Using Mirrors to Form Images. Reflections of Reflections. Key Terms. Find Out ACTIVITY

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1 5.2 Using Mirrors to Form Images All mirrors reflect light according to the law of reflection. Plane mirrors form an image that is upright and appears to be as far behind the mirror as the is in front of it. Depending on the distance of the, a concave mirror can form an image that is inverted or right side up, and that can be larger or smaller than the. Convex mirrors form images that are upright and smaller than the. Key Terms concave converging convex diverging point You can see yourself as you glance into a quiet pool of water or walk past a shop window. You can see unusual reflections of yourself in the wavy mirrors at amusement parks. You can even see reflections of yourself in a spoon. Most of the time, however, you probably look for your image in a flat, smooth mirror called a plane mirror. 5-6 Reflections of Reflections Find Out ACTIVITY In this activity, you will find out how many reflections you can see in two plane mirrors. Materials 2 plane mirrors masking tape protractor paper clip Safety Handle glass mirrors and bent paper clips carefully. Count the images in each mirror. What to Do 1. Create a table to record your data. Give your table a title. 2. Lay one mirror on top of the other with the mirror surfaces inward. Tape them together so they will open and close. Use tape to label them L (left) and R (right). 3. Stand the mirrors up on a sheet of paper. Using a protractor, close the mirrors to an angle of Bend one leg of a paper clip up 90 and place it close to the front of the R mirror. 5. Count the number of images of the clip you see in the R and L mirrors. Record these numbers in your data table. 6. Hold the R mirror still. Slowly open the L mirror to 90. Count and record the images of the paper clip in each mirror. 7. Hold the R mirror still. Slowly open the L mirror to 120. Count and record the images of the paper clip in each mirror. What Did You Find Out? 1. What is the relationship between the number of reflections and the angle between the two mirrors? 2. How could you use two mirrors to see a reflection of the back of your head? 182 MHR Unit 2 Optics

2 Plane Mirrors Looking at yourself in a plane mirror, you can see that your image appears to be the same distance behind the mirror as you are in front of the mirror. How could you test this? Place a ruler between you and the mirror. Where does the image touch the ruler? You also see that your image is oriented as you are and matches your size. This type of reflection is where the expression mirror image comes from. If you move toward the mirror, your image moves toward the mirror. If you move away, your image also moves away. How do reflected rays form an image that we can see in a mirror? Study Figure 5.14 to answer this question. Light from a lamp shines on a blueberry. This light reflects off all points on the blueberry, in all directions. In the figure, only the rays coming from one point are shown. All of the rays from the blueberry that strike the mirror reflect according to the law of reflection. The rays that reach your eye appear to be coming from a point behind the mirror. The same process occurs for every point on the blueberry. Your brain knows that light travels in straight lines. Therefore, your brain interprets the pattern of light that reaches your eye as an image of a blueberry behind the mirror. In fact, it might even be possible to trick the observer into thinking the blueberry was behind a glass window, rather than in front of a very good mirror. A house of mirrors uses this trick to create a maze. Did You Know? The mirror on the Hubble Space Telescope is one of the smoothest mirrors ever made. If the mirror were as large as Earth, the biggest bump on it would be only 15 cm tall. plane mirror image Figure 5.14 Only a small fraction of the light reflecting from an enters the eye of the observer. Chapter 5 Optical systems make use of mirrors and lenses. MHR 183

