Physics
Image Formed by Plane Mirror
When an object is placed in front of a plane mirror, the mirror forms a virtual image that appears to be behind the mirror. The image is laterally inverted, meaning left and right are swapped, but not top and bottom. The size of the image is the same as the size of the object.
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10 Key excerpts on "Image Formed by Plane Mirror"
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
2 | GEOMETRIC OPTICS AND IMAGE FORMATION Figure 2.1 Cloud Gate is a public sculpture by Anish Kapoor located in Millennium Park in Chicago. Its stainless steel plates reflect and distort images around it, including the Chicago skyline. Dedicated in 2006, it has become a popular tourist attraction, illustrating how art can use the principles of physical optics to startle and entertain. (credit: modification of work by Dhilung Kirat) Chapter Outline 2.1 Images Formed by Plane Mirrors 2.2 Spherical Mirrors 2.3 Images Formed by Refraction 2.4 Thin Lenses 2.5 The Eye 2.6 The Camera 2.7 The Simple Magnifier 2.8 Microscopes and Telescopes Introduction This chapter introduces the major ideas of geometric optics, which describe the formation of images due to reflection and refraction. It is called “geometric” optics because the images can be characterized using geometric constructions, such as ray diagrams. We have seen that visible light is an electromagnetic wave; however, its wave nature becomes evident only when light interacts with objects with dimensions comparable to the wavelength (about 500 nm for visible light). Therefore, the laws of geometric optics only apply to light interacting with objects much larger than the wavelength of the light. Chapter 2 | Geometric Optics and Image Formation 53 2.1 | Images Formed by Plane Mirrors Learning Objectives By the end of this section, you will be able to: • Describe how an image is formed by a plane mirror. • Distinguish between real and virtual images. • Find the location and characterize the orientation of an image created by a plane mirror. You only have to look as far as the nearest bathroom to find an example of an image formed by a mirror. Images in a plane mirror are the same size as the object, are located behind the mirror, and are oriented in the same direction as the object (i.e., “upright”). To understand how this happens, consider Figure 2.2.
- David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Plane mirrors A mirror is a surface that can reflect a beam of light in one direction instead of either scattering it widely in many directions or absorbing it. A shiny metal surface acts as a mirror; a concrete wall does not. In this module we examine the images that a plane mirror (a flat reflecting surface) can produce. Pdf_Folio:796 796 Fundamentals of physics FIGURE 34.3 A point source of light O, called the object, is a perpendicular distance p in front of a plane mirror. Light rays reaching the mirror from O refect from the mirror. If your eye intercepts some of the refected rays, you perceive a point source of light I to be behind the mirror, at a perpendicular distance i. The perceived source I is a virtual image of object O. O I Mirror p i θ θ In a plane mirror the light seems to come from an object on the other side. Figure 34.3 shows a point source of light O, which we shall call the object, at a perpendicular distance p in front of a plane mirror. The light that is incident on the mirror is represented with rays spreading from O. The reflection of that light is represented with reflected rays spreading from the mir- ror. If we extend the reflected rays backward (behind the mirror), we find that the exten- sions intersect at a point that is a perpendicu- lar distance i behind the mirror. When you look into the mirror, your eyes intercept some of the reflected light. To make sense of what you see, you perceive a point source of light located at the point of intersec- tion of the extensions. This point source is the image I of object O. It is called a point image because it is a point, and it is a virtual image because the rays do not actually pass through it. (As you will see, rays do pass through a point of intersection for a real image.) Ray tracing FIGURE 34.4 Two rays from fgure 34.3. Ray Oa makes an arbitrary angle with the normal to the mirror surface.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
25.3 The Formation of Images by a Plane Mirror A virtual image is one from which all the rays of light do not actually come, but only appear to do so. A real image is one from which all the rays of light actually do emanate. A plane mirror forms an upright, virtual image that is located as far behind the mirror as the object is in front of it. In addition, the heights of the image and the object are equal. 25.4 Spherical Mirrors A spherical mirror has the shape of a section from the surface of a hollow sphere. If the inside surface of the mirror is polished, it is a concave mirror. If the outside surface is polished, it is a convex mirror. The principal axis of a mirror is a straight line drawn through the center of curvature and the middle of the mirror’s surface. Rays that are close to the principal axis are known as paraxial rays. Paraxial rays are not necessarily parallel to the principal axis. The radius of curvature R of a mirror is the distance from the center of curvature to the mirror. The focal point of a concave spherical mirror is a point on the principal axis, in front of the mirror. Incident paraxial rays that are parallel to the prin- cipal axis converge to the focal point after being reflected from the concave mirror. The focal point of a convex spherical mirror is a point on the principal axis, behind the mirror. For a convex mirror, incident paraxial rays that are parallel to the principal axis diverge after reflecting from the mirror. These rays seem to originate from the focal point. The fact that a spherical mirror does not bring all rays parallel to the principal axis to a single image point after reflection is known as spherical aberration. The focal length f indicates the distance along the principal axis between the focal point and the mirror. The focal length and the radius of curvature R are related by Equations 25.1 and 25.2.
