# Day 56

Today we looked at the results of the diverging lens data. Here is a quick pic of some results:

As you can see, the -1 slope still comes up, but now the line is in quadrant IV of the Cartesian coordinate system. The inverse of the focal length is still the focal length, but now it is negative, which is the convention used for diverging lenses. So the thin lens equation still applies.

Once we discussed this, I proposed the following challenge: Find the object location for your diverging lens that will result in the image being 1/5th the object size. I used 1/5 instead of 5x because the image for a diverging lens is always smaller than the object. Something to do with the pesky geometry of the lens.

# Day 55

Today the kids collected data using the double lens technique to graph the do and di for a diverging lens. The goal here is to see if the thin lens equation still fits, and if there are any differences between the results of a converging and diverging lens.

I spoke at length about this technique yesterday, but here is a document i dug up in my files, that talks about it at length.

The initial results look pretty good. I will post some of the results tomorrow after we look at them in class.

I also plan on having the kids go back and solve those double lens problems they got late last week. Since they had to look at them before learning how a double lens system works, I want them to go back and look at their old methods and compare it to how they should be done. We will look at those later this week too.

Bonus Stuff:

This is for my chemistry students, who were slightly confused yesterday when I declared that not only are metals a better conductor of thermal energy than water, but that it was as much a fact as bears eating beets.

Also, it has been a while since I posted something from Smarter Every Day. this video is just to awesome.

# Day 54

It has been a while since I posted last. Life has been getting in the way. Namely the upcoming gun deer season and planning school around my future trip to Trees for Tomorrow.

As such, as of now, I am going to focus on Physics for this blog. I only teach this curriculum every other year, and as it digs deeper into the Light models than probably most classes, I am going to try and share what I can about this class.

Days 51-Today

We wrapped up looking at lens action, and with the conclusion of the Converging lens lab, we did a problem set dealing with quantitative lens problems. The problem set has some nice features:
– a set of problems that gives the students do, di, hi, ho, f, or any combination thereof. They have to pose a verbal solution to the question, do the algebra to solve for stuff, then a scale drawing for comparison.
– some questions that force the students to deal with the fact that M=hi/ho=-di/do. That negative sign (oh you gotta love the negative signs if you love physics) shows up in a few problems that only work IF you don’t ignore it. By the way, that sign is an indication that the image formed is inverted compared to the object.
-there is also a few questions that make the students deal with the diverging lenses, but just enough to kind of get them thinking.

The last few questions involve adding a second lens, specifically a converging lens. Most students, due to lack of another option, use the image formed by the first lens, as the object for the second lens. One question in particular though, makes them deal with an image that forms beyond the second lens, so that their is no light coming from a real image and passing through the screen. To add to the challenge, the image forms directly on the focal point.

Most kids say that there is no image as a result. They know from previous experience that if an object sits on the focal point, then no image forms. The problem is that there is no object or image forming on that focal point. Because the second lens is dropped in before the light that forms the image from the first lens can converge, it creates a problem. Still, that second lens acts like there is an object 20 cm from it even though it is not there.

Doesn’t that sound kind of I like a virtual image? Only this time, it’s acting like an object. So letters treat it like a “virtual object.” In this case do is negative. Using that along with f, you can use the thin lens equation to find the image placement.

We develop this solution because it leads to yet another possibility: can we use two lenses to figure out where a virtual image forms, such as with a diverging lens. So we set it up, and take a look. Sure enough we can set up a light source, diverging lens, and converging lens and get an image to for on a screen. How do you use this to figure out where the virtual image formed with the diverging lens?

Take the diverging lens out. Ok, now your image on the screen is all blurry. But if you slide the light source forward, all of a sudden, the image reforms. Why? Because the light source is where the virtual image was! From this, you can get the image distance for the virtual image.

What if we took a bunch of data for do and di for the diverging lens. Does the thin lens equation still work? We find out tomorrow.

# Day 50

Tuesday, November 11

Physical Science: Today kids worked in groups to answer post-lab questions for the double beaker lab. The questions are really just guiding questions. I will probe for deeper understanding when they present their results. I like this activity because it gets kids thinking about the role of energy in phase changes, behaviors of matter, and also forces them to supply evidence for their conclusions or hypotheses.

By the end of the hour kids were preparing white boards for tomorrows presentations.

Chemistry: Today’s class was shortened due to our Veteran’s Day program. We did get white boards of the Icy Hot Lab prepared, and we shared in a small group presentations, with 3 out of the 4 other groups in class. Findings were all pretty much the same:

The one thing that nobody really mentions or even thinks about is what is happening at those plateau’s.

“Is energy being constantly added to the system?”

“Yes.”

“Well then why isn’t the temperature changing at those flat spots? We’re adding energy, shouldn’t the particles be moving faster?”

Most will guess (as will my Freshmen in their lab discussion tomorrow) that the ice keeps the water cool and from changing. Of course, this is logical, but incorrect. What about at the high end? nothing is keeping the water “cool,” so why isn’t it changing? That is the big question to answer today.

