light energy shadows and earth s surface

© Learning A–Z All rights reserved. www.sciencea-z.com1

LIGHT ENERGY

Shadows and Earth’s Surface

Illustration Credit: Signe Nordin/© Learning A–Z

Purpose To demonstrate how a curved surface affects the lengths of shadows at two different locations

Process Skills Observe, measure, collect data, interpret data, identify and control variables, communicate, draw conclusions

Background With modern technology such as spaceships and satellites, people can observe Earth or view images of it and clearly see that our planet is shaped like a ball, or sphere. But even before modern technology, people were making observations that revealed Earth’s shape.

Eratosthenes (eh-ruh-TOSS-thuh-neez) was a Greek librarian and scientist who lived two thousand years ago. His observations of shadows helped prove that Earth is a sphere. Eratosthenes noticed that at noon on the summer solstice, the Sun was directly overhead in a town called Syene. He knew the Sun was directly overhead because its reflection was visible on the water at the bottom of a deep, narrow well. Also, columns that were standing straight cast no shadows at all. At the same time of day, in a town directly to the north called Alexandria, columns that were standing straight cast shadows that he could measure. Eratosthenes knew that this observation would only be possible if Earth’s surface was curved. If the surface were flat, the columns in Alexandria would not have cast shadows, either.

In this experiment, you will observe and measure how a curved surface affects the shadows made by two identical objects at different locations.

Time – 45–60 minutesGrouping – Small groups

Alexandria

Earth

Syene

sunlight

not to scale

Materials(per group)q data sheetq a piece of poster board

or thick, flexible paper about 22 cm (8.5 in.) x 36 cm (14 in.)

q 2 large paper clipsq tapeq a bright flashlightq a 30 cm (12 in.) ruler


Light Energy—Shadows and Earth’s Surface


Part 1: Shadows on a Flat Surface1. With the board lying on a desk, position

the flashlight above the left side of the board at an angle pointing toward the paper clips (see Figure 1). This represents sunlight in the morning.

2. Have another member of your group use the ruler to measure the shadows created by paper clips A and B. Record the measurements in the Part 1 table on the data sheet.

3. Repeat steps 1 and 2, but this time hold the flashlight directly above the paper clips. This represents sunlight at noon. Record the shadow lengths in the Part 1 table on the data sheet.

4. Repeat steps 1 and 2, but this time hold the flashlight at an angle to the right of the paper clips. This represents sunlight in the afternoon. Record the shadow lengths in the Part 1 table on the data sheet.

ProcedureSetting Up the Board

1. Gather the poster board, paper clips, and tape. Lay the poster board on a desk or table with one of the long sides facing you. Label the shorter ends “left” and “right”.

2. Bend the two paper clips so they are L-shaped. Make two small slits in the middle of the poster board that are approximately 12 centimeters (4.5 in.) apart. Slide the upright end of one paper clip through each hole. Secure the paper clips on the bottom of the poster board with tape. The paper clips should be placed standing up, perpendicular to the poster board. Be sure the board is still flat after securing the paper clips (see Figure 1).

3. Label the paper clip closer to the left side of the board “A” and the paper clip closer to the right side of the board “B”.

4. Before collecting data, check to make sure your paper clips are straight by holding a lit flashlight directly above them and looking at the shadows created by both. Adjust the distance of the flashlight and the positions of the paper clips until very little shadow is cast by either paper clip. Note the distance of the flashlight from the paper clips during this step and use a similar distance throughout your experiments.

Figure 1

left

right AB

EXPERIMENT




5. In the last column of the Part 1 table, calculate the difference between the shadow lengths made by each paper clip for the three different flashlight positions. Discuss the results with your group.

Part 2: Shadows on a Curved Surface1. Use the same set-up as in Part 1, but

this time one member of the group should hold the poster board in a curved position. With the right hand, support the board below paper clip B while letting the board under paper clip A droop down. The board should have a sloped curve, or arc, that is not too extreme. Do not fold the board. Use the left hand to steady the left side of the board and keep it in place. The person holding the board should keep it in this same position while measurements of shadow lengths are collected for the three flashlight positions.