No longer available |Learn morePhysics for Scientists and Engineers
Foundations and Connections, Extended Version with Modern Physics
- Debora Katz(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
So, in effect, the brain traces these rays back along two straight lines that meet at an imaginary point behind the mirror, but there is no light behind the mirror. (Your bathroom mirror is probably hanging on a wall.) Nevertheless, your brain interprets the point where these rays appear to meet as the location of the image. We define a real image as one in which light rays from every point of an object converge or come together to create every point of the image. This convergence of light rays makes it possible to project a real image on a detector like film, a screen, or your retina. A movie camera lens and a camera obscura both produce real images. By contrast, we call the image produced by your bathroom mirror a virtual image. Light rays appear to diverge or spread from every point of a virtual image, just as they actually diverge from every point of an object. This divergence of light rays means it is not possible to project a virtual image on a screen, just as an object by itself does not project an image. A screen behind your bath- room mirror does not capture your image because there is no light there. A screen facing a bathroom mirror does not capture your image either. Nevertheless, because your eye has a lens, you see a virtual image of yourself in a plane mirror. Some curved mirrors produce real images (Section 37-4), but plane mirrors always produce virtual images. Finding the Image Formed by a Plane Mirror Your experience looking at your image in a flat mirror provides you with a set of expectations. First, imagine sharing the mirror with a roommate who is standing behind you. Your roommate’s image is behind your image, so we expect that the image distance d i is proportional to the object distance d o . Second, the image is PLANE MIRRORS ▲ Special Case RAY DIAGRAMS Tool VIRTUAL AND REAL IMAGES ★ Major Concept FIGURE 37.15 We have drawn two rays emitted from the tip and two from the base of the object’s arrow.
eBook - PDF- David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
If any of these in- gredients is inconsistent with the others, your brain does the best job it can to make sense of it all. Sometimes, as in the case of “optical illusions,” the brain can be fooled completely. The process is similar when you view light coming from a mirror or lens. Your brain tries to process the infor- mation into the most consistent interpretation it can make. In the case of your image in a plane mirror, for example, your brain seems to want to place you somewhere behind the wall to which your mirror is attached! The type of image that is formed by a plane mirror, and also in some cases by curved mirrors and lenses, is called a virtual image. It is characterized by several properties: (1) No light is actually passing through the apparent location of the image. In fact, as in the case of the plane mirror, the image might appear in a location where the light cannot pos- sibly travel. (2) The image cannot be focused on a screen. To see the image, you must look into the mirror or the lens. (3) A virtual image produced by a single mirror or lens is al- ways upright (not inverted), although (as we discuss at the end of this chapter) optical systems with two or more lenses or mirrors can produce virtual images that may be either up- right or inverted. MIRRORS AND LENSES O ptical systems containing mirrors and lenses are of great practical importance. We can use such systems to correct faulty vision, project an image on a screen where it can be viewed by many people at the same time (such as in a movie theater or in your class- room), and make small objects appear large (as in a microscope) or distant objects appear close (as in a telescope). In this chapter we study the formation of images by mirrors and lenses. We will develop both algebraic and graphical methods for analyzing image formation, and we will extend these methods to systems with two or more components, such as microscopes or telescopes. CHAPTER 40 CHAPTER 40
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
d o is 2 if the object is behind the mirror (virtual object).* *Sometimes optical systems use two (or more) mirrors, and the image formed by the first mirror serves as the object for the second mirror. Occasionally, such an object falls behind the second mirror. In this case the object distance is negative, and the object is said to be a virtual object. R 5 22f (1) (2) f 5 a 1 d o 1 1 d i b 21 ? Concept Summary 715 CONCEPT SUMMARY 25.1 Wave Fronts and Rays Wave fronts are surfaces on which all points of a wave are in the same phase of motion. Waves whose wave fronts are flat surfaces are known as plane waves. Rays are lines that are perpendicular to the wave fronts and point in the direction of the velocity of the wave. 25.2 The Reflection of Light When light reflects from a smooth surface, the reflected light obeys the law of reflection: The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of reflection u r equals the angle of incidence u i (u r 5 u i ). 