Teacher Guide

# Magnifying Marbles

## Experimenting with an object's size and magnification

How does the radius of the sphere affect how much it magnifies an object?

This resource was originally published in PhysicsQuest 2015: Light Science.

This is the teacher guide for this lesson. A student-focused guide to assist learners as they perform the activity is available.

View the student guide: Magnifying Marbles

How does the radius of the sphere affect how much it magnifies an object?

• Three sizes of water gel spheres
• Binder clips
• Transparency
• Flashlight
• Water
• Stiff paper
• Permanent marker
• White piece of paper
• Dark room

The day before the experiment, students will grow gel spheres and observe how they grow. They will experiment with how the size of a sphere affects the magnification. At the end, they will use their data to discuss magnification with different objects.

• Total time
45 - 60 minutes
• Education level
• Content Area
Light Science
• Educational topic
Light, magnification

Usually when we teach or learn about lenses, there isn’t much talk about the shape of the lens. If you’ve done a lot of lens experiments you notice that the ones that bulge out more usually magnify images more than flatter lenses. There are almost no experiments that deal with this or even talk at all about how shape, magnification, and focal length are related. Almost all lenses you deal with are spherical lenses. Sometimes people will talk about the radius of curvature of the lens. It may seem strange to call them spherical when they look closer to flat. A converging spherical lens, which is convex, can be thought of as a being made by taking a sphere and cutting off the ends and then sandwiching them together.

The radius of curvature is the radius of the sphere from which the ends used for the lens were cut. For a diverging, concave lens, the radius of curvature is the radius of the sphere that would fit in the “cave.” Every spherical lens has a focal point. This is the point where rays are focused if they hit the lens parallel to the optical axis. If you are trying to find the focal point of a lens you can hold it over a desk or piece of paper and try to focus the sun’s rays or the overhead lights to a point. Because those light rays are hitting the lens roughly parallel, the focused spot is the focal point.

In the final experiment of PhysicsQuest you will focus the sun’s light to a point. You are focusing it at the focal point of the Fresnel lens. If you would like, have your students find the focal point of the gel spheres using this method. The distance from the center of the lens to the focal point is called the focal length. The focal length of a lens is determined by two different things.

First, the index of refraction of the lens material affects the focal length. If you’ve had a chance to do the “Bendy Light” experiment you have an idea why. Though that aspect is not dealt with in this activity, you can have your students discuss how index of refraction affects focal length as an extension of this activity. If you have extra gel spheres you could grow them in sugar water or sucralose water and see how that affects the focal length.

The second thing that affects the focal length is the radius of curvature of the lens. The radius of curvature and the focal length of the lens are directly proportional, meaning that as the radius of curvature is increased the focal length also increases. Larger spheres focus farther distances and smaller spheres focus closer to the lens. In this experiment your students are going to see how the radius of curvature can affect a different, but related, property of lenses, magnification.

Magnification is a numerical way to describe how much bigger an image is than the object that it is magnifying. If a particular image is magnified 10 times, it means the image is 10 times bigger than the object. If you measured the object height and multiplied times 10 you would get the image height. Or, if you measure the image height and divide it by 10 you should get the object height. But most importantly, if you divide the image height by the object height you should get 10. You can find how much a lens is magnifying by dividing the image height by the object height. What’s really cool about lenses is that object distance and image distance have the same ratio as object height and image height. We’re going to find the magnification of the sphere in both of these ways.

Magnification is proportional to 1/(radius of curvature)and 1/(focal length). We call this “inversely proportional.” When the radius of curvature gets smaller, the lens can magnify more. This activity is really, really cool because when the gel spheres are used, the students can actually measure the radius of curvature. This is something that’s pretty impossible to do with a normal magnifying glass. Sure, it's possible to talk about how much it magnifies and what the focal length is, but there is no easy way for students to relate this numerically to the shape of the lens. Because magnification is proportional to 1/(radius of curvature) the graph your students make will look a little strange. It’s not going to be a straight line. What might be even more frustrating is that there will only be three points on the graph so it's hard to see what type of shape it really is.

The goal is to understand that as radius decreases, magnification increases and it doesn’t do that in a straight line type of way. Hopefully that is clear from the graphs they make. There are many ways to extend this experiment. You could look at the focal length and how that compares to radius of curvature or you could look at how focal length compares to magnification or other ideas that your class may come up with.

Key terms

These are the key terms that students should know by the END of the two lessons. They do not need to be front loaded. In fact, studies show that presenting key terms to students before the lesson may not be as effective as having students observe and witness the phenomenon the key terms illustrate beforehand and learn the formalized words afterwards. For this reason, we recommend allowing students to grapple with the experiments without knowing these words and then exposing them to the formalized definitions afterwards in the context of what they learned.

However, if these words are helpful for students on an IEP, ELL students, or anyone else that may need more support, please use at your discretion.