2. With the poster board in this curved position, hold the flashlight above the left side of the board at an angle pointing toward the paper clips (see Figure 2). Have another member of the group use the ruler to measure the lengths of the shadows created by paper clips A and B. Record the measurements in the Part 2 table on the data sheet.

3. Repeat step 2, but this time move the flashlight to directly above the paper clips. Record the shadow lengths in the Part 2 table on the data sheet.

4. Repeat step 2, but this time move the flashlight to an angle to the right of the paper clips. Record the shadow lengths in the Part 2 table on the data sheet.

5. In the last column of the Part 2 table, calculate the difference between the shadow lengths made by each paper clip for the three different flashlight positions. Discuss the results with your group.

Figure 2

left

right AB

EXPERIMENT


Name ______________________________________________ Date ______________

Light Energy—Shadows and Earth’s Surface Data Sheet

Part 1: Shadows on a Flat Surface

Collect Data

Flashlight PositionShadow Length of

Paper Clip A Shadow Length of

Paper Clip B

Difference Between Shadow Lengths of

Paper Clips A and B

Left

Center

Right

Part 2: Shadows on a Curved Surface

Collect Data



Paper Clip B

Difference Between Shadow Lengths of

Paper Clips A and B

Left

Center

Right

EXPERIMENT


Light Energy—Shadows and Earth’s Surface Questions

Analyze Data 1. In Part 1, when the board was flat, how did changing the position of the flashlight

affect the lengths of the shadows made by the paper clips?

2. In Part 1, when the board was flat, how would you describe the differences between the shadow lengths of paper clips A and B?

3. In Part 2, when the board was curved, how did changing the position of the flashlight affect the lengths of the shadows made by the paper clips?

4. In Part 2, when the board was curved, how would you describe the differences between the shadow lengths of paper clips A and B?

EXPERIMENT



Draw Conclusions 1. How do shadows change, depending on whether they form on a flat or curved surface?

2. Using the results of your experiment as evidence, write an argument supporting the fact that Earth is shaped like a sphere.

EXPERIMENT


LIGHT ENERGY

Shadows and Earth’s SurfaceTEACHING TIPS

This Process Activity will help students understand how the position of a light source and whether objects are on a flat or curved surface affect the length of shadows. The model used in this experiment mimics the apparent movement of the Sun across the sky and the curved shape of Earth’s surface. When a light source is at a low angle relative to objects, the shadows made by the objects are longer than when the light source is directly overhead. For example, in early morning and late afternoon, the Sun is low in the sky, and the shadows on Earth’s surface are longer than at midday.

The shape of the surface also affects shadow length. Shadows from similar-sized objects measured on a flat surface will be similar in length. (Depending on where the light source is held, the object farther from the light source will have a slightly longer shadow, which is likely to be observed in this model. In the real Earth-Sun system, these differences are negligible because the Sun is so far away.) On a curved surface, shadows from similar-sized objects will differ more significantly in length. This was the observation made by Eratosthenes two thousand years ago when he noticed that the lengths of shadows differed in Syene (now Aswan) and Alexandria at noon on the summer solstice—the day of the year when the Sun is at its highest point in the sky.

This activity provides students with a deeper understanding of how shadows on Earth’s surface offer one way to prove the planet’s spherical shape while also providing a connection to the history of science.

n The results of the experiment will be most evident if the paper clips are as close to perpendicular to the board as possible. Assist students with this step. Consider making your own board for demonstration purposes.

n Explain to students that the height at which the flashlight is held can also affect shadow length and that they should do their best to control for this variable during the entire experiment. Invite students to propose ways to keep the light positions consistent. To simplify the experiment, have students only measure shadows with the flashlight at the center position.

n Actual measured shadow lengths will vary, depending on the set-up of each group’s board and the distance and angle at which they hold the flashlight.

MATERIALS n Legal-size paper could also be used for this experiment, but students may find that it is too flimsy to hold the paper clips and hard to hold steady in the curved position. Stronger paper is recommended.

n Toothpicks or straws cut into 5-centimeters (2 in.) pieces are good substitutes for paper clips. Use glue or tape to secure the toothpicks or straws to the poster board.

