Chapter 36. Image Formation

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1 Chapter 36 Image Formation

2 Image of Formation Images can result when light rays encounter flat or curved surfaces between two media. Images can be formed either by reflection or refraction due to these surfaces. Mirrors and lenses can be designed to form images with desired characteristics. Introduction 2

3 Notation for 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 the mirror or lens. Denoted by q The lateral magnification of the mirror or lens is the ratio of the image height to the object height. Denoted by M Section

4 Images Images are always located by extending diverging rays back to a point at which they intersect. Images are located either at a point from which the rays of light actually diverge or at a point from which they appear to diverge. A real image is formed when light rays pass through and diverge from the image point. Real images can be displayed on screens. A virtual image is formed when light rays do not pass through the image point but only appear to diverge from that point. Virtual images cannot be displayed on screens. Section

5 Images Formed by Flat Mirrors Simplest possible mirror Light rays leave the source and are reflected from the mirror. Point I is called the image of the object at point O. The image is virtual. No light ray from the object can exist behind the mirror, so the light rays in front of the mirror only seem to be diverging from I. Section

6 Images Formed by Flat Mirrors, cont. A flat mirror always produces a virtual image. Geometry can be used to determine the properties of the image. There are an infinite number of choices of direction in which light rays could leave each point on the object. Two rays are needed to determine where an image is formed. Section

7 Images Formed by Flat Mirrors, Geometry One ray starts at point P, travels to Q and reflects back on itself. Another ray follows the path PR and reflects according to the law of reflection. The triangles PQR and P QR are congruent. Section

8 Images Formed by Flat Mirrors, final To observe the image, the observer would trace back the two reflected rays to P. Point P is the point where the rays appear to have originated. The image formed by an object placed in front of a flat mirror is as far behind the mirror as the object is in front of the mirror. p = q Section

9 If you can't see the image above, please install Shockwave Flash Player. If this active figure can t auto-play, please click right button, then click play. 36.2: Images Formed by Flat Mirrors In this animation we explore the properties of flat mirrors using an object represented by a blue arrow. We choose two light rays directed from the object toward the mirror to determine where its image is formed. Adjusting the position of the object shows that the image formed by an object placed in front of a flat mirror is as far behind the mirror as the object is in front of it. What other properties of flat mirrors can you deduce from the animation? 9

10 Lateral Magnification Lateral magnification, M, is defined as M Image height Object height h h (36.1) This is the lateral magnification for any type of mirror. It is also valid for images formed by lenses. Magnification does not always mean bigger, the size can either increase or decrease. M can be less than or greater than 1. Section

11 Lateral Magnification of a Flat Mirror The lateral magnification of a flat mirror is +1. This means that h = h for all images. The positive sign indicates the object is upright. Same orientation as the object Section

12 Reversals in a Flat Mirror A flat mirror produces an image that has an apparent left-right reversal. For example, if you raise your right hand the image you see raises its left hand. Section

13 Reversals in a Flat Mirror, cont. The reversal is not actually a left-right reversal. The reversal is actually a front-back reversal. It is caused by the light rays going forward toward the mirror and then reflecting back from it. Section

14 Properties of the Image Formed by a Flat Mirror Summary The image is as far behind the mirror as the object is in front. p = q The image is unmagnified. The image height is the same as the object height. h = h and M = +1 The image is virtual. The image is upright. It has the same orientation as the object. There is a front-back reversal in the image. Section

15 Application Day and Night Settings on Auto Mirrors With the daytime setting, the bright beam (B) of reflected light is directed into the driver s eyes. With the nighttime setting, the dim beam (D) of reflected light is directed into the driver s eyes, while the bright beam goes elsewhere. Section

16 Quick Quiz 36.1 You are standing approximately 2 m away from a mirror. The mirror has water spots on its surface. True or False: It is possible for you to see the water spots and your image both in focus at the same time. Answer: false 16

17 Example 36.1 Two flat mirrors are perpendicular to each other as in Figure 36.4, and an object is placed at point O. In this situation, multiple images are formed. Locate the positions of these images. 17

