RayTracingMirrorsSE.docx

Name: Date: Student Exploration: Ray Tracing (Mirrors) Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. Vocabulary: concave mirror, convex mirror, focal point, magnification, real image, reflect, virtual image Prior Knowledge Questions (Do these BEFORE using the Gizmo.) For these questions, it would be helpful to have a metal spoon on hand. If you don’t have one, try to imagine looking at yourself in a spoon. 1. Look at yourself in front of the spoon (the side where the food sits). What do you see? When my face is far away, I see my image smaller and inverted, as I get closer to the spoon, the image becomes larger and disappears for a second. Then, the image becomes larger and then becomes smaller. The front of a spoon is an example of a concave mirror . I can see my image become smaller and upright. 2. What do you see when you look at yourself on the back of a spoon? The back of a spoon is an example of a convex mirror . Gizmo Warm-up The Ray Tracing (Mirrors) Gizmo shows a side view of a light bulb positioned to the left of a mirror. Light rays passing from the light bulb to the mirror are shown. To begin, select the Concave mirror . Turn on Colorize lines . Under Show lines , turn off the Central line and the Line through the focal point so that only the Parallel line is showing. 1. The blue dot in front of the mirror is the focal point of the mirror. Move the light bulb on the left around. What is always true about the ray that is reflected from the parallel ray? The reflected rays from parallel rays always go through the local points. 2. Turn off the Parallel line and turn on the Line through the focal point . Move the light bulb around. What do you notice about the reflected ray in this situation? The light rays incident through the focus points always reflect parallel from the PA. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

Activity A: Real and virtual images Get the Gizmo ready: ● Check that the Concave mirror is selected. ● Turn on the Parallel line , Central line , and Line through focal point . ● Place the light bulb above -24 on the central axis, with the focal point at -12. Introduction: A concave mirror is also called a “converging mirror” because it reflects light rays into a point. A real image is formed where the reflected light rays converge at a point. Unlike a virtual image that forms behind a mirror, a real image can be projected onto a screen. Question: How do mirrors create real and virtual images? 1. Observe: In its current configuration, the distance from the light bulb to the focal point is slightly more than 12 units. The distance from the focal point to the mirror is exactly 12 units. A. What do you notice about the size of the light bulb’s image? B. The image is slightly smaller. C. What do you notice about the orientation of the light bulb’s image? D. The image is inverted. 2. Investigate: Complete each action described in the table below, and state how that action affects the image. Action Effect on image Move the light bulb to the left. The image becomes smaller as the object moves to the left. Move the light bulb to the right. The image becomes larger as the object moves to the right, it disappears when the object is right above the focal point and the image moves behind the mirror and becomes larger when the object is inside the focal point. Move the focal point to the left. The image becomes larger. Move the focal point to the right. The image becomes smaller. 3. Analyze: Examine the results recorded in your table. A. In general, how do the size and position of the image change when the distance between the light bulb and the focal point increases? Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

Activity B: The mirror equation Get the Gizmo ready: ● Select the Concave mirror . ● Move the light bulb to -15 and the focal point to -10. ● Turn off all lines, and turn on Show ruler . Question: How is the position of the image related to the position of the object and the focal length of the mirror? 1. Measure: In this activity, you will measure the relationships between several values: d o : Distance between object and mirror f : Distance between focal point and mirror d i : Distance between image and mirror What are the current values of each of these variables? (Note: You can use the ruler to measure d o and d i .) d o = 15 f = 10 d i = 29 2. Gather data: Measure d i for each of the following values of d o and f . For the last two rows of the table, use your own values of d o and f . (Note: If the light bulb is to the right of the focal point ( d o < f ), the image is virtual and d i is negative.) d o f d i 15 10 30 0.067 0.033 0.1 25 10 16.67 0.04 0.06 0.1 30 10 15 0.033 0.067 0.1 40 10 13.33 0.025 0.075 0.1 3. Calculate: Find the reciprocal of each value and fill in the last three columns of the table. 4. Analyze: For each row of the table, find the sum of and . Record these values here: 0.1 0.1 0.1 0.1 What do you notice? the sum of 1/do and 1/do equal to the 1/f every time. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

5. Make a rule: Express the relationship between , , and as an equation. 1/f = 1/do+1/di This equation is called the mirror equation . For the spherical mirror shown in this Gizmo, the equation works well so long as the object is close to the central axis. 6. Practice: You place a light bulb 8 cm in front of a concave mirror. You then move a sheet of paper back and forth in front of the mirror. The image of the light bulb focuses on the paper when the paper is 12 cm in front of the mirror. What is the focal length of the mirror? f=4.8cm Show your work: 1/f=1/do+1/di=⅛+1/12, f=4.8cm 7. Practice: A light bulb is placed 20 cm in front of a concave mirror with a focal length of 8 cm. How far from the mirror will the image of the light bulb be focused? 13.33cm Show your work: 1/f=1/do+1/di, 1/di=1/f-1/do=⅛-1/20, di=13.33cm 8. On your own: Does the mirror equation work for a convex mirror? Use the Gizmo to find out and describe your findings below. (Hint: In this situation, d i and f are negative.) Yes, it does. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

6. Make a rule: 1. The magnification of an image is equal to the ratio of the image height to the object height. If the image is inverted, the magnification is negative. Using the ratios from the table on the previous page, write three equations to calculate magnification: 7. Manipulate: If = , what is true about the product of s o and s i ? Use the data you collected on the previous page to confirm that this relationship holds. 8. Practice: A candle is placed 14 cm in front of a concave mirror. The image of the candle is focused on a sheet of paper that is exactly 21 cm in front of the mirror. A. What is the magnification of the image? B. What is the focal length of this mirror? (Hint: Use the mirror equation.) Show your work: 9. Practice: A candle is placed 9 cm in front of a concave mirror with a focal length of 6 cm. A. How far from the mirror will the image be located? B. What is the magnification of this image? Show your work: 10. Challenge: When an object is between the focal point and a concave mirror an upright virtual image is created behind the mirror. Because the image is upright, the value of h i is positive. In this case, what must be true about the values of d i , s o , and s i ? Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved