2.1

Laws of Reflection

Figure 1 shows a mirror on the top of a Hartl disc, and two laser beams: one corresponding to the incident light and the other to the reflected one. This figure was taken from a video, available at http://www.fc.up.pt/physletspt/Videos/Reflection_1.mp4, which can be used in class as an experimental activity, or out of class as a homework.

Figure 1:

Incident and reflected beams on a flat mirror

To analyze the video and extract experimental data, students have to position the origin of the local referential frame at the ray’s incident point, and align one of the referential axis with the mirror’s surface while the other axis points to the normal direction (perpendicular to mirror plane). Then they only have to use the protractor tool (either from the Hartl disc, or from Tracker) to measure the angle of the incident and reflected rays against the normal axis (figure 2).

Figure 2:

Analysis of one frame of the video with Tracker. The local referential and protractor tools are visualized: the red protractor measures the incident angle while the blue protractor measures the reflected angle.

As the incident angle changes along the video, students can measure the incident and reflected angles for different frames (don’t forgetting to readjust the referential frame at each measurement). This way experimental data is obtained, which will allow them to realize that both incident and reflected angles are equal within an experimental error.

The proposed video based experimental activity (VBEA) has several advantages to students: (1) Manipulation of concepts such as normal axis, incident and reflected rays, incident and reflection angles; (2) Use of the protractor as a tool to measure incident and reflection angles; (3) Understanding the need of a reference frame and; (4) Learn the laws of reflection in a “hands on” point of view.

2.2

Snell’s Law

The refraction phenomena is more complex than reflection, and the association with quotidian situations like the broken spoon image when submerse in a glass of water, will be better understood if students see what happens with a light ray, at the interface of two transparent media.

The classical classroom experiments of refraction with a glass prism or water, are very important to allow the discussion of this phenomenon, and once again the video analysis can be a good complement to it. By recording a video of the refraction phenomena with a transparent medium, students can use Tracker to analyze it, in a similar way as described above. In our experiment, we have used a semi-circular transparent body that rotates while a red laser beam is placed at a fixed position (figure 3).

Figure 3:

Video frame from our experiment, where a semi-circular body is crossed by a laser beam.

The incident ray is refracted at the flat interface between the body and air. We can observe in figure 3 that the incident angle (θ_i) is bigger than the refraction (or transmitted) angle (θ_t). Using the protractor tool from Tracker, students can measure these angles for several frames. From Snell’s law,

and by considering n_air≈1, the refraction index of the body can be easily obtained. A statistical treatment of data (linear fit and corresponding standard deviation) can be done from graphic representation of sin θ_i vs. sin θ_t. The value obtained for n_body can be compared to those listed in reference books for acrylic and glass materials, to identify the possible composition of it.

Students can also study the total reflection of light, by providing them a video or a sequence of photos where the incident angle (measured from the transparent body) increases until no light is transmitted, and we can only see the incident and reflected light rays at the flat body-air interface. This will allow teachers to introduce the concept of critical angle, θ_c, and students measure it with the protractor tool. Using, in that case, equation(2),

students can determine nbody and compare this value to the one previously calculated.