18 Example 36.1 Solution: The image of the object is at I 1 in mirror 1 (green rays) and at I 2 in mirror 2 (red rays). In addition, a third image is formed at I 3 (blue rays). This third image is the image of I 1 in mirror 2 or, equivalently, the image of I 2 in mirror 1. That is, the image at I 1 (or I 2 ) serves as the object for I 3. To form this image at I 3, the rays ref lect twice after leaving the object at O. 18

19 Example 36.2 Most rearview mirrors in cars have a day setting and a night setting. The night setting greatly diminishes the intensity of the image so that lights from trailing vehicles do not temporarily blind the driver. How does such a mirror work? Solution: Figure 36.5 shows a cross-sectional view of a rearview mirror for each setting. The unit consists of a reflective coating on the back of a wedge of glass. In the day setting (Fig.36.5a), the light from an object behind the car strikes the glass wedge at point 1. 19

20 Example

21 Example 36.2 Most of the light enters the wedge, refracting as it crosses the front surface, and reflects from the back surface to return to the front surface, where it is refracted again as it re-enters the air as ray B (for bright). In addition, a small portion of the light is reflected at the front surface of the glass as indicated by ray D (for dim). This dim reflected light is responsible for the image observed when the mirror is in the night setting (Fig. 36.5b). In that case, the wedge is rotated so that the path followed by the bright light (ray B) does not lead to the eye. Instead, the dim light reflected from the front surface of the wedge travels to the eye, and the brightness of trailing headlights does not become a hazard. 21

22 Spherical Mirrors A spherical mirror has the shape of a section of a sphere. The mirror focuses incoming parallel rays to a point. A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curve. A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve. Section

23 Concave Mirror, Notation The mirror has a radius of curvature of R. Its center of curvature is the point C Point V is the center of the spherical segment. A line drawn from C to V is called the principal axis of the mirror. The blue band represents the structural support for the silvered surface. Section

24 Paraxial Rays We use only rays that diverge from the object and make a small angle with the principal axis. Such rays are called paraxial rays. All paraxial rays reflect through the image point. Section

25 Spherical Aberration Rays that are far from the principal axis converge to other points on the principal axis. The light rays make large angles with the principal axis. This produces a blurred image. The effect is called spherical aberration. Section

26 Image Formed by a Concave Mirror Distances are measured from V Geometry can be used to determine the magnification of the image. h' q M h p (36.2) h is negative when the image is inverted with respect to the object. Section

27 Image Formed by a Concave Mirror Geometry also shows the relationship between the image and object distances p q R This is called the mirror equation. If p is much greater than R, then the image point is half-way between the center of curvature and the center point of the mirror. p, then 1/p 0 and q R/2 (36.4) Section

28 A Satellite-dish antenna is a Concave Reflector 28

29 Focal Length When the object is very far away, then p and the incoming rays are essentially parallel. In this special case, the image point is called the focal point. The distance from the mirror to the focal point is called the focal length. The focal length is ½ the radius of curvature. Section

30 Focal Point, cont. The colored beams are traveling parallel to the principal axis. The mirror reflects all three beams to the focal point. The focal point is where all the beams intersect. The colors add to white. Section

31 Focal Point and Focal Length, cont. The focal point is dependent solely on the curvature of the mirror, not on the location of the object. It also does not depend on the material from which the mirror is made. Since the focal length is related to the radius of curvature by f = R / 2 the mirror equation can be expressed as p q f (36.6) Section

32 Focal Length Shown by Parallel Rays Section

33 Convex Mirrors A convex mirror is sometimes called a diverging mirror. The light reflects from the outer, convex side. The rays from any point on the object diverge after reflection as though they were coming from some point behind the mirror. The image is virtual because the reflected rays only appear to originate at the image point. Section

34 Image Formed by a Convex Mirror In general, the image formed by a convex mirror is upright, virtual, and smaller than the object. Section

35 Sign Conventions These sign conventions apply to both concave and convex mirrors. The equations used for the concave mirror also apply to the convex mirror. Be sure to use proper sign choices when substituting values into the equations. Section

36 Sign Conventions, Summary Table Section

37 Ray Diagrams A ray diagram can be used to determine the position and size of an image. They are graphical constructions which reveal the nature of the image. They can also be used to check the parameters calculated from the mirror and magnification equations. Section

