The Reflection of Light in Curved Mirrors
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1 The Reflection of Light in Curved Mirrors Now that you have had a change to review and reflect upon the nature of light on plane mirrors, it is time to proceed on to the study of curved mirrors. To review, go to this website and continue the tutorial. Try the interactive quizzes Check your Understanding. This corresponds with Chapter 10 in On Science 10. Go to this website: Just in case you neglected to make notes, the info in the following box is important! Rules for Rays in Curved Mirrors of Both Types 1. A ray that is parallel to the principal axis is reflected through (or as if it had gone through) the principal focus - real or virtual. 2. A ray passing through (or appearing to pass, through) the principal focus is reflected parallel to the principal axis. 3. A ray passing through (or appearing to pass through) the centre of curvature is reflected back along the same path. Sign Convention 1. All distances are measured from the vertex of a curved mirror. 2. Distances of real objects and images are positive. 3. Distances of virtual objects and images are negative. 4. Object heights and image heights are positive when measured upward and negative when measured downward from the principal axis. Now, test yourself with these problems: Communication Questions 1. A converging mirror reflects light from a distant object, causing it to focus 20 cm from the mirror. What is the radius of curvature of the mirror? 2. You are given a converging mirror, a lighted object, and a white screen. Explain how you would find the centre of curvature. 3. When you look at the sun in a wavy lake, it appears distorted. Why? 4. According to the legend, the Roman fleet at Syracuse was burned when Archimedes focused the sun's rays using a large converging mirror. Was this practical? 5. Diverging mirrors are often used in stores to discourage shoplifting. Why are they useful in this application?
2 6. You are given some sheets of polished steel and told to design fun-house mirrors with each of the following groups of characteristics. (a) Every dimension of a person standing in front of the mirror is enlarged. (b) Every dimension is reduced. (c) All vertical dimensions are made larger, while horizontal dimensions remain the same (that is, the person appears taller and thinner). (d) The upper features are enlarged vertically and the lower features are reduced vertically, while the horizontal dimensions remain the same (that is, the head appears very long and the legs short). With sketches, indicate how you would bend the metal in each case. 7. Two students are doing the same laboratory investigation using identical converging mirrors with a focal length of 25 cm. Each places a candle in front of the mirror and creates an image three times larger. But when they compare notes, they find their object distances are different. How is this possible? Practice Problems 8. List the names of the parts numbered 1 to 5 in this diagram:
3 9.In each of these diagrams, an object and its image appear. Copy the diagrams into your notebook. Locate the centre of curvature in each case.
4 10. On each of these diagrams, the images formed by curved mirrors are indicated. Copy the diagrams into your notebook and, using ray diagrams, locate the objects.
5 11. An object and its image, formed by a converging mirror, are indicated on each of these diagrams. Copy the diagrams into your notebook and, using ray diagrams, locate the principal focus of the mirror.
6 12. A candle 3 cm high is placed 30 cm from a converging mirror with a focal length of 20 cm. By means of a scale ray diagram, locate the image, and determine its height. State the image's characteristics. 13. Use careful scale drawings to locate the images in each of the following cases. State the characteristics of each image. (a) A converging mirror has a focal length of 20 cm. An object is placed at (i) 10 cm, (ii) 30 cm, and (iii) 40 cm from the vertex of the mirror. (b) A diverging mirror has a focal length of 20 cm. An object is placed (i) 10 cm, and (ii) 30 cm from the vertex of the mirror. 14. A woman looks at herself in a magnifying converging mirror whose focal length is 20 cm. If her face is 10 cm from the mirror, (a) at what distance from the mirror is her image? (b) what is the magnification of her face? 15. A 2.0 cm high candle is placed 15 cm in front of a converging mirror with a focal length of 30 cm. How far "behind" the mirror does the candle appear, and how large is it? 16. A dentist holds a converging mirror with a focal length of 20 mm a distance of 15 mm from a tooth. What is the magnification of a filling in the tooth? 17. A trucker sees the image of a car passing her truck in her diverging rear-view mirror, whose focal length is -60 cm. If the car is 1.5 m high and 6.0 m away, what is the size and location of the image? 18. A spherical, polished metallic ball is used as a diverging mirror if = -20 cm) over a birdbath. A bird, 25 cm tall, standing 50 cm away, looks directly at the mirror. What are the size and position of the bird's image?
7 19. When standing 2.0 m in front of an amusement park mirror, you notice that your image is three times taller. What is the radius of curvature of the mirror? 20. A child looks at his reflection in a spherical Christmas tree ornament 8.0 cm in diameter, and sees that the image of his face is reduced by one-half. How far is his face from the ornament? 21. A converging mirror has a focal length of 15 cm. Where would you place an object in order to produce an erect virtual image twice as tall as the object? Answers to selected problems 14. (a) -20 cm (b) cm, 16 cm cm, m cm, -14 cm m cm 21. d o = 7.5 cm
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Notation for Mirrors and Lenses Chapter 23 Mirrors and Lenses The object distance is the distance from the object to the mirror or lens Denoted by p The image distance is the distance from the image to
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text concept Ch 24. Geometric Optics Fig. 24 3 A point source of light P and its image P, in a plane mirror. Angle of incidence =angle of reflection. text. Fig. 24 4 The blue dashed line through object