Images in Curved Mirrors

Transcription

1 11.9 Images in Curved Mirrors OVERALL EXPECTATIONS investigate, through inquiry, the properties of light, and predict its behaviour, particularly with respect to reflection in plane and curved mirrors and refraction in converging lenses demonstrate an understanding of various characteristics and properties of light, particularly with respect to reflection in mirrors and reflection and refraction in lenses SPECIFIC EXPECTATIONS Developing Skills of Investigation and Communication use appropriate terminology related to light and optics use an inquiry process to investigate the laws of reflection, using plane and curved mirrors, and draw ray diagrams to summarize their findings predict the qualitative characteristics of images formed by plane and curved mirrors, test their predictions through inquiry, and summarize their findings Understanding Basic Concepts describe, on the basis of observation, the characteristics and positions of the images formed by plane and curved mirrors, with the aid of ray diagrams and algebraic equations, where appropriate identify ways in which the properties of mirrors and lenses (both converging and diverging) determine their use in optical instruments KEY CONCEPTS Optical devices benefit our society in many ways. Curved mirrors produce a variety of images. Time min Vocabulary concave (converging) mirror convex (diverging) mirror centre of curvature principal axis vertex converge focus real image diverge Assessment Resources Assessment Rubric 1: Knowledge and Understanding Assessment Summary 1: Knowledge and Understanding Other Program Resources BLM Two-Column Table BLM Term Box website /scienceperspectives/10 EVIDENCE OF LEARNING Look for evidence that students can describe the images formed by concave mirrors describe the images formed by convex mirrors understand how incident rays are used to determine whether an image is formed by a curved mirror SCIENCE BACKGROUND Curved Mirrors Both concave and convex mirrors can be thought of as portions of spheres. Visualizing this is essential because C, the centre of curvature, determines the location of the principle axis of the mirror. It is the centre of the shape that would be formed if the mirror were a complete sphere. Concave mirrors are also called converging mirrors; convex mirrors are also called diverging mirrors. This is because concave mirrors cause parallel light rays to converge, whereas convex mirrors cause parallel light rays to diverge. Images formed in concave mirrors have differing characteristics depending upon the distance between the object and the mirror. Related Resources Gizmo: Ray Tracing (Mirrors) Meiani, Antonella. Light (Experimenting With Science). Lerner Publications, De Pree, Christopher. Physics Made Simple. Broadway Books, ExamView Test Bank Teacher esource SUITE Upgrade website /scienceperspectives/10 NEL Chapter 11 The Production and Refl ection of Light 809

2 The characteristics of images formed in convex mirrors are diminished size (when compared to the actual object), upright, behind the mirror, and virtual. These characteristics do not change no matter where the object is located. The side mirrors on cars are convex, so their images are diminished in size. This distorts depth perception. Many car mirrors carry the warning Objects in mirror are closer than they appear. The distortion occurs because the convex mirror produces a small image, making the object appear to be farther away than it actually is. POSSIBLE MISCONCEPTIONS Identify Students may think that the image formed in a concave mirror always has the same characteristics no matter where the object is located. Clarify The characteristics of images formed by plane mirrors and convex mirrors are always the same no matter where the object is located, but this is not true for concave mirrors. The characteristics of the image formed by a concave mirror vary depending on the location of the object. Ask What They Think Now At the end of the section, ask, What do you need to know to determine the characteristics of an image formed by a concave mirror? (the location of the object in relation to the centre of curvature and the focus) TEACHING NOTES Engage To introduce the section, have students think of examples of concave and convex mirrors that are useful in everyday life. Examples include ATM mirrors, car mirrors, elevator mirrors, sunglasses, car headlights, flashlights, and telescopes. For each example named, have students state why the concave or convex mirror is more useful than a plane mirror for that application. Use students responses to begin their exploration of the characteristics of images formed by concave and convex mirrors. Reading Tip Relate It to Yourself Encourage students to write the examples that they think of in their notebook. Have students share examples aloud or trade notebooks, as this may remind students of examples that they had not considered. Explore and Explain Before assigning the reading for this section, have students make a twocolumn table by drawing a line down the centre of a sheet of paper. Have students label one side Concave Mirrors and the other side Convex Mirrors. Alternatively, you could distribute BLM Two-Column Table. Tell students to use this table to organize facts and information as they read the section. This table will provide a convenient location for students to refer to as they continue to learn about mirrors, to remind them of the characteristics of these two mirror types. At intervals, remind students to make notes in their table. Use Figure 2 on page 496 to help students visualize how the location of C, the centre of curvature, is determined. Note that it may be helpful to draw the rest of the circle that is the cross-section of the mirror. Because the centre of curvature is the centre of a sphere, it must be the centre of every circular cross section of the sphere. 810 Unit E: Light and Geometric Optics NEL

3 Move on to Figure 3. Emphasize that the focus, F, is located on the principal axis, between the centre of curvature and the vertex. Ask, Why are concave mirrors called converging mirrors? (This type of mirror causes parallel light rays to converge.) Discuss with the class each of the numbered rays in Figure 5 on page 497. Ask students to explain what is going on with each ray in their own words. Explain that the way in which each reflected ray behaves is dependent upon the way in which the incident ray approaches the mirror. This behaviour depends upon whether the ray is parallel to the principal axis as it approaches and whether the ray passes through the focus. As each ray is discussed, have students trace the light ray that corresponds to the numbered statement. The imaging rules are applied in Figure 6. Emphasize that the characteristics of the image depend on the location of the object in relation to C and F. Spend time explaining the difference between a real image and a virtual image for a concave mirror. In Figure 6(a) on page 497, for example, if you held a sheet of paper at the location on the diagram where the image appears, you would actually see an image on the paper. Contrast this with the image in Figure 10 on page 499, which appears behind the mirror as a virtual image that would not show up on the sheet of paper. Discuss images in a converging mirror as explained on page 498. Ask, How does a real image differ from a virtual image? (A virtual image is an image in which light does not actually arrive at or come from the image location; a real image is formed when light actually arrives at the image location.) After discussing the information on pages 498 and 499 describing how the location of the object in relation to C and F determines the characteristics of the image formed by a concave mirror, have students examine the summary found in Table 1. Then have students create a Venn diagram comparing three items. Have students use the headings shown in the sample below, which also includes sample answers. Reading Tip Take Time with Diagrams Tell students that one way to enhance understanding of diagrams is to duplicate the diagram in a notebook. Drawing and labelling the diagram can lead to a deeper understanding of the concepts illustrated in the diagram and can identify concepts that are confusing. Writing Tip Using Signal Words Encourage students to pay special attention to signal words as they read the Student Book. It may be helpful to record the signal words (including those listed in the Writing Tip) and their meanings in BLM Two-Column Table as a reference during any reading they are doing. Object location beyond C smaller between C and F inverted real image formed upright behind mirror virtual Object location inside F Object location between C and F larger beyond C Have students examine the three imaging rules for a convex mirror on page 500 of the Student Book. Because the imaging characteristics for a convex mirror never change, any two of the three rules listed in the text will always locate the image without requiring the use of a protractor. Writing Tip Writing Persuasive Text Stress the importance to students of a strong conclusion that ties together the main idea and key points. Readers often remember best what they read last, so one s conclusion may be what makes the greatest impact on the reader and has the opportunity to be the most persuasive part. NEL Chapter 11 The Production and Refl ection of Light 811

4 Have students visit the Nelson Student esource to access computer simulations involving curved mirrors. The imaging properties of concave and convex mirrors are summarized below. Review the scenarios with the class and discuss any situations for which students have questions of a concave mirror. When the object is placed beyond C of a concave mirror, the image is real, inverted, smaller than the original object, and located between C and F. When the object is at C of a concave mirror, the image is real, inverted, the same size as the original object, and located at C. When the object is located between C and F of a concave mirror, the image is real, inverted, larger than the original object, and located beyond C. When the object is located between the concave mirror and F, the image is virtual, upright, larger than the original object, and located at C. For a convex mirror, the image is always upright, smaller than the original, and virtual regardless of the position of the object. Extend and Assess Review how to locate images in concave and convex mirrors. Ask students to explain similarities and differences in the methods for locating images in these two types of mirrors. Ask them to describe the images formed by concave and convex mirrors. Have students complete the Check Your Learning questions on page 501 of the Student Book. CHECK YOUR LEARNING Suggested Answers 1. Sample answers: Concave mirrors are used for parking lot lighting, and are found in reflecting telescopes in the science classrooms. Convex mirrors are used in the library to provide wide angle views. 2. Light rays actually arrive at the location of a real image, so it can be formed (projected) on a screen. Light rays that form a virtual image do not pass through or come from the image location; they just appear to. 3. The diagram should show that rays entering the mirror parallel to the principal axis are reflected through the focus. focus (F ) 4. Sample answer: Rays that are parallel to the principal axis will reflect through the focus. Rays that pass through the focus as they head toward the mirror reflect parallel to the principal axis. Rays that pass through the centre of curvature heading toward the mirror will reflect back upon themselves. A ray that strikes the vertex will obey the laws of reflection. 5. My head is between the focus and the mirror. 812 Unit E: Light and Geometric Optics NEL

5 6. Diverging rays can only be traced back by the observer s brain to an apparent point of origin, and thus never come from or pass through the image location. Reflected rays from a convex mirror always diverge. Real images can only form when reflected rays from a mirror converge. F image object 7. (a) This is a convex mirror. (b) The image is located behind the mirror. (c) This is a virtual image. 8. (a) image 5 smaller, inverted, between C and F, real F C (b) image 5 same size, inverted, at C, real C F (c) image 5 smaller, upright, on the other side of the mirror between the mirror and F, virtual C F 9. Real images are inverted, and virtual images are upright. 10. (a) Drivers can see around corners due to the wide angle view the mirrors provide. (b) Sample answers: right hand side-view mirror on a car, security mirrors in stores, decorations in homes. NEL Chapter 11 The Production and Refl ection of Light 813

6 Unit Task B ookmark Have students discuss the optical devices that were described in this section. Ask, How do these devices apply the imaging rules for curved mirrors? (answers will vary) Ask students to think about how they could apply this same information as they complete the Unit E Task: Building an Optical Device. Ask volunteers to share their thoughts with the class. DIFFERENTIATED INSTRUCTION Point out that diagrams are used to illustrate concepts throughout this section. Visual/spatial learners will enjoy making diagrams for the class to use. However, keep in mind that other learners may also benefit from actually drawing the diagrams. Verbal/linguistic learners may benefit from writing out the four rules for locating an image in a concave mirror (page 497) and displaying them in class. Visual/spatial learners and artistic students can create diagrams to accompany the rules. Visual/spatial learners and bodily/kinesthetic students may enjoy making models of the diagrams using strings to represent light rays. ENGLISH LANGUAGE LEARNERS Make sure that English language learners understand the four rules for locating an image in a concave mirror (page 497). Show how each rule corresponds to the diagram. Have students explain the rules in their own words. Have students prepare a glossary of the terms introduced in this section. Have them include each term, a short definition in their own words, and, if applicable, a simple diagram or picture to represent the term. BLM Term Box will be useful for this purpose. 814 Unit E: Light and Geometric Optics NEL