring device and then proceeding with amore qualitative and subsequent quantitative analysis of a phenomenon and discussionson the results has the potential to improve their understanding on a given subject,promoting a more active attitude towards learning. For students these kind of activitiesare rich opportunities which facilitate a more experiment based study similar to theactual work performed in physics research laboratories.On the other hand, the reproduction in laboratory classes of the calibration andexperiments presented by this paper can be performed in different ways depending onthe didactic purpose intended and time available. In general, the acquisition of thedata presented in sections 2 and 3 are relatively short and analyses can be made withthe help of a computer and spreadsheet to speed up and avoid repetitive calculations.Although simple, performing the proposed experiments require adequate positioningand alignment of the materials so they are not displaced or rotated mid measurementscans. In some activities it might be of interest the students be left to figure out theirown methods to set up an experiment. On other situations initial instructions can begiven on how to run the experiment if a well defined procedure is expected to be done.For instance, in case the observation of the illuminance in a given situation is the onlygoal, the calibration step can be skipped if the experiment preparation is secondary. easuring light with light dependent resistors: an easy approach for optics experiments
5. Conclusions
The feasibility of the use of LDR as suitable detectors for optical laboratory activitieswas evaluated. Calibration of LDRs with satisfactory precision ( ∼ Acknowledgments
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