3 Image size and distance Another important feature of images in plane mirrors is demonstrated in Figure Rays are shown coming from three different points on the bird. These rays reflect off the mirror and back to the bird s eye. Figure 5.15 We know that what we see in a mirror is just an image. However, a pet bird will chatter for hours to a friend in the mirror. bird plane mirror image of bird Notice that the points appear to be coming from behind the mirror. Each point appears to be coming from a point that is as far behind the mirror as the real point is in front of the mirror. Also notice that the three points are exactly the same distance apart in the image as they are on the, the bird. These observations explain why an image in a plane mirror is the same size as the and appears to be the same distance from the mirror as the. image mirror Figure 5.16 When the boy blinks his right eye, the left eye of his image blinks. Image orientation A plane mirror produces an image with the same orientation as the. If you are standing on your feet, a plane mirror produces an image of you standing on your feet. If you are doing a headstand, the mirror shows you doing a headstand. However, there is a difference between you and the appearance of your image in the mirror. Follow the sight lines in Figure The ray that diverges from the right hand of the boy converges at what appears to be the left hand of his image. Left and right appear to be reversed by a plane mirror. 184 MHR Unit 2 Optics

4 Concave Mirrors A concave mirror is a mirror that curves inward. Concave mirrors, like plane mirrors, reflect light rays to form images. The difference is that the curved surface of a concave mirror reflects light in a unique way. As shown in Figure 5.17, parallel light rays bounce off the curved surface of a concave mirror and then meet at a single point called the point. Light rays that are coming together at a point are described as converging. The image formed by a concave mirror depends on how far the is from the point of the mirror (see Figure 5.18). If a distant is reflected in a concave mirror, its image is small and upside down. As the approaches the point, its image remains inverted but gets ever larger. If the is between the point and the mirror, then the image appears to be larger than the and is upright. Concave mirrors have many uses (see Figure 5.19). If a bright light is placed at the point, then all the light rays bounce off the mirror and are reflected parallel to each other. This makes an intense, focussed beam of light. Spotlights, flashlights, lighthouses, and car headlights use this kind of mirror. The largest telescopes all use concave mirrors to collect light because the mirror concentrates the light so effectively. Shaving mirrors and make-up mirrors are also concave mirrors. They form an enlarged, upright image of a person s face so it is easier to see small details. point Figure 5.17 Light rays collected by a concave mirror converge on a point before spreading out again. (a) A point (b) B point (c) C point Figure 5.18 The image formed by a concave mirror depends on how far away the is. Figure 5.19 The boy is between the concave mirror and its point. Chapter 5 Optical systems make use of mirrors and lenses. MHR 185

5 Figure 5.20 The reflected rays from a convex mirror diverge and do not meet. point Convex Mirrors A convex mirror is a mirror that curves outwards. Convex mirrors also reflect light rays to form an image, but they do so in an opposite way to concave mirrors. A convex mirror reflects parallel light rays as if they came from a point behind the mirror (see Figure 5.20). Light rays that spread apart after reflecting are described as diverging. The image formed is always upright and smaller than the actual. The reflection from a convex mirror has two main characteristics: 1. Objects appear to be smaller than they are. 2. More s can be seen in a convex mirror than in a plane mirror of the same size. Security mirrors, such as those in convenience stores, are large convex mirrors. Convex mirrors make it possible to monitor a large region of the store from a single location. Convex mirrors can also widen the view of traffic that can be seen in rearview or side-view mirrors of automobiles. However, because distances and sizes seen in a convex mirror are not realistic, most convex side-view mirrors carry a printed warning that the s viewed are closer than they appear to be (see Figure 5.21). Suggested Activity Conduct an Investigation 5-7 on page 187 A B Find out about the centre of curvature and radius of curvature for a concave lens. What is the relationship between the radius of curvature and the length? If a person stands at the centre of curvature in front of a large concave mirror, where will his or her image form and what will be its size and orientation? Visit Figure 5.21 Convex mirrors are used in stores as security mirrors (A), and in cars as rearview and side-view mirrors (B). Reading Check 1. What size does the image in a plane mirror appear to be? 2. What distance from the mirror does an image in a plane mirror appear to be? 3. How is a concave mirror shaped differently from a plane mirror? 4. What are some uses for concave mirrors? 5. How is a convex mirror shaped differently from a plane mirror? 6. What are some uses for convex mirrors? 186 MHR Unit 2 Optics

