The Value of Observations: An Optics Activity

Dedication: I dedicate this and everything I do to the one educator who helped me appreciate the value of learning in the grandest of fashions, my late father Ibrahim Nadji (RhA!) Thank you Didi and may Allah (SWT) reward you for your dedication to raising educated citizens!

Physics, like other sciences, thrives with careful observations by its practitioners. Thus, it is imperative that we foster amongst our students the faculty of careful, deliberate, and conclusive observations. This would empower our students to appreciate even more the outcomes of the experiments they would conduct afterwards.

In what follows, I shall describe an activity that I use as a transitional activity that leads up to the discovery of the lens/mirror equation. The observations that the students make would eventually be confirmed or refuted by the said experiment and its emerging equation.

At each lab pod (the name I give my lab tables; another post shall explain the name ISA) four envelopes with optical pieces within them are set (the figure below show the optical pieces above their respective envelopes.) Two of the optical pieces are curved mirrors (one convex and another concave) and the other two are lenses (one converging and the other is diverging.)

White envelopes contain curved mirrors & yellow envelopes contain lenses

Two huge curved mirrors are also set on yet another lab pod. These will serve as further confirmations of the validity of what students may claim to have observed with the smaller mirrors.

Large Curved Mirrors

The students in each group are asked to rotate the optical pieces amongst themselves for observation purposes. And if at any point any one of them is done with their task, they should head to the big mirrors to complete similar observations to the ones they did with their respective small ones.

Curved Mirrors Observations Tasks: 

• The students are to hold the mirror close to their face within 10 cm or so. This set up shall be referred to as Short Range (SR) observation. 
• They would focus on a facial feature such as their nose for example and examine its image and pay close attention to its properties. 
• They would sketch a table similar to the one shown below and record what are the properties of the image of the object they are looking at. 

Observations Recording Table

• They must decide as to whether the image is upright or inverted.
• They must decide whether the image of the object is bigger, smaller, or the same size as the object
• They also must decide whether the image is real or virtual.
• Note: A formal definition of real or virtual image is not provided yet. And, when students ask me what is real and virtual, I tell them to conjure up a definition of their own for now but they must be consistent as they make their choices. I want this property of images to emerge from the students' own observations rather than from me or some other source.
• The students then would move the mirror farther but not much beyond 20 cm or so. This is the Mid-Range (MR) case.
• Finally, the Long Range (LR) case, which involves distances farther than 30 cm, is to be completed next.
• Once the students finish the above tasks, they are to repeat the same process with the other curved mirror and also with the two big mirrors but they do not have to record the observations for the large mirrors; it is optional.

Lenses Observations Tasks: 

• The students are to hold the lens close to one of their eyes and then look through the lens at an object around the room. The object has to be within 10 cm or so from the lens. This set up shall be referred to as Short Range observations case.
• Students then repeat similar steps for MR and LR situations and record the observations each time in a new table every time.

Once all of the above is completed, the whole class now is going to be involved in reaching ultimate conclusions regarding what has been commonly observed. Any variations amongst class members are going to become very visible now and the students must decide how to deal with the differences.

I put the original table (scroll above) back on the smart board and then began pulling three students' names at random from my index card set that has all the students names in it. I began with the convex mirror case first and I asked each of the randomly selected students to pick a favorite color of theirs to use to record their observations for the SR items. And, I kept doing this until all cases were taken in consideration. At that point I asked the class to select a class color and used that to poll the whole class as to what their choices were for each one of the situations, SR, MR, & LR still for the convex mirror case. The outcome of this whole process is summarized in the figure shown below.

Orange color is the Class chosen color while the other colors are those of the randomly selected students.

 I was expecting the last row to be the most problematic in showing variations amongst students answers as it did for another section of my Physix classes. But, in this class period, the majority of the students seems to have chosen the image to be virtual in all possible distance ranges. The fact that the students were not in full agreement about the size of the image is a bit surprising and I hope the lab along with its deduced lens/mirror equation would settle this beyond a shadow of a doubt. This process of selecting three students at a time and then polling the whole class takes up a good chunk of time but it is worth doing so that every student feels that their observations were acknowledged, appreciated, and ultimately cross checked with those of the whole class. The process that I follow with the mirror and the lenses is going to be different as described below.

The clicker system is fired up and the students with their clickers in hand, a set of rapid-fire clickerisms round is set to begin. Multiple choice letters are given to each of the choices amongst each of the properties (for example, A for upright image and B for inverted image). The students then are prompted to lock in their choices for each of the observations they recorded for each of the ranges of the concave mirror case. The results of this quick round of class-wide observations reporting is shown in the figure below.

Orange color is still the Class chosen color and the results of the present students' observations are shown with their corresponding ratios.

The second and third rows offer great teaching opportunities when the lab is going to finally be conducted and its relationship is arrived at. Students must confront their uncertainties about their claims regarding observations and a need for more precise ways of describing image properties becomes a necessity now. Qualitative observations can only take us so far but quantitative approaches help us pin down the nitty gritty of our claims.

Class ended with the above board complete and awaiting how it would look like for the lenses. I predict that the lenses observations are going to be a bit wilder, especially for the converging lenses.

Once the process is complete for the lenses, a demo shall be conducted so that the students begin the process of differentiation between real and virtual image concepts. Then, the students are to write a brief reflection on what they have learned thus far. Afterwards, the experimental set up is shown to students, a couple of experimental challenges are given, and finally the actual data collection process shall start. Hopefully, the details of what transpires next would be described in a future post.

