Visualizing focal point of a lens in 3-D

This post is about a simple experiment that excited my class and me. I have done a lot of experiments showing t focal points of lenses by using flat optical systems like magnetic set on the board, horizontal set on the table etc. Obviously, these were good illustrations for drawing optical diagrams. Last week I came up with the way to show my students a focal point of the converging lens in 3-D with no screen or the likes. The system consists of three identical lasers creating parallel rays, a converging lens, and humidifier to create a fog.

three-laser system

The picture below shows what we have seen in class. Three rays intersect in the middle of the air in the focal point. Later we calculated a focal distance using standard methods and proved that the focal point was correctly identified. Video can be seen here.

three rays focal point

What do you think of this experiment? Was it worth our excitement? Did you do something similar? If yes, can you share your experiments?

Damped oscillations in mechanics and electromagnetic induction

Do your students like the topic of electromagnetic induction? I believe my AP2 does. We try to do a lot of experiments, and usually, they work well for understanding. Lately, my colleague Dr. Feofanov and I came up with something new to us and I would like to share it with you. I already wrote about a simple experiment with a solenoid, magnet, and oscilloscope. It showed an induced current. A new experiment shows the effect on the source of the EM induction.  An idea for this experiment came up when we were playing with Vernier force probe for damped oscillations in mechanics. I believe that all the teachers in the world tell their students about the analogy between EM induction and inertia. Our experiment is one of the simple illustrations of this analogy.

Let us start with a mass on a spring.

mass on a spring

Force probe shows almost ideal harmonic oscillations.


Then we added a paper plate to create damped oscillations.

damped mass-spring

The resulting graph is below


These two experiments work well for AP1. Now let us play with EM induction.

spring-mass-coil Our system consists of the set of magnets on a spring and a solenoid. Initially, a solenoid is not connected to any circuit. The result – harmonic oscillations due to the absence of any induced current and magnetic field.

harmonic magnet

Then we short-circuited the coil. The induced current created a magnetic field that, according to the Lenz Law, has the same effect on the magnet as a paper plate on a simple mass. Magnetic force worked exactly the same as a force of air resistance.

damped by induction

We played more with the magnets of different masses and strengths. The best results we got with the addition of neodymium magnets. I think we added a nice experiment to our long EM induction list.

What do you think? Any good ideas on improving this experiment? Your thoughts will be helpful.

A simple mechanical energy lab with Vernier probes

Time is always a factor in class, especially if you teach AP courses. To set up and run a good lab assignment takes a while. The more we work with Vernier Dynamics Cart and Track System with Go Direct® Sensor Carts, the more we appreciate them. They are real time savers. For example, the law of conservation of mechanical energy lab (one of the versions). The setup takes 2-3 minutes per group. Students experiment with the conversion of potential gravitational energy to kinetic energy. From my experience, usually, students understand well that kinetic energy is zero at the starting point and potential gravitational energy is zero on the floor (if we make it a zero level). More troubles they have for intermediate moments of time. I always do a lot of problems that involve these intermediate points, including graphs of kinetic and potential energies. But some students have problems with it anyway. I believe that the described lab can help to eliminate some of these difficulties.


The simplest setup that includes a cart, track, super pulley, and weight on a string. If you run it once, you get graphs of position and velocity.


Now you can analyze as many points as you want. Calculate kinetic energy, potential gravitational energy, work of gravity etc. Changing masses of the cart and/or the weight on the string, you can get as much material for the analysis as you want. I asked my students to analyze just one graph because it was only the first part of the lab, the second was on the spring potential energy. But the results were really good. Graphical Analysis 4 allows you to modify graphs to present different calculated values. Below are the examples:

  1. Potential energy

potential 2. Kinetic energy


3. And the best of all – both on the same graph (I added also total mechanical energy)


Due to a really low friction total energy is almost horizontal. For many years I have given to my students a problem that required to draw these graphs. Now we can on the fly get these graphs from the lab experiment.

All these experiments you can run with non-wireless Vernier equipment but I was never successful with motion detectors, and the process of setup always have taken a lot of time. With new equipment, it takes just 2-3 minutes.

