Teaching Refractive index with a Virtual Experimental Activity

The refractive index of a transparent medium is a physical property taught in the schools at the secondary level. It depends on the medium characteristics that can be easily shown with a simple experimental setup. This property also depends on the wavelength of the light and on the temperature of the medium. These dependencies are very smooth and schools usually do not have accurate experimental setups to allow students exploring the dependency in order to better understand this phenomenon. This work presents a simulation from the class Virtual Experimental Activity, to help teachers to provide experimental activities in the classroom to engage concepts that otherwise should only be approached theoretically.


1.
Introduction The refractive index of a medium (n) is a physical property that students learn in secondary school when they study the light refraction phenomenon.Formally, it is defined as the ratio between the speed of light in the vacuum (c) and in the crossing medium (v),  =   . (1) However, students get a better understanding of this concept as physical property of the medium when they do experiments with the refraction of light and apply the Snell's Law, equation (2), where the refractive index appears as a parameter in the formula [1], where n1 and n2 are respectively the refraction index of medium 1 and medium 2, θi is the incident angle and θr is the refraction angle.The Snell Law can, therefore, be easily verified at schools as the relationship between the incident and the refraction angles of a laser beam crossing the interface of two transparent media, leading to the concept of relative refractive index between the two media.An experimental setup with an ordinary protractor, a laser and a semi-circular prism made of any transparent material, can provide a good accuracy for this physical property up to two decimal places, expressing the dependence of the refractive index with the characteristics of the medium.So, a simple experimental activity helps teachers to engage students' understanding of the refractive index concept.
In physics the experimental activities, when correctly implemented, play an important role in the teaching-learning process, especially because abstract concepts can be better understood or contextualized [2].
However, students also learn that the refractive index depends on the light wavelength and on the medium temperature.
From a qualitative point of view the wavelength dependency can be demonstrated using a prism of glass to show the dispersion of the white light, and the temperature dependency can be logically inferred by the relation between the refractive index and the density and this one with the temperature.However, it is important for students to understand these dependencies in a quantitative way in order to better understand the graphs n(λ) and n(T) (figure 1) [3,4].
Figure 1: Examples of experimental graphs, taken from the literature [3,4], showing (A) the refractive index dependence of BK7 glass with the light wavelength, and (B) the refractive index dependence of water with the temperature.Therefore, we consider that the best way to improve this understanding is to provide experimental activities for students.Students can better understand these relations if they contextualize them with an experimental activity [5,6].That approach not only enhances the conceptual attributes of the refractive index but also helps students to develop experimental skills especially when the experiment is explored interactively as an inquiry-based learning, which is very important for any scientific training [2,7,8,9,10,11].
Unfortunately, in practice, the refractive index has a relatively small dependence on wavelength and temperature, so the value variation occurs after the 2 nd or 3 rd decimal places.This means that a variation of 400 nm in frequency or 100 °C in temperature, results in a refraction angle variation that can be less than 1 degree.Therefore, a more complex and accurate setup is required to measure the variation of the refraction angle, which usually schools do not have.That is why usually at schools, these phenomena have only a theoretical approach with graphs interpretation.
Since the beginning, simulations have been used to enhance the teaching-learning process in physics.They are very important pedagogical materials that improve the understanding of physics concepts [12,13,14,15].In most cases, they work on the conceptual aspects, but only a few develop some experimental features of the phenomena.

A B
For the topic of the refraction of light, there are simulations like the PHET [16] (figure 2) that allow a quantitative study of the refractive index dependence with the light wavelength.In that particular case, students can build graphs, but in fact, they do not make any kind of direct measures, they simply collect data that is displayed in the simulation by activating the "Angles" function.This proceeding does not correspond to what is done in a true experimental activity, so we decided to create a simulation that allows students to make experimental activities as if they were in a laboratory with very accurate equipment.Light" (https://phet.colorado.edu/en/simulations/bending-light).The virtual protractor cannot measure the tiny variation of the refraction angle (0.4º) due to wavelength variation.Students have to read the angle value after choosing to visualize angle data.

2.
The simulation

Simulation characteristics
The simulation that we present in this work is classified as a Virtual Experimental Activity (VEA).VEAs are computational pedagogical simulations designed to help students to develop experimental, conceptual and procedural skills [17] whereas studying a phenomenon with an experimental setup in a virtual environment.
Its goals is to provide students (secondary schools and faculties) the experimental study of the reflection and the refraction phenomena for monochromatic or polychromatic light, and particularly the experimental study of the refractive index dependence with the light wavelength and the medium temperature, focused on the experimental skills of the users.
The simulation was built with the Easy Java Simulations software developed by Francisco Esquembre [18] and has two versions, the teacher version, with features that allow seeing hidden data and the student version with no possibility to access relevant data or help features, such as the position of the normal axis in the interface of the media [19].
The simulation has two main environments (Figure 3).The simple one is similar to many other simulations of the refraction phenomenon (Figure 3A), while the other one is an experimental setup environment that provides accurate virtual instruments to allow measuring tiny variations of the refraction angle (Figure 3B).Another feature of this simulation is the possibility to visualize the white

