Math/Physics. Pinhole Project

Transcription

1 Math/Physics Pinhole Project Title of Activity: Pinholes in Math and Science Content Area: Geometry and Physics Rogers Public Schools Group Mark Bauer, David Conaway, David Koch, Mark Morley Description: This activity is designed to observe images that are created from a pinhole aperture and assess the transformations that happen through the aperture. Students will build a dark box with a light background and pass a lightsource across the pinholes to observe the images. 1

2 Connection to common core and standards: Level of complexity: Geometry Grade 10 Low complexity. Step-by-step process will be supplied. 1-2 class periods Physics Grade 11 Low complexity. Step-by-step process will be supplied. 1-2 class periods Math: Similar Figures CCSS.Math.Content.HSG-SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor: CCSS.Math.Content.HSG-SRT.A.1a A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. CCSS.Math.Content.HSG-SRT.A.1b The dilation of a line segment is longer or shorter in the ratio given by the scale factor. CCSS.Math.Content.HSG-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Science: 1. Next Generation Science Standards: PS4.B: ELECTROMAGNETIC RADIATION What is light? Electromagnetic radiation (e.g., radio, microwaves, light) can be modeled as a wave pattern of changing electric and magnetic fields. How can one explain the varied effects that involve light? At the surface between two media, like any wave, light can be reflected, refracted (its path bent), or absorbed. What occurs depends on properties of the surface and the wavelength of the light. 2

3 2. Arkansas State Frameworks: Students shall compare and contrast the law of reflection and the law of refraction. 3

4 Description of the project: This is a longer description that includes all necessary information for implementing the project including: pre-lab, experimental process, data collection charts, data analysis, etc Pre-Lab Math Physics - Concepts Skills Diffraction Magnification List of Equipment Cardboard Box/Tube Aluminum Foil LED Flashlight White Copy Paper Duct Tape and Painters Tape Scissors/Box Knife 4

5 Assessment component: Math Pre Assessment - After constructing the dark box having students predict what will happen when they shine the light through the pinhole. Formative - Observation of student work and discussions during project. Summative - Connections and Concepts ( calculating scale factor and image size from linear measurements), worksheet, and unit test. Physics Pre Assessment - Vocabulary (magnification, image, object), verbal/whiteboard Formative - Skills (calculating lens makers equation, magnification), quickquiz Summative - Connections and Concepts (calculating focal length and calculating magnification from linear measurements), student presentation Link to Physics Rubric 5

6 Pinhole Project Physics Class Student Presentation Rubric Category 1(Below Basic) 2(Basic) 3(Proficient) 4(Advanced) Content Use of measured quantities and vocabulary minimal or missing. Some errors in use of vocabulary and measured quantities. Vocabulary used in correct context. Measured and calculated quantities are used in correct context. Vocabulary and measured quantities used in examples and models which demonstrate expanded understanding beyond the project at hand. Connections Vocabulary, measurements and calculations are irrelevant or presented independently without correlation. Some connections are made between vocabulary terms, measurements, observations and calculations. Vocabulary, observations, measurements, and calculations are used to support each other in presentation. Vocabulary, measurements, and calculations are used to connect concepts to real world observations in and beyond the project. Calculations Calculations minimal or missing. Measurements are unrealistic or used incorrectly. APPLIES Lens Makers equation and Magnification equation to measured distances. CORRECTLY solves for Magnification AND Focal Length from measured distances. Proficient PLUS accurate description of mathematical process AND multiple data points Style and Organization Presentation is unsequenced, disorganized, visually unappealing, and/or dull. Presentation has organized elements and lacks overall attractiveness or audience engagement. Presentation is in a logical sequence and has attractive and engaging elements. Presentation is organized, engaging and attractive. 6