38 Drawing a Ray Diagram To draw a ray diagram, you need to know: The position of the object The locations of the focal point and the center of curvature. Three rays are drawn. They all start from the same position on the object. The intersection of any two of the rays at a point locates the image. The third ray serves as a check of the construction. Section

39 The Rays in a Ray Diagram Concave Mirrors Ray 1 is drawn from the top of the object parallel to the principal axis and is reflected through the focal point, F. Ray 2 is drawn from the top of the object through the focal point and is reflected parallel to the principal axis. Ray 3 is drawn through the center of curvature, C, and is reflected back on itself. Draw as if coming from the center C is p < f Section

40 Notes About the Rays A huge number of rays actually go in all directions from the object. The three rays were chosen for their ease of construction. The image point obtained by the ray diagram must agree with the value of q calculated from the mirror equation. Section

41 Ray Diagram for a Concave Mirror, p > f The center of curvature is between the object and the concave mirror surface. The image is real. The image is inverted. The image is smaller than the Section object 36.2(reduced). 41

42 Ray Diagram for a Concave Mirror, p < f The object is between the mirror surface and the focal point. The image is virtual. The image is upright. The image is larger than the object Section 36.2 (enlarged). 42

43 The Rays in a Ray Diagram Convex Mirrors Ray 1 is drawn from the top of the object parallel to the principal axis and is reflected away from the focal point, F. Ray 2 is drawn from the top of the object toward the focal point and is reflected parallel to the principal axis. Ray 3 is drawn through the center of curvature, C, on the back side of the mirror and is reflected back on itself. Section

44 Ray Diagram for a Convex Mirror The object is in front of a convex mirror. The image is virtual. The image is upright. The image is smaller than the Section object 36.2(reduced). 44

45 If you can't see the image above, please install Shockwave Flash Player. If this active figure can t auto-play, please click right button, then click play : Images Formed by Spherical Mirrors In this animation we explore the properties of concave, convex, and parabolic mirrors using an object represented by a blue arrow. In the animation the center of curvature is marked by point C and the focal point is marked by point F. You may want to review the section on spherical mirrors starting on page 1047 of your textbook as you work with the animation. What basic properties can you deduce for each type of mirror? 45

46 Notes on Images With a concave mirror, the image may be either real or virtual. When the object is outside the focal point, the image is real. When the object is at the focal point, the image is infinitely far away. When the object is between the mirror and the focal point, the image is virtual. With a convex mirror, the image is always virtual and upright. As the object distance decreases, the virtual image increases in size. Section

47 Quick Quiz 36.2 You wish to start a fire by reflecting sunlight from a mirror onto some paper under a pile of wood. Which would be the best choice for the type of mirror? (a) flat (b) concave (c) convex Answer: (b) 47

48 Quick Quiz 36.3 Consider the image in the mirror in Figure Based on the appearance of this image, would you conclude that (a) the mirror is concave and the image is real, (b) the mirror is concave and the image is virtual, (c) the mirror is convex and the image is real, or (d) the mirror is convex and the image is virtual? Answer: (b) 48

49 Example 36.3 A spherical mirror has a focal length of cm. (A) Locate and describe the image for an object distance of 25.0 cm. Solution: 1 q 1 q M 1 f 1 p cm q 16.7 cm q p cm 16.7 cm cm 49

50 Example 36.3 (B) Locate and describe the image for an object distance of 10.0 cm Solution: q f p q 10.0 cm 10.0 cm q (C) Locate and describe the image for an object distance of cm. q f p Solution: q 10.0 cm 5.00 cm q 10.0 cm q 10.0 cm M 2.00 p 5.00 cm 50

51 Example 36.4 An automobile rearview mirror as shown in Figure 36.l5 shows an image of a truck located 10.0 m from the mirror. The focal length of the mirror is 0.60 m. 51

52 Example 36.4 (A) Find the position of the image of the truck. Solution: (B) Find the magnification of the image. Solution: 1 q 1 q 1 f 1 p m q 0.57 m M m q 0.57 m p 10.0 m 52

53 Images Formed by Refraction Consider two transparent media having indices of refraction n 1 and n 2. The boundary between the two media is a spherical surface of radius R. Rays originate from the object at point O in the medium with n = n 1. Section