SET-UP and PROCEDURES



n Provide each group with a bright flashlight or ask students to bring a flashlight from home. Flashlights built into smartphones will work for this experiment; however, the light they produce is very focused. A phone will need to be held at a greater distance from the paper clips to ensure that the light hits both objects evenly. In either case, darken the room lighting during testing.

n Variation: Allow students to take their model outdoors so they can use the Sun as the light source. Encourage them to measure the paper clip shadows with the board held flat and in a curved position and to try the test at morning, midday, and late afternoon.

n Critical Thinking / Writing: Ask students to write about how their experiment relates to the apparent movement of the Sun across the sky and shadow lengths they observe outdoors at different times of day. Challenge them to speculate on how a similar object might cast a shadow at the same moment at a different location on Earth.

n Home Connection: Encourage students to collect data on shadows at home. Have them pick one or more outdoor objects and measure their shadows at various times throughout a day.

n Research: Have students use the library or online resources to learn more about Eratosthenes and his discoveries.

n Geography / Inquiry Science: Have students use the library or online resources to find the locations of Alexandria and Syene (now Aswan) on a map of modern-day Egypt. Then instruct them to draw the map on their board, aligning Alexandria with paper clip A and Syene with paper clip B to show the locations of the cities where Eratosthenes took his shadow measurements. Ask students to try the flashlight tests again, this time positioning the flashlight as it moves from east to overhead to west relative to their Egypt map. They should find that the shadow lengths of paper clips A and B would remain similar in all three light positions if Earth were flat. But with a curved surface, one shadow will clearly be longer than the other when the light source is overhead, which is similar to what Eratosthenes observed.

EXTENSIONS and VARIATIONS

EXPERIMENT



ANSWER KEY


Name ______________________________________________ Date ______________


Part 1: Shadows on a Flat Surface

Collect Data



Paper Clip B

Difference Between Shadow Lengths of Paper Clips A and B

Left Actual measurements will vary. Students should find that when the flashlight is held to the left or to the right of the paper clips, the shadow lengths are longer than when the flashlight is centered above the paper clips. However, the difference in length of the shadows made by paper clips A and B should be relatively small when made on the flat surface at all three flashlight positions.

Center

Right

Part 2: Shadows on a Curved Surface

Collect Data



Paper Clip B

Difference Between Shadow Lengths of Paper Clips A and B

LeftActual measurements will vary. Students should find that when the flashlight is held to the left or right of the paper clips, the shadow lengths are longer than when the flashlight is centered above the paper clips—as was the case on the flat surface. However, on the curved surface, the difference in length of the shadows made by paper clips A and B will be greater than they were on the flat surface, particularly when the flashlight is held at a low angle. Also, the differences in shadow lengths made by overhead versus side lighting will be greater on the curved surface than they were on the flat surface.

Center

Right

EXPERIMENT

EXPERIMENT



ANSWER KEY AND EXPLANATIONS

Analyze Data

1. In Part 1, when the board was flat, how did changing the position of the flashlight affect the lengths of the shadows made by the paper clips?

The shadows were longer when the flashlight was held to the left or right of the paper clips. The shadows were smallest when the flashlight was held directly above the paper clips.

2. In Part 1, when the board was flat, how would you describe the differences between the shadow lengths of paper clips A and B?

The differences between the shadow lengths made by paper clips A and B were small. The shadows were about the same length for both paper clips at each flashlight position.

3. In Part 2, when the board was curved, how did changing the position of the flashlight affect the lengths of the shadows made by the paper clips?

Just as when the board was flat, the shadows were longer when the flashlight was held to the left or right of the paper clips. The shadows were smallest when the flashlight was held directly above the paper clips.

4. In Part 2, when the board was curved, how would you describe the differences between the shadow lengths of paper clips A and B?

The differences between the shadow lengths made by paper clips A and B were greater than when the board was held flat, at each flashlight position.

EXPERIMENT



Draw Conclusions

1. How do shadows change, depending on whether they form on a flat or curved surface?

The position of a light source affects the lengths of shadows. When a light source shines on an object at a low angle, the shadow is longer. When a light source is directly above an object, the shadow is shorter or there is no shadow at all. This effect of light source position is true whether the shadows are measured on a flat or curved surface. But when comparing the shadows made by objects of the same height, the surface on which the objects are resting determines how much the shadows will differ in length. On a flat surface, the lengths of shadows made by objects of the same height that are some distance apart will be similar, with minimal or no difference. On a curved surface, the difference between the shadow lengths will be greater.