Disclaimer: I have never worked for Vernier nor got any payments from them 🙂 I just appreciate their new products.


How Vernier wireless equipment helps to solve AP problems

Two months ago our department was able to buy a class set of Vernier Dynamics Cart and Track System with Go Direct® Sensor Carts. This is a fantastic set of equipment that allows us to do on the fly a lot of different experiments on mechanics. I will try to describe how it helped to show our students to see the solution of a typical AP problem. The problem I am talking about asks to compare the time a block on an incline moves up to the highest point with the time it returns back to the initial point. Despite drawing correctly the force diagrams for moving up and down, most of the students still thought that it takes the object more time to go up than down. Simple explanations did not work. The only way to change their minds was to run an experiment. The initial idea came from Brian Frank’s tweet. My colleague Dr. Feofanov and I ran this experiment with our  Go Direct® system.


If you run this experiment with a small incline angle, the results will be the best. We just gave a cart a tiny push and collected the graphs of displacement and velocity.

incline up-down 1 Looks like a perfect parabola, but if you apply quadratic approximation,

incline up-down 2 it becomes obvious that the way down will take more time. The results are even more obvious for the graph of velocity.

incline up-down 3.png

You can even compare the areas under the graph and see the immediate time difference

incline up-down 4

incline up-down 5

Vernier Graphical Analysis software is so easy to use. I was always a big fan of Logger Pro, but this one works on Chromebooks and all phones and tablets. All the play with the graphs that are described above takes two minutes of class time but the effect is invaluable.

Astronomy experiments using Vernier sensors (Part 2)

As many of us remember, Kepler mission discovered that more than 2000 stars have exoplanets. 650 stars have multiple discovered planets. After creating a model of planet transit described in part 1 of this post, I tried to use the same idea to model a light curve for a star with more than one planet.

Multi-planet star system

I used the same pendulum as in part 1 to model the first planet. The second planet was modeled with a smaller bob (the size of a ping-pong ball) and shorter length of a string (about 0.8 m). Shorter string gives a shorter period. According to Kepler’s Third Law, I put this pendulum closer to the “star” (same light bulb as before). Below you can see the resulting light curve.

two planets curve   We can clearly see that the smaller “planet” gives us sharper and narrower gaps. The gaps have comparable deepnesses due to the close light flux covered. If you play with different distances from the “star”, you can get a larger difference in deepness.

The main features are clear: periods (distances between minima) can be easily found for each “planet”. I will try to set up a lab assignment that involves both single- and multiple-planet systems. This topic comes in my astronomy course later.

In part 3 I will describe how I was able to model a binary star system using the same Vernier Light Sensor.

Astronomy experiments using Vernier sensors (Part 1)

I have not written anything for a while but now I have a good reason to do it. I believe that I was able to improve some experiments from the Vernier website and introduce something new. This post is about modeling planet transit using Vernier light sensor. The second part will be on modeling ecliptic binary system.

Planet transit

Planet transit is a passing of a planet in front of the star’s disc. We can see Mercury and Venus transits from the Earth. Next Mercury transit will occur on November 11, 2019, Venus’s transit will happen in 2025. Planet transit is the major event in a process of finding exoplanets. When a planet moves through the star’s disc, the star’s luminosity decreases and our instruments can measure this decrease. On the so-called light curve of the star (graph luminosity vs. time), we can see a typical gap.

Light Curve of a Planet Transiting Its StarImage from

Vernier website has a description of an experiment to model this event

This experiment shows a one-time event. But we can change it to show a periodic nature of the event. I put a pendulum with a bob of a tennis ball size in front of a light bulb. I used a long 1.8-meters pendulum to increase its period. Light bulb on the right is a standard 60 W LED. On the left is a Vernier light sensor.


The resulting light curve is shown.

transit light curve

On the graph, we can easily find a period of the “planet” revolution. Changing the distance from the “star” to the “planet” as well as the size of the “planet”, students can see how the light curve changes. They can also change the pendulum length (“planet’s” year).

In the second part of the post, I will describe a model of a multi-planet system.

