Math and Optics PINHOLES and TRIANGLES Based on a Dumpster Optics activity that was adapted from Tutorials in Introductory Physics, McDermott and Schaffer, 2002 and the PHOTON Explorations in Optics, 2013 Developed with an outreach grant from
Math and Optics This activity has several parts: Learning about pinhole images and how the sizes of object and image are related by similar triangles- about one hour. Using similar triangles to predict image size OR to measure the height of a tree (depending on the class and the weather)- about one hour. Pinhole cameras- requires a darkroom and takes about 2 hours.
Part 1 Pinhole images Similar triangles
What is it? (Hint: Look under a leafy vine or tree.) Hangzhou, China San Diego, California
RULES Each of the following activities shows a picture and asks what you think you will see on a screen. Make your prediction by drawing what you think you will see before trying the experiment! If your prediction is correct, proceed to the next activity. If it s not correct, try to figure out why before continuing.
Vocabulary Illuminate Ray Similar triangles Point source of light Pinhole image Rectilinear
Activity 1: How Does Light Travel? You will use LED lights and a piece of paper with a triangle hole in the center. We call this a mask.
Activity 1: How Does Light Travel? Place the cardboard with the hole about 30 cm from a wall or screen, and the LED about 30 cm to the other side. What will you see on the wall? Make your prediction! point source of light cardboard mask wall or screen
Activity 1: How Does Light Travel? Turn off the light source but leave everything in place. What will happen if you move the light source UP? What will happen if you move the light source DOWN? point source of light cardboard mask wall or screen
Activity 1: How Does Light Travel? On the observation sheet, draw the path light takes when it goes from the bulb through the hole in the cardboard to the screen hole point source of light cardboard with hole wall or screen
Activity 2: Two Light Sources Repeat Activity 1 but with TWO different color point sources of light, one above the other. What do you think you will see on the screen? point source of light cardboard mask wall or screen
Activity 3: More Light Sources If you use 3 bulbs in a row, what do you think you will see on the screen? point source of light cardboard mask wall or screen
Activity 3: More Light Sources If you use many, many bulbs in a row, what do you think you would see on the screen? point source of light cardboard mask wall or screen
Activity 3: More Light Sources It would be difficult to stack that many bulbs so closely, but we can use a single straight line source of light instead. What do you think you will see on the screen? point source of light cardboard mask wall or screen (round hole)
Activity 4: How Big? Follow the light rays from the top and bottom of the bulb through the hole to the screen. What do you notice about the geometry of the object (bulb), hole and image on the screen? With your team, try to identify the relationship between the two triangles.
How Big? Using Similar Triangles Suppose the light bulb is 9 cm tall and is located 30 cm from the hole. The screen is 20 cm from the hole. How big is the image? Show your work! 9 cm H 30 cm 20 cm
What is it? Leafy trees form pinhole images of the sun. The small spaces between overlapping leaves are the pinholes. During an eclipse of the sun the images are crescents.
Part 2 Using similar triangles How large is the image? OR Using similar triangles How tall is a tree?
How Big is the Image? Measure the length of the filament in the bulb as carefully as you can. Record the filament length on the data sheet. Set up a small triangle or circle hole mask 30 cm from the light bulb filament. How big will the image be if the screen is 20 cm on the other side of the mask? Show your calculations!
How Big is the Image? After you finish your calculation, put the screen at 20 cm and measure the image. Fill in the table with your calculated and measured value. Repeat for more distances as instructed.
How Tall is a Tree? Look at the drawing and figure out a a way to determine the height of a tree. Available materials: Meter sticks Rulers Tape measure (shared) ruler meter stick
How Tall is a Tree? Carefully explain your method and label all measurements. Show all calculations. Questions: How close do you think your measurement is to the real height of the tree? What are some sources of error in your measurements? Be precise!
Part 3 Using similar triangles- How tall is a tree?
Make a Pinhole Camera This is a fun activity BUT it requires a darkroom to load and develop the film. When no darkroom is available, we load a few cameras at home (in the dark, in the basement), bring them to school to make the exposure, then develop the film at home. We use liquid film developer and fixer (for example, Ilford brand) for ease of mixing. Complete instructions for creating and using an oatmeal box pinhole camera can be found at http://users.rcn.com/stewoody/makecam.htm
Make a Pinhole Camera You need: An empty oatmeal box. If you can paint the inside flat black, even better A piece (about 3 cm) cut from an aluminum soda can (be careful!) A pencil A sewing needle A small piece of fine sandpaper Lots of electrical tape Light blocking black paper Optional: Magnifying glass to check the pinhole Black and white film paper Developing chemicals (developer, fixer)- liquids are easiest to use
Step 1- Make a pinhole 1. CALCULATE THE SIZE OF THE PINHOLE The diameter is calculated from the focal length of the box (distance from pinhole to film) D = 0.01496 f pinhole goes here D film goes here
Step 1- Make a pinhole 2. Make a drill from a needle and the eraser end of a pencil as shown. Be careful! 3. Slowly drill a tiny hole into a piece of soda can. Drill from one side, turn over and drill from the other side until the needle just breaks through. 4. Lightly sand each side of the hole. 5. If you can, check the hole by looking at it with a magnifier.
Step 2 The box 1. Cut a small hole in the middle of the side of the box. 2. Tape the pinhole over the center of the hole. 3. Line the cover with black opaque paper. You can also wrap the box top with aluminum foil after loading the film to be sure no light gets in. 4. Make a shutter by taping a loop of electrical tape over the pinhole. sticky not sticky- covers pinhole
Step 3 The photo 1. In a darkroom, load the film into the box. (If you don t have a darkroom, do it at night with the lights off. You can use a small red light under the table if you need one.) 2. Put the box on a firm surface to expose the film. You can t hold it still enough in your hands! Outside, start with a 5-6 second exposure (sunny day). 3. Develop the film as directed on the developer. Rinse, fix as directed*, rinse again. 4. Enjoy! *Note: Fixer contains silver and may be considered hazardous waste in some jurisdictions.
6 second exposure, sunlight
30 minute exposure, classroom lighting
Problem to Think About A photography class in New York City makes small pinhole cameras and leaves them all day in Times Square. When they develop the film there are no cars or people, only buildings.