In the meantime, please, share how you approach this very same topic of geometric optics in your own classes? Or, if you are a student or a general curious reader, how does this chime with how you learned these concepts in your respective Physix courses. Thank you!

Extensions to SHM in AP-Physics

Introduction:
It is very important that students in AP-Physics classes be pushed to go beyond the usual curriculum material. We owe it to them to conduct harder labs that would push their thinking and analysis limits.

What to do?
As an option that instructors may choose is to extend regular topics to include situations that are different, unusual, or simply more difficult to arrive at definitive answers. For instance, this year, the subject of Simple Harmonic Motion (SHM) was expanded to include the following extensions and twists.

Example 1: [From Simple Pendulum to Compound Pendula]
In this case, the students are handed rectangular wooden blocks and triangular prism wooden blocks and are asked to make predictions regarding these compound pendula. For instance, what would the period be? Will it depend on mass? Will the amplitude matter? How would this kind of pendulum compare to a simple pendulum? etc.

Student was using her mobile device to measure the period.

Example 2: [From SHM to Damped Oscillations]
In this case, the students are presented with a situation where the would collect data involving a spring-mass system whereby the mass is oscillating in water as opposed to in the air as is usually the case in regular labs. The following images show the lab set up and the results of the activity.

Closing Thoughts:

Student appreciate being challenged, especially in courses such as AP-courses where the expect an added level of difficulty and rigorousness. The added benefit of such extensions is that it offers instructors the chance to detect and address any lingering misconceptions related to simpler items from the regular curriculum. This is bourn by the fact that students who have gaps in their understanding of regular material, this gaps are bound to surface in these new challenging settings. And as such, these challenging additions may serve as a safety valves that enable us, educators, to address less understood concepts in our main curriculum.

Thank you for taking the time to read this blog entry and I hope you would add your own comments on the subject matter. What kind of extensions do you have your own students contemplate and go through?

Dance of the Changes: ∆p vs. ∆K

Once momentum p and kinetic energy K were derived and the connection between them was established, our task as a class was to find any connections, if any, between ∆p & ∆K. The derivations shown below were conducted in class with the participation of everyone using what I call "Stand/Sit Participation Method". This ensures that every student is active in the derivation process from beginning to end with emphasis on understanding all along.

Students were asked to compare and contrast the two relationships that were derived and only then did the following slide show up.

This, my friends, led to the Free Body Diagrams (FBD) challenges activity that eventually  led to the formulation of Newton's 2nd Law of Motion (N2L.)

A simple harmonic oscillator (SHO) attached to a force probe with a motion detector set below the mass that is attached to the spring provided the conformation of N2L.

The above derivation is aimed at achieving three goals.

1) To help students realize that Physix concepts are not disconnected islands, rather they are individual cells within the organism of Physix knowledge.

2) To establish the emergence of acceleration as a quintessential aspect of any changes in the state of motion of particles.

3) To overemphasize the complementarity between between space and time that relativity asserted and Heisenberg's Uncertainty Principle alluded to in Quantum Mechanics.

Thank you for reading this post and I look forward reading your valuable comments.   

Dedicated to the memory of my beloved father (RA).

Derivation of classical Kinetic Energy formula from STR

This year, thanks to NMC's media folks, I was able to use a lightboard (click here to read an article that describes how to build one) to put together two videos about Special Theory of Relativity (STR).

The first video (see the link shown below), goes through the process of deriving the classical formula of kinetic energy (K) from its relativistic sibling. The student were sent the link shown below and were asked to view it, take notes on it, record the said notes onto their IONs (Input/Output Notebooks), and then write a reflection paper on the subject matter as well as the video itself.

Kinetic Energy in STR Video (12:52 min): https://www.youtube.com/watch?v=-RfR-3-jiv4

The second video contrasts the two relativity relationships as understood by Galileo on one hand and the one formulated by Einstein on the other hand. The latter is also used to assist students in their understanding of how light speed remains constant in all inertial frames of reference.

Galilean vs. Einsteinean Relativity (6:21 min): https://www.youtube.com/watch?v=NGpVPG8Uilw

Once the students' reflections papers were collected, I challenged the students to justify the reasoning behind the Physicists insistence on inventing yet another relationship (that of K) that depends on the same physical quantities, mass and velocity.

Once satisfactory responses were obtained, I stated, "Now that we established connections between momentum p and kinetic energy K, would there be any relationship between ∆p & ∆K?" This led to the changes presentation, which I shall address in the following post.

After watching the two videos listed above, please, share your thoughts, reflections, and ideas about how you might use them in your own curriculum. Thank you

Dedicated to the memory of my beloved father (RA).

Physix Curriculum Map a la Mr. Le Nadj!

Students love Modern Physics topics. Unfortunately, most introductory Physics courses eschew Special Theory of Relativity (STR), General Theory of Relativity (GTR), and Quantum Mechanics (QM) because of their perceived difficulty.

For the past four years, I have been introducing more and more of STR early on in the year/semester. But, this year I used STR as a means of introducing classical Physics concepts such as kinetic energy. The mind map below summarizes the gist of this approach. It is important to mention that the Modeling Approach serves as the backbone and the glue that holds this teaching method together. Thus, the use of many abbreviations that only modelers would know.

Physix a la Mr. Le Nadj! Curriculum Map

In future posts, I shall address each of the branches. I shall also give samples of presentations material, examples of students reactions/reflections, and typical artifacts that assist in making the case for such a pedagogical approach.

Please, feel free to share your thoughts in the comments area so that readers like you would benefit from them personally or their students indirectly. Thank you

Dedicated to the memory of my beloved father (RA).