2. Using the results of your experiment as evidence, write an argument supporting the fact that Earth is shaped like a sphere.

The results of this experiment support the fact that Earth is shaped like a sphere. They showed that shadows made by two objects of the same height on a curved surface are different lengths. This observation matches observations made on Earth’s surface. Because Eratosthenes saw a difference in the lengths of shadows made by similar objects at the same time of day in two different locations, he inferred that Earth’s surface was curved and that Earth must be a sphere.

ANSWER KEY AND EXPLANATIONS

EXPERIMENT

1© Learning A–Z All rights reserved. www.sciencea-z.com

Name Date

Evidence That Earth Is Spherical

Lesson 2

Part 1: Evaluate the EvidenceEvaluate whether each fact about shadows provides evidence that Earth is spherical. Circle Yes or No, then explain why or why not.

1. People of the same height who are standing next to one another make shadows that are similar in length.

Does this fact provide evidence that Earth is spherical?

Yes No

Why or why not? ___________________________________________________________________________

_______________________________________________________________________________________________

_______________________________________________________________________________________________

2. When walking together, people and dogs make shadows that are different lengths.


Yes No

Why or why not? ___________________________________________________________________________

_______________________________________________________________________________________________

_______________________________________________________________________________________________

3. If the Sun shines on two objects of the same height in different locations at noon, their shadows will be different lengths.


Yes No

Why or why not? ___________________________________________________________________________

_______________________________________________________________________________________________

_______________________________________________________________________________________________

sunlight

not to scale

Storyline Assessment


Name Date


Lesson 2

Part 2: Analyze the DataStudents in Miss Klein’s class worked with poster board, toothpicks, and a flashlight to create shadows and measure their lengths. The students taped two toothpicks to the poster board so they stood upright on the board’s surface. One student held the flashlight in the same position during the entire experiment. Another student changed the poster board by holding it flat during one test and bending it during a different test. A third student measured the length of the shadow made by each toothpick during each test. The graphs below show some of the results from their experiment. Analyze the data in the graphs and then answer the questions.

Graph A

Graph B

Toothpick 1

Toothpick 1

Toothpick 2

Toothpick 2

10

8

6

4

2

0

10

8

6

4

2

0

Leng

th o

f Sh

adow

(cm

)Le

ngth

of

Shad

ow (

cm)



Name Date


Lesson 2

1. Which graph shows data collected while the poster board was held in a flat position? How can you tell? ___________________________________________________________

____________________________________________________________________________

____________________________________________________________________________

2. Which graph shows data collected while the poster board was held in a curved position? How can you tell? ___________________________________________________________

____________________________________________________________________________

____________________________________________________________________________

3. Eratosthenes measured shadows at two different locations to show that Earth has a curved surface. How are the results of the experiment similar to observations made by Eratosthenes? ____________________________________________________________

____________________________________________________________________________

____________________________________________________________________________

4. Use the results of this experiment as evidence to support an argument that Earth is shaped like a sphere. ______________________________________________________

____________________________________________________________________________

____________________________________________________________________________


ANSWER KEY AND TEACHING TIPS


* Next Generation Science Standards is a registered trademark of Achieve. Neither Achieve nor the lead states and partners that developed the Next Generation Science Standards was involved in the production of, and does not endorse, this product.


Lesson 2

Connections to the Next Generation Science Standards*Target Science and Engineering Practice: Engaging in Argument from Evidence• Support an argument with evidence, data, or a model.

Associated Performance Expectation: 5-PS2-1. Support an argument that the gravitational force exerted by Earth on objects is directed down.

All questions in this assessment relate to the Disciplinary Core Ideas DCI of this Performance Expectation. Look for the SEP and CCC symbols for questions that specifically address Science and Engineering Practices and Crosscutting Concepts.

SummaryStudents evaluate facts to determine whether each provides evidence of Earth’s spherical shape. Then they analyze data to identify cause-and-effect relationships between a flat or curved surface and shadow length, and connect those relationships to Earth’s actual shape.