6 Checking Concepts 1. Describe how your image changes as you move closer to: (a) a plane mirror (b) a concave mirror (c) a convex mirror 2. One side of a soupspoon is convex and the other is concave. Imagine you are having soup and you lift the spoon out of the soup bowl, holding some soup. Is the part of the spoon touching the soup convex or concave? 3. Do convex and concave mirrors obey the law of reflection? Explain. 4. Explain the difference between divergent and convergent light rays. 5. Draw and label a mirror that produces: (a) divergent light rays (b) convergent light rays 6. Suppose you find a shiny metal bowl that has been left outside in the sunlight. (a) Are you more likely to see the reflection of direct sunlight by viewing the outside or the inside of the bowl? (b) Is it more dangerous to look at the outside or the inside of the bowl? Explain. 10. Design and label an arrangement of mirrors to do each of the following: (a) see over the top of a fence without having to raise your eyes above the top of the fence (b) read a book by reflected light without having the words backwards in a mirror image (c) collect and concentrate the Sun s light into a small space and then conduct the light around two corners to a solar panel Pause and Reflect When you look across a lake, you might see the reflection of the distant mountains and trees in the water. The image of the trees and mountains appears to be upside down. However, when you look straight down at the surface of the lake, you see an upright reflection of yourself. Why would your image be upright while the image of the mountains is upside down? Understanding Key Ideas 7. Why is an image in a plane mirror the same size as the that is reflected? 8. List several uses of: (a) plane mirrors (b) concave mirrors (c) convex mirrors 9. (a) Draw a ray diagram that shows an arrangement of mirrors that would allow you to see the back of your own head. Draw the diagram as if looking down from above. The rays should leave the back of your head and end in your eye. Show the normal and angles of incidence and reflection. (b) Will left and right be reversed in the image? Explain. Chapter 5 Optical systems make use of mirrors and lenses. MHR 189

7 5.3 Using Lenses to Form Images A lens is a piece of transparent material that can bend, or refract, light rays in useful ways to help form a well-focussed image. Concave lenses are thinner in the middle than at the edge. They are used to diverge light rays. Convex lenses are thicker in the middle than at the edge. They are used to converge light rays. Key Terms concave lens convex lens length lens Light rays refract through a piece of glass in a predictable way. Recall from Section 5.1 that when a light ray passes from air into a denser material, such as glass, it bends toward the normal. When the light ray passes out of the glass, back into the air, it bends away from the normal. Using these facts about light it is possible to design and construct lenses. A lens is a curved piece of transparent material, such as glass or plastic, that refracts light in such a way as to converge or diverge parallel light rays. The image that a lens forms depends on the shape of the lens. Like curved mirrors, a lens can be convex or concave. 5-8 Observing Light Rays Find Out ACTIVITY In this activity, you will observe how light rays refract as they pass through lenses. Materials ray box concave lens convex lens printed page What to Do 1. Shine the ray box at a concave lens. Observe how the rays are affected. Draw your observations. 2. Look through the concave lens at some printed text. Observe the appearance of the print. Draw your observations. 3. Shine the ray box at the convex lens. Observe how the rays are affected. Draw your observations. 4. Look through the convex lens at some printed text. Observe the appearance of the print. Draw your observations. What Did You Find Out? 1. Compare what you observed about the appearance of the text with each of the two lenses. 2. Which type of lens would be best used as a magnifying glass? Why? 3. What might the other kind of lens be used for? 190 MHR Unit 2 Optics

