Can you look at some real physics with Angry Birds? Of course. Normally, I just like to make models of the physics (realistic or not) in the Angry Birds games - but this is a little different. Above you see one of the Angry Birds Telepods. Basically, this is something you can purchase in a real life store. This one is for Angry Birds Go! it's a car that comes with a stand. When you place the car and stand on top of the camera in your phone, you can load that car into the Angry Birds Go! game. Pretty cool, right?
But there is some real physics here. If you look at the bottom of the toy car, there is a small QR code. The stand has a little lens in it so that the camera gets a magnified view of the code to scan it in and load your car.
Converging Lenses
The telepod stand just has one lens in it. It's a converging lens. The basic idea is that when light goes from air to this plastic, it can bend (refraction). The lens is curved such that parallel light rays pass through the lens and then converge at one point. We call this point the focal point. Here is a basic light ray diagram. A quick note about light rays. These light rays are one way to give a visual representation of the way light waves are traveling. If you like, you can imagine each of these rays are straight from a laser pointer.
Maybe you can see why it is called a "converging" lens now. There is also a focal point on the other side of the lens. If a light ray passes through this focal point first and then enters the lens, the ray will come out parallel to the axis of the lens. There is one more special case for light rays. A ray that passes through the middle of the lens will not be deflected.
But how does this lens work? How does it create an image of something? Suppose I put an object (we like to draw the object as an arrow so we can tell which way it is oriented) in front of the lens. Light from somewhere will reflect off this object and go out in many different directions. Some of this light will probably reflect to your eye so that you can see the object directly. However, some of the light will also go through the lens. Here is a diagram that shows just three of these rays that reflect off the object and go through the lens.
I have labeled the distance from the object to the lens as o and the distance to the image as i. But why is there an image there at all? Suppose you were on the left side of this lens and the object was on the right. Since the light rays from the top of that object all cross at the location of the image, your eye would think (well, your brain) that the object is RIGHT THERE. In fact, it's not just a trick of your brain. Since the light rays are actually all meeting in that one location, you could put a piece of paper there. These light rays would then reflect off the paper and form an image on the paper. It's pretty cool.
You just need a couple of extra items and you can see this real projected image with the Angry Birds telepod. Grab a flashlight and something to project the image onto. I used a sheet of paper. You will need it to be dark, but here's what it looks like with with the lights on.
The key is to have the screen dark. This means you want to just shine the flashlight at the Angry Birds car. The light reflects off the car, goes through the lens and makes an image on the screen. You will need to play around with the position of the car and the lens until you get a focused image. It's not so easy to take a picture of this but I at least have something.
Yes, that's the same car but it's upside down just like in the diagram above.
One last thing about the lens before I take some measurements. It turns out that the location of the image depends on both the focal length of the lens and the location of the object according to the following equation:
Since the image distance changes with the object distance (but the focal length is constant), we can take some measurements to find the focal length.
Determining the focal length
If I used the Angry Birds Go! car, it might be difficult to get some useful data. In order to get a brighter object, I am going to use this.
It's just an arrow drawn on a piece of paper that is taped to the front of a flashlight. With the flashlight on, I will get a bright section of paper around a dark arrow. This should be able to be projected onto a screen (and be much brighter and thus easier to see).
In order to make a moveable screen, I built a LEGO wall with paper taped to the front. Here is my whole experimental setup.
Now I just need to measure both the distance from the lens to the object (the flashlight) and to the image (the screen). Oh, be careful. The lens is on the bottom of the telepod stand so measure your distances from that side.
Here is the data I collected.
If I rewrite the image equation above, I can get this:
If I make a plot of 1/o vs. 1/i, it should be a straight line. Also, the y-intercept should be 1/f. Here is that plot.
Since I know the slope should theoretically be -1, I fit an equation that only had the intercept as a free parameter. This gives a y-intercept of 0.2652 (1/cm). Setting this equal to 1 over the focal length, I get a focal length of 3.77 cm.
I'm not completely happy with that value - actually, it's the data I question. So, to compensate, I am going to assign homework.
- What if you plot the same data above but fit a linear function such that it gives you the slope and the intercept. What value for the focal point would you get in this case?
- Find a better way to collect data such that there is a better fit.
- I didn't say anything about magnification, did I? Do a google search to determine how to calculate the magnification of an object. How magnified would a QR code be if it were 5 cm from the lens? What about 2 cm? (there is a trick here - but I will leave it for you to figure out).
- Could you burn a piece of paper with the sun and this telepod?
- What happens if you get the object closer to the lens than the focal length? Something weird happens. Try it out or draw a ray diagram and see. Hint: virtual image.
There is another part of this telepod that I haven't really said anything about - the car. The car has some cool physics to go with it also. That will be a later post.