Part 1: Evaluate the Evidence Answers may vary, but possibilities include:

1. �No.�This�is�not�good�evidence�of�the�fact�that�Earth�is�a�sphere.�Since�the�people�are�standing�next�to�each�other,�they�are�too�close�together�to�measure�a�difference�in�shadow�length�caused�by�the�curve�of�Earth’s�surface.�

2. �No.�This�is�not�good�evidence�of�the�fact�that�Earth�is�a�sphere.�Things�that�are�different�heights�can�make�shadows�that�are�different�lengths,�regardless�of�the�shape�of�the�surface�they�are�on.�

3. �Yes.�This�is�good�evidence�of�the�fact�that�Earth�is�a�sphere.�These�shadows�were�created�at�the�same�time�of�day�by�objects�of�the�same�height�at�two�different�locations�on�Earth.�The�shadows��can�only�be�different�lengths�if�the�surface�they�are�sitting�on�is�curved.�If�the�surface�were�flat,�the�objects’�shadows�would�be�the�same�length.

Part 2: Analyze the DataThe scenario and results described here are similar to the experiment within the Shadows and Earth’s Surface Process Activity that students completed during Lesson 2. Information about Eratosthenes is found in the introductory section of this Process Activity and sets up a purpose for the experiment. Answers may vary, but some possibilities include:

1. �Graph�B�shows�data�collected�while�the�poster�board�was�held�flat.�I�can�tell�because�the�graph�shows�that�the�shadows�are�the�same�length.�This�matches�what�we�saw�during�our�own�test��with�shadows�on�a�flat�surface.

2. �Graph�A�shows�data�collected�while�the�poster�board�was�curved.�I�can�tell�because�the�graph�shows�that�the�shadows�are�different�lengths.�This�matches�what�we�saw�during�our�own�test��with�shadows�on�a�curved�surface.

SEP

SEP


Storyline Assessment Evidence That Earth Is Spherical

Lesson 2

3. �Eratosthenes�measured�shadow�lengths�at�different�locations�on�Earth.�In�the�experiment,�students�measured�shadow�lengths�on�poster�board�that�was�flat�and�curved.�Eratosthenes�didn’t�know�that�Earth�was�a�sphere,�but�his�observations�could�only�be�explained�if�the�shadows�were�created�on�a�curved�surface.�The�data�collected�by�the�students�supports�Eratosthenes’s�claim.�

4. �The�experiment�showed�that�toothpicks�on�the�flat�poster�board�create�shadows�of�the�same�length.�But�when�the�poster�board�is�curved,�the�lengths�of�the�shadows�are�different.�This�evidence�matches�observations�of�shadows�on�Earth.�When�the�Sun�is�directly�overhead�so�that�no�shadows�form�in�one�location�on�Earth,�objects�of�the�same�size�that�are�some�distance�away�create�shadows�that�can�be�measured.�This�proves�that�Earth�must�be�curved�because�on�a�flat�Earth,�there�would�be�no�difference�in�the�lengths�of�the�shadows�at�the�two�locations.�

Teaching TipsIf students have trouble performing the tasks on this assessment, review with the class several ways in which people learned that Earth is spherical. Explain that even without satellites and other forms of modern technology, plenty of evidence exists that demonstrates Earth’s shape. Have them look back at their results from the Shadows and Earth’s Surface Process Activity. Explain that their observations of shadow lengths on a curved surface support measurements made by Eratosthenes hundreds of years ago. Both provide evidence that Earth is shaped like a sphere. Remind them that a good argument consists of evidence and logical reasoning that connects the evidence to the claim.

ExtensionsFor students who complete their work early or are ready for an extra challenge, assign additional resources related to this topic found on the Grade 5 Space Systems NGSS page on Science A–Z.

CCC

Photo credits: page 1: top: UrbanZone/Alamy Stock Photo; center: Andrew Findlay/Alamy Stock Photo

Illustration credit: page 1: Signe Nordin/© Learning A–Z.com

https://www.sciencea-z.com/main/NextGenerationScienceStandards/from_ngss_resource_menu/true/ngss_topic_id/21

light energy shadows and earth s surface

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