We also need to look at what kids have for particle diagrams at these stages. I took this picture out of a notebook yesterday that I plan on sharing in class tomorrow:

Physics of Light: Kids took the Lens Action Quiz today.

# Day 49

Monday, November 10

Physical Science: Today we started a new unit on States of Matter and their properties/behaviors. To get us going we do a lab called the “Double Beaker Lab.” Here is a picture of the setup.

One beaker is on the hot plate, and another is suspended above it. There are all sorts of goodies to talk about with this. The kids have to add either water or ice to the beakers, and then slowly heat them up until I call time. They measure the temperature every minute for both beakers. Every 3 minutes they have to make a set of observation. Tomorrow they will work on some post-lab questions.

Chemistry: Today they did a lab called the “Icy Hot Lab.” This ties into the question from the end of class Friday. It really is not at all different from the above set up, but we use a large beaker of ice and digital temperature probes. Tonight they are making graphs, and answering a few short questions.

Physics of Light: Today they had to complete their Post-Lab challenge. Most groups went with the quickest method over the most accurate method. The quickest is to just set up a real image and take the do and di and the lens equation to find “f.” The most accurate method is to collect several points, make the graph, and analyze it. The graph method also makes short work of finding do and di for M=3 if you use the graph method I discussed in the last post.

Groups were successful to varying degrees. most did not use the method we developed in lab, which is the most accurate method. A lot of groups just took one data point, used the thin lens equation, and called it good. 1 data point does not always work, it’s pretty hit or miss. Graphing several data points and using LoggerPro was the best way to go about this. plus, they could have used the graphical method to find the do and di for the Magnification. But most just did the algebra.

# Day 48

Friday, November 7.

Physical Science: This was a bit of a hodge podge today. 2 classes played Chem Scrabble, a game invented by some bored study hall kids about 10 years ago. Basically they make words out of the atomic symbols. It’s a fun game, plus it subliminally gets them reading and figuring stuff out with the periodic table. A benefit for when that unit comes up later.

The odd class out read and worked on the “Particles in Motion” article that the other classes did a few weeks back.

Chemistry: We reviewed what temperature was all about, and then introduced the difference between this and thermal energy. For good measure, we also introduced the concept of heating (heat). We watched an episode of Eureka! to do this.

I do disagree with some of this video. What it calls heat, I call thermal energy: the total energy of all of the particles in a sample of matter. Heat is a process, one of the 3 methods of energy transfer (working and radiating are the others.) Heating is the trnasfer of energy when particles bounce off of each other.

From this we got back to talking about energy and states of matter. I posed a question that came up about Anders Celsius:

“How did he know when to mark off his thermometer? Doesn’t the mercury in his test tube keep expanding?”

So I thought maybe we should look into that finally. So we will on Monday.

Physics of Light: We finished up with our converging lens lab discussion. I thought it was important to tie in the relationships we saw in the Pre-Lab portion with our new data, specifically the image sizes. So, we looked at the geometry of the lens, and found that di/do = hi/ho, where we have the height of the image and the height of the object. This gives us the chance to see what do and di would have to be for a certain magnification.

So we used the thin lens equation to figure it out. Then I showed the kids how, if you have data for the lens, you could find do and di graphically. Basically, if you have the Converging Lens data, you can create a data set with the line: 1/di = 1/Mdo + 0, where M is the magnification you are looking for. Where the two lines cross, is the 1/do and 1/di that will give you the magnification you are looking for.

You can do the same thing by graphing 1/di = -1/Mdo + 0, but this is a little outside of what we have talked about so far, especially since it means you get a negative image distance…another day my friends.

I then gave the kids a lab challenge, instead of the typical post-lab write up: find the focal length and power of an unknown lens, and find do and di such that M=3. We will be doing this on Monday.

# Day 47

Thursday, November 6

Physical Science: Today we took the Unit 2 Exam.

Chemistry: Today we took the Unit 2 Exam.

Physics of Light: Today was the bid discussion day. Students presented white boards on their converging lens lab. Below you can check out their white boards.

As you can see, most groups managed to figure out the important things. Such as the y-intercept is the inverse of the focal length (1/f). They also managed to see that (1/fh) + (1/fb) = (1/fhb). This is used to see what happens when you stack lenses together and combine their bending powers. It actually makes for a great way to introduce lens power (Power = 1/f in diopters when the units are inverse meters.) Basically power is a rating for how well the lens bends the light. The larger the lens power, the shorter the focal length, and the faster (shorter focal length) the light reaches the focal point.

We also talked about the meaning of the slope, as we always do. A lot of groups said it was the ratio of (1/di) to (1/do). When you look at the data though, one group said it best:

“We think it represents that as the (1/do) increases, (1/di) decreases at the same rate. So basically since it the inverse, as the object distance gets smaller, the image distance increases by the same amount.”

That would certainly explain  -1 slope. It also only works for situations where a real image forms…or maybe not. We still have to investigate and deal with virtual images at some point.

We did of course derive the thin lens equation as well. But more on that later.