25.3 The Formation of Images by a Plane Mirror A virtual image is one from which all the rays of light do not actually come, but only appear to do so. A real image is one from which all the rays of light actually do emanate. A plane mirror forms an upright, virtual image that is located as far behind the mirror as the object is in front of it. In addition, the heights of the image and the object are equal. 25.4 Spherical Mirrors A spherical mirror has the shape of a section from the surface of a hollow sphere. If the inside surface of the mirror is polished, it is a concave mirror. If the outside surface is polished, it is a convex mirror. The principal axis of a mirror is a straight line drawn through the center of curvature and the middle of the mirror’s surface. Rays that are close to the principal axis are known as paraxial rays. Paraxial rays are not necessarily parallel to the principal axis.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Two Types of Image For you to see, say, a penguin, your eye must intercept some of the light rays spread- ing from the penguin and then redirect them onto the retina at the rear of the eye. Your visual system, starting with the retina and ending with the visual cortex at the rear of your brain, automatically and subconsciously processes the information provided by the light. That system identifies edges, orientations, textures, shapes, and colors and then rapidly brings to your consciousness an image (a reproduction Images 34.1 IMAGES AND PLANE MIRRORS Learning Objectives After reading this module, you should be able to . . . 34.1.1 Distinguish virtual images from real images. 34.1.2 Explain the common roadway mirage. 34.1.3 Sketch a ray diagram for the reflection of a point source of light by a plane mirror, indicating the object distance and image distance. 34.1.4 Using the proper algebraic sign, relate the object distance p to the image distance i. 34.1.5 Give an example of the apparent hallway that you can see in a mirror maze based on equilateral triangles. Key Ideas ● An image is a reproduction of an object via light. If the image can form on a surface, it is a real image and can exist even if no observer is present. If the image requires the visual system of an observer, it is a virtual image. ● A plane (flat) mirror can form a virtual image of a light source (said to be the object) by redirecting light rays emerging from the source. The image can be seen where backward extensions of reflected rays pass through one another. The object’s distance p from the mirror is related to the (apparent) image distance i from the mirror by i = −p (plane mirror). Object distance p is a positive quantity. Image distance i for a virtual image is a negative quantity. 1073 34.1 IMAGES AND PLANE MIRRORS derived from light) of the penguin; you perceive and recognize the penguin as being in the direction from which the light rays came and at the proper distance.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
R 5 22f (1) (2) f 5 a 1 d o 1 1 d i b 21 ? Concept Summary 643 CONCEPT SUMMARY 25.1 Wave Fronts and Rays Wave fronts are surfaces on which all points of a wave are in the same phase of motion. Waves whose wave fronts are flat surfaces are known as plane waves. Rays are lines that are perpendicular to the wave fronts and point in the direction of the velocity of the wave. 25.2 The Reflection of Light When light reflects from a smooth surface, the reflected light obeys the law of reflection: The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of reflection u r equals the angle of incidence u i (u r 5 u i ). 25.3 The Formation of Images by a Plane Mirror A virtual image is one from which all the rays of light do not actually come, but only appear to do so. A real image is one from which all the rays of light actually do emanate. A plane mirror forms an upright, virtual image that is located as far behind the mirror as the object is in front of it. In addition, the heights of the image and the object are equal. 25.4 Spherical Mirrors A spherical mirror has the shape of a section from the surface of a hollow sphere. If the inside surface of the mirror is polished, it is a concave mirror. If the outside surface is polished, it is a convex mirror. The principal axis of a mirror is a straight line drawn through the center of curvature and the middle of the mirror’s surface. Rays that are close to the principal axis are known as paraxial rays. Paraxial rays are not necessarily parallel to the principal axis. The radius of curvature R of a mirror is the distance from the center of curvature to the mirror. The focal point of a concave spherical mirror is a point on the principal axis, in front of the mirror. Incident paraxial rays that are parallel to the principal axis converge to the focal point after being reflected from the concave mirror.