54 Images Formed by Refraction, 2 We will consider the paraxial rays leaving O. All such rays are refracted at the spherical surface and focus at the image point, I. The relationship between object and image distances can be given by n1 n2 n2 n1 (36.8) p q R Section

55 Images Formed by Refraction, 3 The side of the surface in which the light rays originate is defined as the front side. The other side is called the back side. Real images are formed by refraction in the back of the surface. Because of this, the sign conventions for q and R for refracting surfaces are opposite those for reflecting surfaces. Section

56 Sign Conventions for Refracting Surfaces Section

57 Flat Refracting Surfaces If a refracting surface is flat, then R is infinite. Then q = (n 2 / n 1 )p (36.9) The image formed by a flat refracting surface is on the same side of the surface as the object. A virtual image is formed. Section

58 Quick Quiz 36.4 In Figure 36.16, what happens to the image point I as the object point O is moved to the right from very far away to very close to the refracting surface? (a) It is always to the right of the surface. (b) It is always to the left of the surface. (c) It starts off to the left, and at some position of O, I moves to the right of the surface. (d) It starts off to the right, and at some position of O, I moves to the left of the surface. Answer: (d) 58

59 Quick Quiz 36.5 In Active Figure 36.18, what happens to the image point I as the object point O moves toward the right-hand surface of the material of index of refraction nl? (a) It always remains between O and the surface, arriving at the surface just as O does. (b) It moves toward the surface more slowly than O so that eventually O passes I. (c) It approaches the surface and then moves to the right of the surface. Answer: (a) 59

60 Example 36.5 Objects viewed under water with the naked eye appear blurred and out of focus. A scuba diver using a mask, however, has a clear view of underwater objects. Explain how that works, using the information that the indices of refraction of the cornea, water, and air are l.376, l.333, and l.00029, respectively. Solution: Because the cornea and water have almost identical indices of refraction, very little refraction occurs when a person under water views objects with the naked eye. In this case, light rays from an object focus behind the retina, resulting in a blurred image. When a mask is used, however, the air space between the eye and the mask surface provides the normal amount of refraction at the eye-air interface; consequently, the light from 60 the object focuses on the retina.

61 Example 36.6 A set of coins is embedded in a spherical plastic paperweight having a radius of 3.0 cm. The index of refraction of the plastic is n 1 = One coin is located 2.0 cm from the edge of the sphere (Fig ). Find the position of the image of the coin. Solution: n q 1 q 2 n 2 n R cm 1 q 1.7 cm n1 p cm 61

62 Example 36.7 A small fish is swimming at a depth d below the surface of a pond (Fig ). 62

63 Example 36.7 (A) What is the apparent depth of the fish as viewed from directly overhead? Solution: (B) If your face is a distance d above the water surface, at what apparent distance above the surface does the fish see your face? Solution: n q p d d n n q p d 1. 33d n

64 Images Formed by Thin Lenses Lenses are commonly used to form images by refraction. Lenses are used in optical instruments. Cameras Telescopes Microscopes Light passing through a lens experiences refraction at two surfaces. The image formed by one refracting surface serves as the object for the second surface. Section

65 Locating the Image Formed by a Lens The lens has an index of refraction n and two spherical surfaces with radii of R 1 and R 2. R 1 is the radius of curvature of the lens surface that the light of the object reaches first. R 2 is the radius of curvature of the other surface. The object is placed at point O at a distance of p 1 in front of the first surface. Section

66 Locating the Image Formed by a Lens, Image From Surface 1 There is an image formed by surface 1. Since the lens is surrounded by the air, n 1 = 1 and If the image due to surface 1 is virtual, q 1 is negative; and it is positive if the image is real. n n n n p q R n n 1 p q R (36.10) Section

67 Locating the Image Formed by a Lens, Image From Surface 2 For surface 2, n 1 = n and n 2 = 1 The light rays approaching surface 2 are in the lens and are refracted into air. Use p 2 for the object distance for surface 2 and q 2 for the image distance. n n n n p q R n 1 1 n p q R (36.11) Section

