Nancy Shikles and Diane Keane

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1 Nancy Shikles and Diane Keane Optics and Sound Institute Dr. Meera Chandrasekhar University of Missouri-Columbia June 25, 2002

2 Teacher Pages Concepts When light is passed through a convex lens, a real image may form on a screen. The focal length (f) of a lens is defined by the euation 1/f = 1/o + 1/I, where o is the object distance and i is the image distance. The focal length of a lens is a constant. When light is reflected off a concave mirror, a real image is formed on a screen. The focal length can be calculated using the same method. A real image by definition is an image that can be caught on a screen and appears inverted. A virtual image by definition is an image that cannot be caught on a screen and appears upright. Description of how activities illustrate the concepts Activity One: Creating a real image using a convex lens. Using the optical apparatus, the students will bring an object into focus. They will notice that the object is inverted (real image). They will then measure the distance of the object to the lens and the distance of the image to the lens. Using these measurements, the students will determine the focal length of the convex lens. Through manipulation of object distance or image distance, students will discover that the focal length of a given lens is a constant. Activity Two: Creating a real image using a concave mirror. Using the optical apparatus, the students will create a real image on a screen by manipulating the object distance and image distance. Students will determine that the concave mirror has a constant focal length. Optics and Sound Institute,

3 Quantitative Applications Students will measure object distance and image distance in metric units. Students will use these measurements to calculate focal length using the euation 1/f = 1/o + 1/i. Students will record measurements from varying distances to determine the constant focal length of the lens or mirror. Qualitative Applications Students will determine when an image is in focus on a screen. Students will conclude that the image is real because it appears on a screen and is inverted. Students will conclude that not all images produced by a convex lens or concave mirror are real. Additional Applications Students can visit the web site to verify their finding and enhance their comprehension. Students can explore the relationship between degree of curvature and focal length. Students can explore the effect of multiple lenses on image formation. Students can explore shadow concepts using various objects and light sources. Students can explore the effect of color filters on shadow projections. Optics and Sound Institute,

4 Activity Instructions Activity One: Creating a real image using a convex lens. Materials: Sliding optical apparatus, light source, convex lens, cutout design board (optional), calculator Prior Knowledge: Students should understand the difference between a lens and a mirror. Students should be able to identify objects that are concave, convex, or planar. They should know how to measure in metric units and be able to solve simple euations. Teacher Background: Light rays pass through a convex lens and come together at a point called the focal point. The distance from the center of the lens to the focal point is the focal length (f). Under certain conditions, a real image can be formed on a screen. A real image is one that can be formed on a screen and is inverted. When an image is formed, the focal length of the lens can be calculated using the formula: 1/f = 1/o + 1/i, where o is the distance between the object and the center of the lens, and i is the distance from the center of the lens to the image. Procedure The teacher will set up the optical apparatus in front of the class and begin the activity with guiding uestions about light projections. Students, in groups of 2 to 4, will set up their apparatus on their lab table. Teacher will review fire safety procedures with the students. With the light source and lens in place (center of block), students will manipulate the blocks of the apparatus until an image is formed and focused on the screen. They will measure and record object distance and image distance, then use these data and the euation to determine the focal length of the lens. Students will repeat this procedure two times using a different object distances. Student groups will draw conclusions from their data. Conclusions will be shared through class discussion. Notes: The cutout design board helps define the image formed by the object (light source). Dimming room lights may enhance image perception. Optics and Sound Institute,

5 Activity Two: Creating a real image using a concave mirror. Materials: Sliding optical apparatus, light source, concave mirror, calculator Prior Knowledge: Students should understand the difference between a lens and a mirror. The students should be able to identify objects that are concave, convex or planar. They should know how to measure in metric units and be able to solve simple euations. Teacher Background: Light rays reflect off a concave mirror and come together at a point called the focal point. The distance from the middle of the mirror to the focal point is called the focal length (f). Under certain conditions, a real image can be formed on a screen. A real image is one that can be formed on a screen and is inverted. When an image is formed, the focal length of the mirror can be calculated using the formula 1/f = 1/o + 1/i, where o is the distance between the object and the center of the mirror, and i is the distance from the center of the mirror s surface to the image. Procedure The teacher will set up the optical apparatus in front of the class and begin the activity with guiding uestions about light projections. Students, in groups of 2 to 4, will set up their apparatus on their lab table. Teacher will review fire safety procedures with the students. With the light source and mirror in place, students will manipulate the blocks until an image is formed and focused. They will measure and record object distance and image distance, then use these data and the euation to determine the focal length of the mirror. Students will repeat this procedure two times using a different object distances. Student groups will draw conclusions from their data. Conclusions will be shared through class discussion. Notes: Dimming room lights may enhance image perception. Optics and Sound Institute,