Mass on a spring through oscilloscope eyes

A few days ago I bought PicoScope 2204A, a digital oscilloscope that uses a computer as a screen. I started to play with it from usual experiments like AC current graph, a voltage on AC/DC converter etc. I showed it to my colleagues, and our department head asked me where I can use it in my course. I teach AC current to my AP physics 2 class after the exam, and that is what I told her. Then I started to think where else I can use it. Here is my first idea.

This instrument, unlike old scopes, can show stable signals of low ( less than 1 Hz) frequencies. I put a few round magnets on a spring and placed them inside a big diameter coil connected to the scope. When I started mass-on-a-spring oscillations, the result was almost a perfect sine graph. Changing springs and a number of round magnets in a stack, we can easily find how frequencies change depending on the system parameters. Or we can find a spring constant and compare it with direct measurements done using Hooke’s Law. I believe that this idea has some good potential for the experimental problems and labs. What do you think?

Remark 1. This scope does not have a stable software for Macs.

Remark 2. After this post was written I saw the great author of the blog Teach.Brian.Teach. Brian Frank’s tweet with another method of mass-on-a-spring oscillations lab using Vernier probes. I really like it.

“Mysteries” of an apparent weight.

A couple of days ago I was working on my notes/plans/lessons for the upcoming school year, and the topic of weight-apparent weight came up. Every year it bothers me how to make it more clear for students. Finally, I decided to dig in. Many textbooks avoid defining apparent weight. Regular weight is defined as the force of gravity on the object. ISO definition (ISO 80000-4:2006, Quantities and units – Part 4: Mechanics) :

Fg = mg, where m is mass and g is a local acceleration of free fall.

Remark: When the reference frame is Earth, this quantity comprises not only the local gravitational force but also the local centrifugal force due to the rotation of the Earth, a force which varies with latitude.

Ok, almost clear 🙂

Now, apparent weight. Out of all strange definitions in different sources, the only one that works for me is the operational one:

Apparent weight is what the scale shows.

Great. It means that it is the force that applies to the scale. That is what I always tell my students. This definition also works well if the buoyancy force is involved as well as if something is weightless.

I just have to remember to tell my students not to read a Wikipedia article on this topic. The definition there is

apparent weight is a property of objects that correspond to how heavy an object is.

Force is “a property of objects”. How about ‘heavy’ in weightlessness. Ok, let’s forget it. I have real questions that bother me.

  1. If a rollercoaster cart or a plane makes loop-the-loop, is an apparent weight of the driver or the pilot directed down?
  2. If a car accelerates horizontally, is apparent weight directed at the angle arctan(a/g) to the vertical?
  3. If the object is in a centrifuge, is apparent weight directed at the angle arctan(v^2/rg) to the vertical?

To me, the answers to all these questions are the same: Yes. What do you think?

Always believe in the laws of physics

Yesterday on Facebook someone posted a picture of a hammer “floating” on the edge of the table with the help of a ruler. One of the comments was “It is possible only theoretically, the picture is a photoshop. I decided to check and prove that physics always works. Here is a picture (not a great angle, but you can get the idea).


Only one inch of the ruler is on the table, but it is enough for the system to stay at equilibrium. You can try it at home, it takes 30 seconds to set up. It is a perfect illustration of a static equilibrium, even better than a bird made of a potato, two forks, and a toothpick. Next year I will give my classes a lab problem to find a position of the center of masses of this system.

Can you recommend your favorite experiments?

Twins Paradox and Special Relativity

This post is a bit off topic to my blog, but there are some things in popular science that really bother me. One of the groups that I follow on Facebook posted a clip on Twins Paradox in Special Relativity. Again! There is no such thing as Twins Paradox in Special Relativity. In order to compare the ages of the twins, you need to return them to the same point.  You have to accelerate (decelerate) at least one of them, making his/her frame of reference a non-inertial one. This means we cannot longer use Special Relativity. Only General Relativity has non-inertial frames of reference. For detailed explanations one can look at the famous Landau & Lifshitz book.

To me, it was always a criterium of a good vs bad book on Special Relativity: if there is a chapter on Twins Paradox, I would never buy a book.