68 Locating the Image, Surface 2 The image due to surface 1 acts as the object for surface 2. Section

69 Lens-makers Equation If a virtual image is formed from surface 1, then p 2 = q 1 + t q 1 is negative t is the thickness of the lens If a real image is formed from surface 1, then p 2 = q 1 + t q 1 is positive Section

70 Lens-makers Equation, cont. Then n 1 p1 q 2 R1 R 2 f (36.13) This is called the lens-makers equation. It can be used to determine the values of R 1 and R 2 needed for a given index of refraction and a desired focal length f. Section

71 Image Formed by a Thin Lens A thin lens is one whose thickness is small compared to the radii of curvature. For a thin lens, the thickness, t, of the lens can be neglected. In this case, p 2 = q 1 for either type of image Then the subscripts on p 1 and q 2 can be omitted. Section

72 Thin Lens Equation The relationship among the focal length, the object distance and the image distance is the same as for a mirror p q f (36.16) Section

73 Notes on Focal Length and Focal Point of a Thin Lens Because light can travel in either direction through a lens, each lens has two focal points. One focal point is for light passing in one direction through the lens and one is for light traveling in the opposite direction. However, there is only one focal length. Each focal point is located the same distance from the lens. Section

74 Focal Length of a Converging Lens The parallel rays pass through the lens and converge at the focal point. The parallel rays can come from the left or right of the lens. Section

75 Focal Length of a Diverging Lens The parallel rays diverge after passing through the diverging lens. The focal point is the point where the rays appear to have originated. Section

76 Determining Signs for Thin Lenses The front side of the thin lens is the side of the incident light. The light is refracted into the back side of the lens. This is also valid for a refracting surface. Section

77 Sign Conventions for Thin Lenses Section

78 Magnification of Images Through a Thin Lens The lateral magnification of the image is h' q M h p (36.17) When M is positive, the image is upright and on the same side of the lens as the object. When M is negative, the image is inverted and on the side of the lens opposite the object. Section

79 Thin Lens Shapes These are examples of converging lenses. They have positive focal lengths. They are thickest in the middle. Section

80 More Thin Lens Shapes These are examples of diverging lenses. They have negative focal lengths. They are thickest at the edges. Section

81 Ray Diagrams for Thin Lenses Converging Ray diagrams are convenient for locating the images formed by thin lenses or systems of lenses. For a converging lens, the following three rays are drawn: Ray 1 is drawn parallel to the principal axis and then passes through the focal point on the back side of the lens. Ray 2 is drawn through the center of the lens and continues in a straight line. Ray 3 is drawn through the focal point on the front of the lens (or as if coming from the focal point if p < f) and emerges from the lens parallel to the principal axis. Section

82 Ray Diagram for Converging Lens, p > f The image is real. The image is inverted. The image is on the back side of the lens. Section

83 Ray Diagram for Converging Lens, p < f The image is virtual. The image is upright. The image is larger than the object. The image is on the front side of the lens. Section

84 Ray Diagrams for Thin Lenses Diverging For a diverging lens, the following three rays are drawn: Ray 1 is drawn parallel to the principal axis and emerges directed away from the focal point on the front side of the lens. Ray 2 is drawn through the center of the lens and continues in a straight line. Ray 3 is drawn in the direction toward the focal point on the back side of the lens and emerges from the lens parallel to the principal axis. Section

85 Ray Diagram for Diverging Lens The image is virtual. The image is upright. The image is smaller. The image is on the front side of the lens. Section

86 If you can't see the image above, please install Shockwave Flash Player. If this active figure can t auto-play, please click right button, then click play : Thin Lenses In this animation we explore the properties of both convex and concave thin lenses. Again, a blue arrow represents an object whose image is formed by the lenses. You may want to review this section in your textbook to help you as you work with the animation. What basic properties can you deduce for each type of lens? 86

87 Image Summary For a converging lens, when the object distance is greater than the focal length, (p > f) The image is real and inverted. For a converging lens, when the object is between the focal point and the lens, (p < f) The image is virtual and upright. For a diverging lens, the image is always virtual and upright. This is regardless of where the object is placed. Section

