Teacher Page
Activity 6b Gathering Starlight, Another Look at Aperture

Standards (see Appendix A:

• Science Content Standards: A. Science as Inquiry, E. Science and Technology, G. History and Nature of Science.
• Mathematics Standards: Measurement, Connections.
• Technology Tools: Productivity; Research; Problem Solving and Decision Making.

Unifying Concepts:    Evidence, Models, and Explanation.

Objective:

Students learn that as aperture increases, the surface area and thus the light gathering ability of a telescope increases.  The increase is by a factor of the ratio of the radii squared.  Aperture as a measure of light gathering power is emphasized.  The understanding of telescopes as instruments that gather and focus light is reinforced in this activity.

Overview:

In this activity students construct physical representations of the aperture sizes used in Activity 4.  They compare the areas covered by the aperture to each other and to the size of a dilated pupil, represented by a dot the size created with a paper punch.  Students consider the mathematical relationships between the area of the circles and the number of dots needed to fill the circle.  A column has been provided on the student page where students record the calculated areas as part of the data gathering and analysis.  This activity further reinforces the idea that a small increase in the diameter of a telescope leads to much greater light gathering ability.

Preparation:

• Gather materials
• Paper
• Rulers
• Scissors
• Many paper punch dots or one paper punch per group
• Glue
• Cut out one 24 inch circle for class use, mask the center of this with a 6 inch black construction paper circle.  This region represents where the secondary mirror blocks the primary mirror and also where there is a central opening in the primary mirror for the light path to the eyepiece or camera.

Time:  approximately 30 min.

Directions:

1. Begin with a class discussion about sight.  Most students recognize that light from the object enters the eye through the pupil, is focused by a lens onto the retina, where an image is formed and sensed by rods and cones; the sensed information is then transmitted to the brain via the optic nerve. The brain interprets the image information.
2. Review the definition of aperture, as the opening of the telescope's main lens or mirror to the sky.
3. Pose the question: “Does anyone know what happens to the aperture of your eye when it is in the dark?”  Your students should understand that the pupil of the eye dilates or gets bigger. “Why does it do this?” Pupils become dilated in order to allow more light in so that one can see better when light levels are low.  Think of the large pupils of an owl's eyes; the owl is a nocturnal hunter.
4. Compare the pupil of the human eye to the paper punch dot. “This dot is approximately the same size as your pupil gets when you have been standing in the dark for a while.  What would it be like if your eye could dilate even more?”  The larger your eye can dilate, the more light it will let in and the better you will be able to see in the dark.  “What if your pupil could dilate to become 2 inches across? 
5. Handout the student pages and instruct groups to follow the directions to complete the chart.  You may want to generate a class average for the information.  Groups that finish first can work on the 24 inch circle. For the 24 inch aperture, subtract the area of the secondary mirror which has a 6 inch diameter.  Encourage students to think of ways to estimate the number of dots that might fit inside the circle.

Discussion

6. When you come back together as a class share your conclusions.  If they have not done so on their own, encourage students to relate their findings to the role of aperture in telescopes.  “What does this activity tell you about what increasing aperture does for telescopes?”  Increasing aperture allows the telescope to collect much more light.
7. Discuss the relationship of surface area to diameter.  Student should be able to conclude that a circle with twice the diameter has four times the area and triple the diameter has nine times the area.  What is the formula for the area of a circle?
8. The telescope can be thought of as a light funnel.  The larger the opening, the more light can be poured down the light funnel.  This analogy can be used as a bridge to the next activities that deal with focusing light.  Now that you have looked at the aperture of a pupil and various telescope openings you can ask the question: “What do you have to do to get all that light that is gathered by an eight inch telescope into a 4 mm pupil?”  Just like a funnel has a cone-shaped back, that directs a liquid from a large opening to a small opening, a telescope has to have some way of focusing the light into a much smaller space.  In a telescope, this is done with a lens or mirror.