8 Concave Lenses Concave lenses are lenses that are thinner in the middle than at the edge. As shown in Figure 5.22, light rays that pass through a concave lens diverge. The rays are refracted outward, and never meet at a point. The image formed is always upright and smaller than the actual (see Figure 5.23 and Table 5.1). Concave lenses are used in some types of eyeglasses and some telescopes, and are often used in combination with other lenses. Figure 5.22 Light rays diverge when they pass through a concave lens. ray 1 ray 2 F image F d i d o Figure 5.23 Concave lenses produce images that are upright and smaller compared to their s. Table 5.1 Images Formed by Concave Lenses Distance of Object from Lens Any location Type of Image Formed Smaller, upright Did You Know? Lenses have been made and used for hundreds of years. In 1303, French physician Bernard of Gordon wrote of the use of lenses to correct eyesight. Around 1610, Galileo used two convex lenses to make a telescope, with which he discovered the moons of Jupiter. Chapter 5 Optical systems make use of mirrors and lenses. MHR 191

9 internet connect Raindrops take on a spherical shape as they fall, which gives them the shape of a convex lens. A drop of water sitting on a glass slide has a nearly spherical shape. Investigate whether a water droplet or a glass bead of the same size would make a good magnifying lens. Start your search at Convex Lenses Convex lenses are lenses that are thicker in the middle than at the edge. As shown in Figure 5.24, light rays that pass through a convex lens come together, or converge. When parallel rays strike a convex lens from one side, they will all come together at the point of the lens. Light passing through the thicker, more curved areas of the lens will bend more than light Figure 5.24 Light rays converge when they pass through a convex lens. passing through the flatter areas. A light ray that passes straight through the centre of the lens is not refracted. The image formed by a convex lens depends on the positions of the lens and the (see Figure 5.25). optical axis ray A two lengths ray B one length point image A When the candle is more than two lengths away from the lens, its image is reduced and upside down. two lengths ray A one length point ray B optical axis image B When the candle is between one and two lengths from the lens, its image is enlarged and upside down. image one length ray A ray B point optical axis C When the candle is less than one length from the lens, its image is enlarged and upright. Figure 5.25 An image formed by a convex lens may be inverted, or flipped upside down. 192 MHR Unit 2 Optics

10 Focal Length in Convex Lenses Convex lenses and concave mirrors share a similar property in that the light rays converge at the point. The distance from the centre of the lens or mirror to the point is called the length (see Figure 5.26). There is a mathematical relationship linking the distance of the in front of the lens to the distance of the image formed by the lens. If the is more than two lengths in front of the lens, the image is smaller than the and inverted. If the is moved closer to the lens so that it is one to two lengths away, the image is larger than the and still inverted. If the is very close, less than one length away, the image appears to be located on the other side of the lens and is both upright and larger than the. As summarized in Table 5.2, the type of image a convex lens forms depends on where the is relative to the point. length Suggested Activities Find Out Activity 5-9 on page 194 Find Out Activity 5-10 on page 195 Figure 5.26 The length of a convex lens point Table 5.2 Images Formed by Convex Lenses Distance of Object from Lens Type of Image Formed More than two lengths Between one and two lengths Object at point Less than one length Reading Check Smaller, inverted Larger, inverted No image Larger upright 1. What happens to parallel light rays that strike a concave lens? 2. What happens to parallel light rays that strike a convex lens? 3. What type of image is formed by a concave lens? 4. What determines the type of image that is formed by a concave lens? Eyeglasses would more correctly be called eyeplastics these days. Glass refracts well but is heavy and can shatter. The highest quality of plastic in widespread use for glasses is polycarbonate plastic. Find out what properties it has that makes it so useful in lenses. Start your search at Chapter 5 Optical systems make use of mirrors and lenses. MHR 193