88 Fresnal Lens Refraction occurs only at the surfaces of the lens. A Fresnal lens is designed to take advantage of this fact. It produces a powerful lens without great thickness. Section

89 Fresnal Lens 89

90 Fresnal Lens, cont. Only the surface curvature is important in the refracting qualities of the lens. The material in the middle of the Fresnal lens is removed. Because the edges of the curved segments cause some distortion, Fresnal lenses are usually used only in situations where image quality is less important than reduction of weight. Section

91 Combinations of Thin Lenses The image formed by the first lens is located as though the second lens were not present. Then a ray diagram is drawn for the second lens. The image of the first lens is treated as the object of the second lens. The image formed by the second lens is the final image of the system. Section

92 Combination of Thin Lenses, example Section

93 Combination of Thin Lenses, example Find the location of the image formed by lens 1. Find the magnification of the image due to lens 1. Find the object distance for the second lens. Find the location of the image formed by lens 2. Find the magnification of the image due to lens 2. Find the overall magnification of the system. Section

94 Example 36.8 A converging lens has a focal length of 10.0 cm. (A) An object is placed 30.0 cm from the lens. Construct a ray diagram, find the image distance, and describe the image. Solution: 1 q 1 q M 1 f 1 p m q p q 15.0 cm m 15.0 cm cm 94

95 Example 36.8 (B) An object is placed 10.0 cm from the lens. Find the image distance and describe the image. Solution: q f p q 10.0 m 10.0 m q 95

96 Example 36.8 (C) An object is placed 5.00 cm from the lens. Construct a ray diagram, find the image distance, and describe the image. Solution: q f p q 10.0 m 5.00 m q 10.0 cm M q 10.0 cm 2.00 p 5.00 cm 96

97 Example 36.9 A diverging lens has a focal length of 10.0 cm. (A) An object is placed 30.0 cm from the lens. Construct a ray diagram, find the image distance, and describe the image. 97

98 Example 36.9 Solution: q f p q 10.0 m 30.0 m q 7.50 cm q 7.50 cm M p 30.0 cm 98

99 Example 36.9 (B) An object is placed 10.0 cm from the lens. Construct a ray diagram, find the image distance, and describe the image. Solution: 1 q 1 q 1 f 1 p m q 5.00 cm M q p m 5.00 cm ( ) cm 99

100 Example 36.9 (C) An object is placed 5.00 cm from the lens. Construct a ray diagram, find the image distance, and describe the image. Solution: q f p q 10.0 m 5.0 m q 3.33 cm M 3.33 cm cm 100

101 Combinations of Thin Lenses If the image formed by the first lens lies on the back side of the second lens, then the image is treated as a virtual object for the second lens. p will be negative The same procedure can be extended to a system of three or more lenses. The overall magnification is the product of the magnification of the separate lenses. Section

102 Two Lenses in Contact Consider a case of two lenses in contact with each other: The lenses have focal lengths of f 1 and f 2. For the first lens, p q f 1 1 Since the lenses are in contact, p 2 = q 1 Section

103 Two Lenses in Contact, cont. For the second lens, p q f q q For the combination of the two lenses f f f 1 2 (36.19) Two thin lenses in contact with each other are equivalent to a single thin lens having a focal length given by the above equation. Section

104 Example Two thin converging lenses of focal lengths f l = 10.0 cm and f 2 = 20.0 cm are separated by 20.0 cm as illustrated in Figure An object is placed 30.0 cm to the left of lens 1. Find the position and the magnification of the final image. 104

105 Example Solution: q f p q 10.0 cm 30.0 cm q cm q 15.0 cm M1 p cm q 20.0 cm 5.00 cm q 2 2 M cm q p ( 6.67 cm) 5.00 cm 1.33 M M M ( 0.500)(1.33)

106 Lens Aberrations Assumptions have been: Rays make small angles with the principal axis. The lenses are thin. The rays from a point object do not focus at a single point. The result is a blurred image. This is a situation where the approximations used in the analysis do not hold. The departures of actual images from the ideal predicted by our model are called aberrations. Section

107 Spherical Aberration This results from the focal points of light rays far from the principal axis being different from the focal points of rays passing near the axis. For a camera, a small aperture allows a greater percentage of the rays to be paraxial. For a mirror, parabolic shapes can be used to correct for spherical aberration. Section

