1. Make sure you have the following materials: A 2-meter stick (or tape measure), a ruler, a cardboard frame (center cut out) and a whole sheet of cardboard (about the size of notebook paper), a sheet of aluminum foil, a razor blade, a thumb tack (or needle or pin), and a piece of white notebook (or printer) paper.
2. Cut the following hole sizes into the aluminum foil: Pinhole (use the thumb tack), 1cm diameter circle, 3cm diameter circle, an equilateral triangle that would fit entirely inside a dime.
3. Tape the aluminum foil with the holes you just cut onto the cardboard frame.
4. Tape the white paper onto the solid cardboard sheet. It will serve as your screen.
5. Take the frame with aluminum foil, the screen, the 2-meter stick (or tape measure), the ruler, and a pencil outside. (An example of the foil mounted to the frame with apertures cut is seen at the bottom of this page.)
6. Allow sunlight to shine through the holes in the aluminum such that the spots of sunlight are visible on your screen. Observe the shapes of and measure the diameters of the images that show up on the screen at the following separation distances between frame and screen, which will be referred to as focal length: 25cm, 50cm, 100cm and 200cm. NOTE: If you only have a tape measure with English units, then do the conversion. For the triangular hole, measure as the diameter what a diagram would label the "height" of the triangle, but also take note of any changes in size and shape. Q1: What is the shape of the image from the triangular hole at very close separation? Q2: What happens to that shape as the focal length grows to a distance corresponding to as high as you can hold it above the ground?
7. Go inside and plot the size of the images (on the y-axis) versus the focal length on the x-axis using MATLAB.
8. Make a linear fit on the plots for each of the sets of four data points so that you can find the relationship between the two variables - image size and focal length. (You should have three sets of four data points, each with a linear fit.) Make sure your lab contains the fit parameters since the slopes and intercepts have very concrete meanings. The meaning of those parameters is the primary goal of this lab! They relate directly to what you should see on the ground below an aperture with sunlight passing through it.
9. Take a look at the fit parameters from the three curve fits, and look back at the hole diameters you cut in the aluminum and answer the following questions: Q3: How do the slopes of the fit lines compare? If they are different, do you suppose it's experimental error, or is supposed to be different for a fundamental reason? Q4: What determines the slope of each line? Look back at the background material if you don't have any idea. Q5: What is the meaning of the y-intercept of each fit line?
10. Based on your answers, please answer these questions. Q6: What would you expect to happen to the image size as the focal length becomes longer as the aperture is lifted higher and higher above the pavement? Q7: For a true pinhole, at what separation between screen and frame would you expect a 1cm diameter sunball image to form? Q8: How does your data match your answer for Q7? Q9: How big is the expected sunball for a 1cm hole held at that same distance above the pavement? Q10: Does your data match this answer? Q11: What size sunball should be expected for a 3cm hole held 2m above the pavement? Q12: Does your data indicate this?