7 Math/Physics Concepts and Skills Math Concepts Similar figures Math Skills- Solving equations Ratio and proportions Measurement Solving equations Physics Concepts Law of Refraction Physics Skills- Solving equations Law of Reflection Measurement Solving equations Math/Physics Language Math- Similar figures, corresponding parts, proportions, scale factor, preimage, image, parallel lines, transversal. Physics - Similar angles, object, image, magnification, focus Equivalent Terms Math Physics preimage image scale factor object image magnification Instructor Reflection: What worked well? What should be improved? What could be changed and why? 7

8 Math/Physics Concepts and Skills Make a list of physics and math concepts and skills necessary to complete the tasks in the math modeling section and the physics investigation. Define and explain the concepts and skills. Math Concepts: Similar figures Parallel lines Math Skills: Solving proportions Measurement Angle Equality Theorems Ratio and proportions Solving equations Physics Concepts: Law of Refraction Law of Reflection Physics Skills: Measurement Solving Equations Solving Equations 8

9 Math/Physics Instructional Time Line Order of concepts and skills Parallel lines and Angle Theorems Math 1. one class Physics Similar Triangles and Solving Proportions Measurement and Activity 2. one class 3. one class Presentations 4. one class Notes: The teacher will need to assign groups which variable to change: d i or d o. 9

10 Project Worksheet: Objective: Build a pinhole camera and observe, measure, and calculate the physical applications of light rays, magnifications (dilations), and similarity. Materials: Shoebox Rulers LED Flashlight Source Cardboard Box/Tube Aluminum Foil White Copy Paper Duct Tape Painters Tape Scissors/Box Knife Pipe Cleaners Instructions: Your team will need to build a pinhole camera box using either a shoe box or cardboard tube brought from home and the diagrams shown. Accuracy in your measurements will be very important. Small variations in pinhole size will create major changes in your transformations. Your tube or box needs to be sealed so that light does not enter from the edges. You will measure the lengths involved and calculate the scale factors involved. 10

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12 Steps: In one end of your box, cut out the cardboard in a rectangular area roughly 2 cm high by 10 cm long. Cover this area with tinfoil. This tin foil will block out light and allow you to make pinholes. It can be replaced in case of mistakes. Use the lead of a mechanical pencil to make a pinhole in the approximate center of the tinfoil at the end of the box. In the same end of the box, find a good location to place a cell phone camera that will not interfere with the pinholes. It is a good idea to keep it close to the edge so you can use the front facing camera also. Cut out a section of the cardboard for your camera. Hint:(Make the hole larger than you need, cover the hole with tinfoil, and use a pencil to get an exact fit for your camera.) Using white paper or cardstock, cut out a screen to go inside your box. Measure and record the distance between your screen and the pinhole as d i. Tape a short plastic ruler or a paper ruler to the screen so that you will be able to measure the size of your image later. Seal your box to keep light out. Remember: you will need to get into your box again, taping it shut may not be the best solution. Attach a pipe cleaner to your flashlight. Measure and record the length of the pipe cleaner in front of the flashlight as d o. This pipe cleaner will help maintain a constant distance from the pinhole for each experiment. Using your camera as a viewer, shine the flashlight through the pinhole. Find the image and measure the image using the ruler attached to the screen. Find the image on your camera, play with the light source and observe what happens. Measure the diameter of your light source and record this as h o. Measure the diameter of the image using the ruler on the screen and record this as h i Use tape to cover one or more LEDs on the flashlight to make an asymmetric pattern. Again, using your camera as a viewer, shine the flashlight through the pinhole. 12

13 Find the image and measure the image using the ruler attached to the screen. In the diagrams above d i = distance from the pinhole to the image d o = distance from the pinhole to the flashlight h i = height of the image h o = diameter of the flashlight Trial # d i d o h i h o What is the relationship of the two triangles? 13

14 What are the scale factors for the trials? What did you observe about the relationships of these variables? What did you observe about the relationship of the pre-image and the image? What type of transformation is this? 14

15 Geometry EOC released items: Loading... is intersected by Loading... at the point C forming the two right triangles shown below. 1. In the figure above, what is the value of x? 2. What is the measure of angle E? Look at the figure below. 3. If AD is 12 inches, how many inches is CE? 15