2.2.
The virtual setup The experimental setup environment is constituted by a collimator (figure 4A) that is a source of monochromatic or polychromatic light and has a slit whose thickness can be controlled by the user.
At the centre of the setup, there is a rotating base with a protractor where two distinct transparent prisms can be fit over (figure 4A).The rotation is controlled by a micrometre cursor that gives the angle of rotation with three decimal places.
The light detector is a telescope fixed to the base but that can move around it, triggered by a micrometre and a nonius (figure 4B) to fine-tuning its angle position up to three decimal places.The telescope has a "virtual system of lens" that ensures the detection of the light deviation due to refraction.The simulation provides the display of the eyepiece of the telescope (figure 4B) where we can see the image of the collimator slit as a colourful line in a black background.The eyepiece has a vertical white crosshair line that represents the centre of the telescope -aligning the white crosshair line with the colourful line gives the angle of refraction of the light ray.The temperature study The simulation allows the experimental study of the water refractive index dependence with the temperature.Therefore, only when, at least, one medium is water the simulation enables access to the Heater/Cooler setup that consists of a heater disk to heat or cool the prisms and a heat controller (slider) to control the flux of the thermal energy in the disk.A thermometer is always available to measure the temperature of the environment (figure 5).

2.4.
The setup errors The exploration of a VEA takes into account the experimental errors coming from the virtual instruments and from the user's dexterity.In this simulation, the virtual instruments of the experimental setup environment were designed to allow students to measure angles more accurately than usual, but without preventing them from introducing uncertainties into the measurements carried out, as it happens in a real experiment.
To estimate the measured error in the telescope's micrometre, students must analyse the smallest variation possible with the nonius.To evaluate the user's error, they can estimate half of the angle variation between the two extremes of the slit image in the display.
Before rotating the setup base, students can calibrate the telescope alignment with the collimator slit in order to control systematic measuring errors.For that, they need to switch on the collimator and then align the white mark of the eyepiece with the colour line from the collimator and then press the button "Calibration".That turns the telescope angle position to zero and the superimpose of the two marks must be done from now on, always in the same way.The temperature measured by the thermometer is conditioned by the variation rate imposed by the heat controller that never reaches the real value.So, the temperature is in constant variation giving a measurement error in degrees Celsius with two decimal places when it is stabilized in the thermometer display.The physics modelling The refraction phenomenon in this simulation is modelled by the Snell Law with the refractive index of the media dependent on the light wavelength by a 2 nd order Cauchy equation.Each medium is characterized by two Cauchy coefficients, A (related to refraction) and B (related to dispersion).The Cauchy formula [20], equation (3), gives a good approximation of the refractive index (n) in the range of the visible light spectrum, where λ is the light wavelength in vacuum.
For the temperature dependence study in water we use an empirical 4 nd order Cauchy equation based on a scientific paper from Bashkatov and Genina [21], where all the four Cauchy coefficients are dependent with the temperature.
The water heating or cooling obey a simple solution from the Newton's Law of cooling to modelling the temperature variation in water, and a spatial condition was imposed to create a temperature gradient along the environment.

3.
Example of data collected and analysed using the simulation As an example, we present some results obtained by using the simulation where the light goes from the vacuum into de water.The uncertainty in measuring the incident angle was the instrument error (0.001º) while the refraction angle was estimated in 0.007º due to human error when aligning the white crosshair line with the colourful one with the default thickness, in the eyepiece display.
We determined the water absolute refractive index for a light frequency of 508.9 THz, at 25ºC, as 1.3321 ± 0.0001 by a fit regression of the data (figure 6).The scientifically tabulated value of 1.3324 for those conditions [22], leads to a relative error of 0.02%.Figure 7 shows the graphs for the water refractive index (nw) dependence with the wavelength (λ) and the temperature (T).

4.
Conclusions We expect that the simulation we created and presented in this paper will enhance the learning of the refractive index concept and, at the same time, develop in students' essential skills that are so important in learning physics and science in general.Both teacher and student versions of the simulation can be downloaded from reference [19].The simulation is still in evolution and more features will be added to in the future.Due to its characteristics, the simulation can be used as classroom activities in high school and first year university courses.In the near future, an investigation will be designed to evaluate the effect of this simulation on students' motivation and understanding of Snell's Law, and how teachers can take advantage of the simulation as a complement to their theoretical classes.

Figure 2
Figure 2: Two screenshots from the PHET simulation "BendingLight" (https://phet.colorado.edu/en/simulations/bending-light).The virtual protractor cannot measure the tiny variation of the refraction angle (0.4º) due to wavelength variation.Students have to read the angle value after choosing to visualize angle data.
the creation of generic media with specific refractive index and specific dispersion rate (figure3B).

Figure 3 :
Figure 3: A -Screenshot of the simple environment of the simulation.B -Screenshot of the experimental setup environment showing the white light dispersion after crossing the interface of two prisms with generic media, each one with a certain refractive index and dispersion rate.

Figure 5 :
Figure 5: Under the base, a heater disk increases the temperature of the setup controlled by the Heater/Cooler controller (placed in the up right of the image).

Figure 6 :
Figure 6: Data table and graph for the water refractive index determination.The refractive index was obtained by linear regression and the error bars indicate the propagated error for the indirect measurements.

Figure 7 :
Figure 7: A -Graph for the water refractive index (nw) dependence with the light wavelength (λ) at 20ºC.B -Graph for the water refractive index (nw) dependence with medium temperature (T) for 589.1 nm wavelength.