11 Checking Concepts 1. What is a lens? 2. (a) Make a sketch of three parallel light rays passing through a concave lens. (b) Make a sketch of three parallel light rays passing through a convex lens. 3. Describe the image formed by a concave lens. 4. As an comes closer to a convex lens what happens to: (a) the size of the image? (b) whether the image is upright or upside down? (c) the location of the image? 5. List two factors that affect the way that light is refracted through a lens. 6. List two uses of convex lenses. 7. List two uses of concave lenses. Pause and Reflect The archer fish is a remarkable hunter that catches insects that are resting on branches or reeds up to 2 m above the water. The archer fish sights the insect from beneath the water and then shoots a stream out of its mouth at the insect. Light refracts when it passes from air into water, so the insect appears to be in a different place than it really is. Yet the archer fish is deadly accurate. How do you think this is possible? Understanding Key Ideas 8. What is the difference between the way parallel light rays are affected by a concave mirror and a concave lens? 9. Does a concave lens affect light more like a concave mirror or a convex mirror? Explain your answer. 10. Explain why a drop of water placed on the page of a book magnifies printing beneath it. 11. Reading glasses help people to see small print. What sort of lens would be used in them? Chapter 5 Optical systems make use of mirrors and lenses. MHR 197

12 Chapter 5 Prepare Your Own Summary In this chapter, you investigated how optical systems make use of mirrors and lenses. Create your own summary of the key ideas from this chapter. You may include graphic organizers or illustrations with your notes. (See Science Skill 10 for help with using graphic organizers.) Use the following headings to organize your notes: 1. The Ray Model of Light 2. Convex Mirrors 3. Concave Mirrors 4. Convex Lenses 5. Concave Lenses Checking Concepts 1. State the law of reflection. 2. Use a ray diagram to explain why a light appears dimmer the farther the observer is from it. 3. What is the difference between reflection and refraction? 4. How is an opaque different from a translucent in terms of its ability to transmit light? 5. How does the direction of a ray of light change as it passes from air into water? 6. (a) What are the three basic shapes of mirrors? (b) With which shape of mirror do light rays converge? 7. How does the reflection from a convex mirror appear to make s seem smaller? Understanding Key Ideas 8. Draw a diagram of a light ray reflecting off the surface of a flat mirror. Label the normal, the incident ray, the reflected ray, the angle of incidence, and the angle of reflection. 9. Copy the diagrams below into your notebook. Complete the missing parts of each diagram. i r =? Draw the reflected ray. i =? r =? Draw the normal. Draw the two reflected rays. Compare the directions of the light striking and bouncing off the mirror. 198 MHR Unit 2 Optics

13 10. Making reference to the normal line, describe the change in the direction of a light ray that travels from: (a) air into water (b) glass into air 11. Draw a diagram to show how an image the same size as an can be produced by reflection from a flat mirror. 12. As an moves closer to a convex lens, what happens to the size and orientation of the image? 13. Draw a ray diagram to show what happens to light rays as they pass through: (a) a convex lens (b) a concave lens 14. (a) How does the relative thickness of a convex lens affect its ability to refract light? (b) Draw a thin and a thick convex lens. Show how light rays pass through each of them. 15. Draw ray diagrams to illustrate the difference between opaque, translucent and transparent. 16. Copy the following table into your notebook. For each of the following examples, decide what kind of lens or lenses need to be used in the light fixtures. Use a diagram to show how the lens is affecting the light. 17. A magnifying glass contains a lens that can focus the light from the Sun at a single point on the ground. (a) What shape of mirror can also do this? (b) Draw a ray diagram to show parallel light from the Sun striking this mirror and to show where the light rays converge. (c) Which is better for focussing the Sun s light at a point on the ground, a lens or a mirror? Explain. 18. Decide whether each of the following is opaque, translucent, or transparent. Explain your reasons. (a) your tooth (b) your skin (c) your fingernail (d) the lens of your eye Pause and Reflect Suppose you have been given a concave mirror and you have been asked to find its point. Describe a procedure that you could use to do this. Light Fixtures (a) A reading light that lights one spot in the room while leaving other areas dark (b) An outdoor light that spreads an even illumination over a wide area (c) A flashlight that spreads a diffuse, dim light over a wide area, while shining a bright focussed beam in the middle Type of Lens How the Lens Affects Light Rays Chapter 5 Optical systems make use of mirrors and lenses. MHR 199

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