• Optical axis: An imaginary line that goes through the center of the lens and the center of the face of the lens.
• Focal point: If light rays hit a lens going parallel to the optical axis, they are bent through the focal point.
• Focal length: Distance from the center of the lens to the focal point.
• Converging lens: A lens that causes light rays to come together.
• Diverging lens: A lens that causes light rays to spread out.
• Convex: Something that curves outward.
• Concave: Something that curves inward.
Objective

Students will experiment to understand how magnification works.

Before the experiment

What happens when you look through a magnifying glass at a tiny bug or small writing?

• Turn & talk protocol
1. Pair students up.
2. Give them a minute to think quietly.
3. Give students 2 minutes to discuss their thinking.
4. Have students record their answers or share out to the whole group.

Setting up
• It can take up to 24 hours for the gel spheres to grow. Be sure to check on them as they are growing. They aren’t going to grow like you think they might.

• Cut a small piece of transparency and use the permanent marker to draw an “A” on it. Make one leg of the “A” longer than the other.

• Take a tiny piece of stiff paper and roll it into a small cylinder that has a radius a bit smaller than the radius of the biggest gel sphere.

• Turn on the flashlight and put it in a binder clip.

• Put the white piece of paper in a binder clip to use as a screen.

• Place the rolled up paper cylinder on the table and balance the largest gel sphere on top.

• Place the flashlight so it shines on the sphere.

• Put the transparency “A” in the small binder clip and place it between the flashlight and the gel sphere.

• Put the screen on the other side of the sphere. The “A” should now be projected on the screen.

During the experiment
• Make sure students are put into intentional groups. See above.

• Students will complete the experiment using the Student Guide where we have outlined the experiment for students and along the way, they record results and answer questions.

• In the Student Guide, they will answer questions that help them understand magnification.

• Continue to listen in on each group’s discussion. Answer as few questions as possible. Even if a group is off a little, they will have a chance to work out these stuck points later.

Teacher tip
1. Suggested STEP UP Everyday Actions to incorporate into activity:
1. When pairing students, try to have male/female partners and invite female students to share their ideas first.
2. As you put students into groups, consider having female or minority students take the leadership role.
3. Take note of female participation. If they seem to be taking direction and following along, elevate their voice by asking them a question about their experiment.
2. Consider using white boards so students have time to work through their ideas and brainstorms before saying them out loud.
3. As students experiment, roam around the room to listen in on discussion and notice experiment techniques. If needed, stop the class and call over to a certain group that has hit on an important concept.

Consider using the RIP protocol (Research, Instruct, Plan) for lab group visits and conferring.

Consider culturally responsive tools and strategies and/or open ended reflection questions to help push student thinking, evidence tracking, and connections to their lives.

Conclusion
• Share-trade protocol to have students share and refine their thinking:

1. Each student writes their individual thoughts about: How do you think a marble the size of a pea would magnify an object? What about a bowling ball?
2. Students stand up with their ideas on paper and move around the room.
3. Each student finds someone they don’t know very well and forms a partnership with them. To form a partnership, students must high five.
4. With their partners, students share their ideas and trade papers.
5. Each student is now responsible for sharing the ideas of the person they just spoke with, even if they don’t agree with those ideas. This isn’t a time for them to critique their partners’ ideas.
6. Students form partnerships three or four times so they see and explain multiple ideas.
7. Students return to their seats and write a final explanation or idea.
• After students have had a chance to discuss key ideas from the lesson and complete their student guides, you can now clarify and give concise definitions to the forces they experimented with.

• Real world connections:
• In order to take a clear picture, one must focus a camera. Using what you learned in this lab, can you explain how to focus a camera? Have students (if access to a camera) play around with cameras and take pictures in and out of focus.
• Invite an optician as a guest speaker to talk about how lenses in glasses work to help correct vision.
• Suggestions for drawing, illustrating, presenting content in creative ways:
• Students can draw a lens diagram of the various setups of the experiment.
• Play this Kahoot with the class.
• Engineering and design challenges connected to the content:

• MS-PS4-2
Develop and use a model to describe how waves are reflected, absorbed, or transmitted through various materials.
• MS-PS4-3-applications
CCC: Influence of Science, Engineering, and Technology on Society and the Natural World. Technologies extend the measurement, exploration, modeling, and computational capacity of scientific investigations. (MS-PS4-3)
• MS-PS4-3-nature-of-science
CCC: Science is a Human Endeavor. Advances in technology influence the progress of science and science has influenced advances in technology. (MS-PS4-3)
• MS-PS4-1-empirical-evidence
SEPs: Scientific Knowledge is Based on Empirical Evidence. Science knowledge is based upon logical and conceptual connections between evidence and explanations. (MS-PS4-1)

### Credits

Written by Rebecca Thompson, PhD

Illustrations by David Ellis

In collaboration with 2015 International Year of Light

Updated in 2023 by Sierra Crandell, MEd, partially funded by Eucalyptus Foundation

Extension by Jenna Tempkin with Society of Physics Students (SPS)