Exam (elaborations) GIZMOS RayTracing Mirrors SE Key

Exam (elaborations) GIZMOS RayTracing Mirrors SE Key Vocabulary: concave mirror, convex mirror, focal point, magnification, real image, reflect, virtual image Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is to activate prior knowledge and get students thinking. Students are not expected to know the answers to the Prior Knowledge Questions.] 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 the front of the spoon (the side where the food sits). What do you see? My head is small in size and upside-down. My face is also distorted. The front of a spoon is an example of a concave mirror. 2. What do you see when you look at yourself in the back of a spoon? My head is small in size and right side up. My face is also distorted. 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 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 ray always passes through the focal point. 2. Turn off the Parallel line and turn on the Line through focal point. Move the light bulb around. What do you notice about the reflected ray in this situation? The reflected ray is horizontal and parallel to the axis of the mirror. This study source was downloaded by from CourseH on :26:34 GMT -05:00 This study resource was shared via CourseH GIZMOS Ray Tracing Mirrors SE Key 2019 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? The light bulb’s image is the same size as the light bulb. B. What do you notice about the orientation of the light bulb’s image? The light bulb’s image is upside-down. 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. Image moves right, gets smaller Move the light bulb to the right. Image moves to the left, gets bigger Move the focal point to the left. Image moves to the left, gets bigger Move the focal point to the right. Image moves to the right, gets 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? The image gets smaller and moves towards the focal point. B. In general, how do the size and position of the image change when the distance between the light bulb and the focal point decreases? The image gets larger and moves away from the focal point. (Activity A continued on next page) This study source was downloaded by from CourseH on :26:34 GMT -05:00 This study resource was shared via CourseH 2019 Activity A (continued from previous page) 4. Explore: Move the light bulb to -10 and the focal point to -20. What do you notice about the image when the light bulb is between the focal point and the mirror? The image is upright, larger than the light bulb, and on the opposite side of the mirror. The image is virtual because no light rays are focused there. This virtual image is what an observer would see looking into the mirror. The dashed lines represent the direction that an observer would perceive the reflected light was traveling from. 5. Investigate: Select a Convex mirror, and turn off the Original light lines and the Apparent light lines. Move the light bulb back and forth (but keep it close to the central axis). A. What do you notice about the three lines reflected from the convex mirror? The three lines are moving apart. B. Is the image of the light bulb a real image or a virtual image? Explain. (Hint: Recall that a real image is formed where actual light rays are reflected.) The image is a virtual image because it is behind the mirror. No real image is formed in front of the mirror because the light rays diverge. C. Move the light bulb back and forth. No matter where the light bulb is located on the central axis, what is always true about the size of the image? The image is always smaller than the original light bulb. 6. Apply: Which type of mirror would you use for the following applications, and why? A. Cooking a hot dog: Use a concave mirror because it can focus sunlight onto the hot dog. B. Surveillance in a convenience store: Use a convex mirror because it shrinks the image, allowing more of the store to be viewed. This study source was downloaded by from CourseH on :26:34 GMT -05:00 This study resource was shared via CourseH 2019 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 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: do: Distance between object and mirror f: Distance between focal point and mirror di : Distance between image and mirror What are the current values of each of these variables? (Note: You can use the ruler to measure do and di .) do = 15 f = 10 di = 30 2. Gather data: Measure di for each of the following values of do and f. For the last two rows of the table, use your own values of do and f. do f di do 1 di 1 f 1 15 10 ~30 (30.0) ~0.067 ~0.033 ~0.1 25 10 ~17 (16.7) ~0.040 ~0.060 ~0.1 Results from student experiments will vary. In each experiment, 1/do + 1/di should equal or be very close to 1/ f. 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 do 1 and di 1 . Record these values here: ~0.1 ~0.1 [The last two values will vary.] What do you notice? In each experiment, the sum of 1/do + 1/di was very close to 1/ f. (Activity B continued on next page) This study source was downloaded by from CourseH on :26:34 GMT -05:00 This study resource was shared via CourseH 2019 Activity B (continued from previous page) 5. Make a rule: Express the relationship between do 1 , di 1 , and f 1 as an equation. 1 1 1 d d f o i   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? 4.8 cm Show your work: do = 8 cm, di = 12 cm, solve for f 1/f = 1/8 + 1/12 = 5/24 f = 24/5 = 4.8 cm 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? 13.3 cm Show your work: do = 20 cm, f = 8 cm, solve for di 1/ di = 1/8 – 1/20 = 3/40 di = 40/3 = 13.3 cm 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, di and f are negative.) Sample answer: Yes, the mirror equation does apply to convex mirrors. I placed the focal point at 20 and the light bulb at -20. In this situation, do = 20, f = -20, and the image was located at 10 so di = -10. 1/20 – 1/10 = -1/20 This study source was downloaded by from CourseH on :26:34 GMT -05:00 This study resource was shared via CourseH