6 Guiding Questions Activity One: What direction is the light travelling? What do you see when light hits a wall? What is a shadow? What is an image? What do you think is happening as light passes through this opening? What do you call going from fuzzy to clear? What do you see when light passes through a lens? Activity Two: What does a mirror do? What happens when light hits a mirror? What is a plane mirror? What do you see in a plane mirror? How is the reflection different in a concave mirror? Optics and Sound Institute,

7 Student Pages Activity One: Creating a real image using a convex lens Purpose: In this activity, you will learn what happens to the image of an object when seen through a convex lens. Using measurements of the object distance and the image distance to the center of the lens, you will determine the focal length of the lens. Materials: Optical apparatus, convex lens, light source, cutout design, calculator Safety: Tie long hair back and roll up long sleeves when working around fire. Be careful when lighting, extinguishing and discarding used matches. Do not lean into the flame. Procedure: 1. Set up optical apparatus according to illustration. 2. Light candle or turn on light source. 3. Move the block with the screen attached along the meter stick until an image of the cutout design is clearly focused on the screen. 4. Draw the image as it appears on the screen on your data chart. Is it real? 5. Measure the distance between the light source and the center of the lens in cm, using the scale on the block and meter stick. Record this value as o (object distance) on your data chart. 6. Measure the distance between the center of the lens and the image on the screen, using the same method as above. Record this value as i (object distance) on your data chart. 7. Move the light source 2 cm away from the lens block. Find the new image location by adjusting the screen block. Measure and record data as in steps 5 and Move the light source 4 cm away from the lens block. Find the new image location by adjusting the screen block. Measure and record data as in steps 5 and Complete the data chart by solving for f (focal length) using the euation on the data chart. Optics and Sound Institute,

8 Data Chart Image Number Draw image. Is it real? Yes or No Object distance In cm Image distance In cm Focal length In cm Light Lens Screen Meter stick Illustration: Optical apparatus with convex lens Euation for determining f (focal length): 1/f = 1/o + 1/i Example: o = 5 cm and I = 10 cm 1/f = 1/5 + 1/10 = 2/10 + 1/10 1/f = 3/10 f = 3.33 What conclusion can you make about this convex lens? Optics and Sound Institute,

9 What have you discovered about the focal length of this convex lens? Predict. What aspect of this lens affects the focal length? Suggest an activity that would test your prediction. Name one situation when you could use this information about a convex lens. Optics and Sound Institute,

10 Activity Two: Creating a real image creating a convex mirror Purpose: In this activity, you will learn what happens to the image of an object when reflected from a concave mirror. Using measurements of the object distance and the image distance to the center of the mirror, you will determine the focal length of the mirror. Materials: Optical apparatus, convex lens, light source, calculator Safety: Tie long hair back and roll up long sleeves when working around fire. Be careful when lighting, extinguishing and discarding used matches. Do not lean into the flame. Procedure: 1. Set up optical apparatus according to illustration. 2. Light candle or turn on light source. 3. Move the block with the screen attached along the meter stick until an image of the cutout design is clearly focused on the screen. 4. Draw the image as it appears on the screen on your data chart. Is it real? 5. Measure the distance between the light source and the center of the mirror in cm, using the scale on the block and meter stick. Record this value as o (object distance) on your data chart. 6. Measure the distance between the center of the mirror and the image on the screen, using the same method as above. Record this value as i (object distance) on your data chart. 7. Move the light source 2 cm away from the mirror block. Find the new image location by adjusting the screen block. Measure and record data as in steps 5 and Move the light source 4 cm away from the mirror block. Find the new image location by adjusting the screen block. Measure and record data as in steps 5 and Complete the data chart by solving for f (focal length) using the euation on the data chart. Optics and Sound Institute,

11 Data Chart Image Number Draw image. Is it real? Yes or No Object distance In cm Image distance In cm Focal length In cm Mirror Light Screen Meter stick Illustration: Optical apparatus with concave mirror Euation for determining f (focal length): 1/f = 1/o + 1/i Example: o = 5 cm and I = 10 cm 1/f = 1/5 + 1/10 = 2/10 + 1/10 1/f = 3/10 f = 3.33 cm What conclusion can you make about this concave mirror? Optics and Sound Institute,

12 What have you discovered about the focal length of this concave mirror? Predict. What aspect of this mirror affects the focal length? How are the convex lens and the concave mirror alike? Different? Where might you use a concave mirror? Now that you have experimented with a convex lens and a concave mirror, what new uestions can be asked about light? Optics and Sound Institute,