108 Chromatic Aberration Different wavelengths of light refracted by a lens focus at different points. Violet rays are refracted more than red rays. The focal length for red light is greater than the focal length for violet light. Chromatic aberration can be minimized by the use of a combination of converging and diverging lenses made of different materials. Section

109 The Camera The photographic camera is a simple optical instrument. Components Light-tight chamber Converging lens Produces a real image Light sensitive component behind the lens Where the image is formed Could be a CCD or film Section

110 Camera Operation Proper focusing will result in sharp images. The camera is focused by varying the distance between the lens and the CCD. The lens-to-ccd distance will depend on the object distance and on the focal length of the lens. The shutter is a mechanical device that is opened for selected time intervals. The time interval that the shutter is opened is called the exposure time. Section

111 Camera Operation, Intensity Light intensity is a measure of the rate at which energy is received by the CCD per unit area of the image. The intensity of the light reaching the CCD is proportional to the area of the lens. The brightness of the image formed on the CCD depends on the light intensity. Depends on both the focal length and the diameter of the lens Section

112 Camera, f-numbers The f-number of a camera lens is the ratio of the focal length of the lens to its diameter. f-number f / D (36.20) The f-number is often given as a description of the lens speed. A lens with a low f-number is a fast lens. The intensity of light incident on the film is related to the f-number: I 1/(f-number) 2 (36.21) Section

113 Camera, f-numbers, cont. Increasing the setting from one f-number to the next higher value decreases the area of the aperture by a factor of 2. The lowest f-number setting on a camera corresponds to the aperture wide open and the use of the maximum possible lens area. Simple cameras usually have a fixed focal length and a fixed aperture size, with an f-number of about 11. Most cameras with variable f-numbers adjust them automatically. Section

114 Camera, Depth of Field A high value for the f-number allows for a large depth of field. This means that objects at a wide range of distances from the lens form reasonably sharp images on the film. The camera would not have to be focused for various objects. Section

115 Quick Quiz 36.7 A camera can be modeled as a simple converging lens that focuses an image on the CCD, acting as the screen. A camera is initially focused on a distant object. To focus the image of an object close to the cam- era, must the lens be (a) moved away from the CCD, (b) left where it is, or (c) moved toward the CCD? Answer: (a) 115

116 Example The lens of a digital camera has a focal length of 55 mm and a speed (an f-number) of f/l.8. The correct exposure time for 1 this speed under certain conditions is known to be s. (A) Determine the diameter of the lens. Solution: f D f - number 55 mm mm 500 (B) Calculate the correct exposure time if the f-number is changed to f/4 under the same lighting conditions. Solution: t1 t2 I1 t1 I2 t2 2 2 ( f -number) ( f -number) f2-number t2 t 1 s s f1-number

117 The Eye The normal eye focuses light and produces a sharp image. Essential parts of the eye: Cornea light passes through this transparent structure Aqueous Humor clear liquid behind the cornea The pupil A variable aperture An opening in the iris The crystalline lens Section

118 The Eye Close-up of the Cornea Section

119 The Eye Parts, cont. Most of the refraction takes place at the outer surface of the eye. Where the cornea is covered with a film of tears. The iris is the colored portion of the eye. It is a muscular diaphragm that controls pupil size. The iris regulates the amount of light entering the eye. It dilates the pupil in low light conditions. It contracts the pupil in high-light conditions. The f-number of the eye is from about 2.8 to 16. Section

120 The Eye Operation The cornea-lens system focuses light onto the back surface of the eye. This back surface is called the retina. The retina contains sensitive receptors called rods and cones. These structures send impulses via the optic nerve to the brain. This is where the image is perceived. Section

121 The Eye Operation, cont. Accommodation The eye focuses on an object by varying the shape of the pliable crystalline lens through this process. Takes place very quickly Limited in that objects very close to the eye produce blurred images 121

122 The Eye Near and Far Points The near point is the closest distance for which the lens can accommodate to focus light on the retina. Typically at age 10, this is about 18 cm The average value is about 25 cm. It increases with age. Up to 500 cm or greater at age 60 The far point of the eye represents the largest distance for which the lens of the relaxed eye can focus light on the retina. Normal vision has a far point of infinity. Section