eBook - PDF- Rudolf Kingslake(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
CHAPTER 9 Plane Mirrors and Prisms I. RIGHT- AND LEFT-HANDED IMAGES If an object is placed in front of a plane mirror, each point in the object will be imaged, along the normal to the mirror, at the same distance behind the mirror as the object is in front. In this way a virtual image of the whole object is formed in the mirror. A side view of the situation is shown in Fig. 9.1. When you look at your image in a mirror, every-thing remains the same except that your image is reversed along the line of sight. Your left side is imaged at the left and your head is imaged at the top; the only difference is that the person in the mirror appears to be left-handed (if you are right-handed). We say that the hand of the image has been reversed by the mirror. When you look in the mirror of your car and watch another car coming up behind, you see that the driver of the other vehicle is sitting at the left side just as you are, and you do not notice anything peculiar until you look at his number plate, which you find is reversed, so that PGS-693 appears as £90-20«! In the printing industry, lead type must be in looking-glass lan-guage so that when it is inked and pressed on paper the lettering will come out correctly. Printers use the terms right-reading and wrong-reading to describe these two situations. In lithography, for example, a right-reading document is inked and rolled against a rubber roller, where it becomes wrong-reading. The image on the roller is then transferred by pressure onto a sheet of paper passing under the roller, thus a right-reading copy of the original document is produced. When using a slide projector, the operator stands behind the projec-tor to insert the slides. He first orients the slide so that it reads correctly as he sees it, and he must then turn it upside down, i.e., he must rotate it in its own plane through 180° before inserting it into the projector, because the lens in the projector will turn the image through another 180° on the screen.
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 35.3 Images Formed by Refraction 937 and 35.13b show these possibilities. We find that we can create both real and virtual images with a refracting surface, also. Figure 35.18 shows these two possibilities for a refracting surface surrounded by a medium of index n 1 . These two types of images can be created by placing the object at different positions relative to the surface. The value for p that determines whether an image is real or virtual can be found by letting q S ` in Equation 35.9. Solving for p, we find p 5 n 1 n 2 2 n 1 R When the object is at this distance from the surface, the image is infinitely far away. If the object is moved farther from the mirror than this position, the image is real as in Figure 35.18a. If the object is moved closer to the surface than this distance, the image is virtual as in Figure 35.18b. Now consider placing an object inside a material of index n 1 and looking at the image from a material of index n 2 , where n 1 . n 2 . Equation 35.9 gives us q 5 pR 1 1 2 n 1 n 2 2 p 2 n 1 n 2 R For the condition n 1 . n 2 , the value of q is always negative. Therefore, the image is always virtual. This is analogous to all images being virtual for a convex mirror, as in Figure 35.13c. See Figure 35.19 and Examples 35.6 and 35.7 for situations in which the object is inside a material. Flat Refracting Surfaces If a refracting surface is flat, then R is infinite and Equation 35.9 reduces to n 1 p 5 2 n 2 q q 5 2 n 2 n 1 p (35.11) From this expression, we see that the sign of q is opposite that of p. Therefore, according to Table 35.2, the image formed by a flat refracting surface is on the same side of the surface as the object as illustrated in Figure 35.19 for the situation in which the object is in the medium of index n 1 and n 1 is greater than n 2 .
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