13 Construction Instructions for Sliding Optical Apparatus Materials: 2 x 6 x 2 wood board, 20 x 30 x _ white foam core poster board, regular poster board, tape, glue, box knife or similar tool, table saw for making straight cuts and dado cuts (or a saw and chisel), meter stick, metal strip, wood screws, metal snips, tubing Instructions: Down the middle of the 2 x 6 board, make a dado cut 3/8 deep and 1 1/8 wide. The meter stick should be able to slide through the dado cut unimpeded. Cut the board into lengths of 6. Check for splintering. Sand any jagged areas as needed. Cut 6 pieces of foam core poster board to fit the top of each section of wood. These should be 5.5 by 6. Glue the poster board on the top (dado cut is on the bottom) of each section of wood. Set aside to dry. Foam Core Poster Board To make the image screen, glue another piece of the pre-cut poster board to the end (face) of one of the wood sections. Make sure that the dado cut is not blocked. Set aside to dry. Image screen Cut two pieces of regular poster board, 5!/2 x 6. Draw a simple non-symmetrical design on the poster board. The design should not exceed 1 1/4 in height. Draw the design such that it is centered ~1 3/8 above the bottom edge of the poster board. Carefully carve the design through both pieces of poster. When you have finished, push the design out. Glue these two pieces together. Set aside to dry. Affix straight pins to the back of the board with tape. The design can then be placed directly where desired in the foam core platform. Optics and Sound Institute, 2002 Construction Instructions

14 To make the lens/mirror holder, cut two 10-cm strips from the metal. Bend the strips into an s shape (see illustration). Attach the strips to center of the outside of a block using the screws. Slide 3-cm pieces of tubing over the ends of the metal that are not screwed to the wood. Find the middle of the block, cut a depression for seating the lens/mirror. Check to see if the lens/mirror fit securely. Adjust as needed. Metal s strip Tubing Seating Depression Draw a metric scale on the top of each block. Metric Scale cm (Option: Cut and paste 1 cm grid paper on the platform.) Special thanks to Diane and Mike Kasparie for cutting and routing the base blocks. Optics and Sound Institute, 2002 Construction Instructions

15 Materials List (one optical apparatus) Materials Properties Number Unit Cost Item Total wood board 2" x 6", cut to 6" lengths 2 board feet $ 0.82 $ 0.82 poster board heavy grade, any size 1 $ 0.33 $ 0.33 foam core poster board white; 20" x 30" x 1/4" 1 $ 1.97 $ 1.97 craft glue Aleene s works well. 4 FL. OZ. 1 $ 0.87 $ 0.87 meter stick 1 $ 3.00 $ 3.00 light source votive 1 $ 0.33 $ 0.33 or tea lights $1.99) or maglight (6 " for $8.93) tin or other metal strip 1/2 to 3/4", firm but bendable ~12" scrounge $ - convex lenses 50 mm, various focal lengths 1 $ 2.95 $ 2.95 concave mirrors 50mm, various focal lengths 1 $ 3.95 $ 3.95 straight pins long dressmaker pins min. 4 scrounge rubber tubing diameter to fit tin width ~2" $ 0.28 $ 0.56 matches scrounge $ - wood screws ~1/2 " 2 scrounge $ - Total $ Most materials were located at WalMart and Lowe s. The meter stick was purchased at a teacher resource store. Lenses and mirrors were purchased from Scientifics Online. Many items were donated from scrap material. Optics and Sound Institute, 2002

16 Resources UNESCO. 700 Experiments for everyone (Revised and Enlarged Edition). (1962). New York: Doubleday; p Chandrasekhar, M., Martin, C. M., Graham, J. S. College and University Physics, Laboratory Manual: physics 21/22 and 175/176. Columbia, MO: University of Missouri; p Aldridge, Bill G. What is light and how do we explain it? (1996). Arlington, VA: NSTA; pp Todd, Robert W.(Ed.). Physical Science: Datasheets for LabBook. (2001). Austin, TX: Holt, Rinehart, & Winston; pp Marson, Ron. Light. (2000). Canby, OR: TOPS Learning Systems; pp Giancoli, Douglas C. Physics: Principles with applications (Fifth Edition). (1998). Upper Saddle River, NJ: Prentice Hall; pp Internet Sites The Physics Classroom Sight and Light Converging Lens Converging Lens by Raman Converging Lens Mirrors Thin Lens (converging/diverging lens/mirrors) Optics and Sound Institute, 2002

Geometric Optics Practice Problems. Ray Tracing - Draw at least two principle rays and show the image created by the lens or mirror.

Geometric Optics Practice Problems Ray Tracing - Draw at least two principle rays and show the image created by the lens or mirror. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Practice Problems - Mirrors Classwork