123 The Eye Seeing Colors Only three types of colorsensitive cells are present in the retina. They are called red, green and blue cones. What color is seen depends on which cones are stimulated. Section

124 Conditions of the Eye Eyes may suffer a mismatch between the focusing power of the lens-cornea system and the length of the eye. Eyes may be: Farsighted Light rays reach the retina before they converge to form an image. Nearsighted Person can focus on nearby objects but not those far away Section

125 Farsightedness Also called hyperopia The near point of the farsighted person is much farther away than that of the normal eye. The image focuses behind the retina. Can usually see far away objects clearly, but not nearby objects Section

126 Correcting Farsightedness A converging lens placed in front of the eye can correct the condition. The lens refracts the incoming rays more toward the principal axis before entering the eye. This allows the rays to converge and focus on the retina. Section

127 Nearsightedness Also called myopia The far point of the nearsighted person is not infinity and may be less than one meter. The nearsighted person can focus on nearby objects but not those far away. Section

128 Correcting Nearsightedness A diverging lens can be used to correct the condition. The lens refracts the rays away from the principal axis before they enter the eye. This allows the rays to focus on the retina. Section

129 Presbyopia and Astigmatism Presbyopia (literally, old-age vision ) is due to a reduction in accommodation ability. The cornea and lens do not have sufficient focusing power to bring nearby objects into focus on the retina. Condition can be corrected with converging lenses In astigmatism, light from a point source produces a line image on the retina. Produced when either the cornea or the lens or both are not perfectly symmetric Can be corrected with lenses with different curvatures in two mutually perpendicular directions Section

130 Diopters Optometrists and ophthalmologists usually prescribe lenses measured in diopters. The power P of a lens in diopters equals the inverse of the focal length in meters. P = 1/ f Section

131 Quick Quiz 36.8 Two campers wish to start a fire during the day. One camper is nearsighted, and one is farsighted. Whose glasses should be used to focus the Sun s rays onto some paper to start the fire? (a) either camper (b) the nearsighted camper (c) the farsighted camper. Answer: (c) 131

132 Simple Magnifier A simple magnifier consists of a single converging lens. This device is used to increase the apparent size of an object. The size of an image formed on the retina depends on the angle subtended by the eye. Section

133 The Size of a Magnified Image When an object is placed at the near point, the angle subtended is a maximum. The near point is about 25 cm. When the object is placed near the focal point of a converging lens, the lens forms a virtual, upright, and enlarged image. Section

134 Angular Magnification Angular magnification is defined as m 0 angle with lens angle without lens (36.22) The angular magnification is at a maximum when the image formed by the lens is at the near point of the eye. q = 25 cm Calculated by m max 1 25 cm f (36.24) Section

135 Angular Magnification, cont. The eye is most relaxed when the image is at infinity. Although the eye can focus on an object anywhere between the near point and infinity. For the image formed by a magnifying glass to appear at infinity, the object has to be at the focal point of the lens. The angular magnification is m min 0 25 cm ƒ (36.26) Section

136 Magnification by a Lens With a single lens, it is possible to achieve angular magnification up to about 4 without serious aberrations. With multiple lenses, magnifications of up to about 20 can be achieved. The multiple lenses can correct for aberrations. Section

137 Magnification Glass 137

138 Example What is the maximum magnification that is possible with a lens having a focal length of 10 cm, and what is the magnification of this lens when the eye is relaxed? Solution: m m max min 1 25 cm 1 f 25 cm f 25 cm 10 cm 25 cm 10 cm

139 Compound Microscope A compound microscope consists of two lenses. Gives greater magnification than a single lens The objective lens has a short focal length, f 0 < 1 cm The eyepiece has a focal length, f e of a few cm. Section

140 Compound Microscope 140

141 Compound Microscope, cont. The lenses are separated by a distance L. L is much greater than either focal length. The object is placed just outside the focal point of the objective. This forms a real, inverted image This image is located at or close to the focal point of the eyepiece. This image acts as the object for the eyepiece. The image seen by the eye, I 2, is virtual, inverted and very much enlarged. Section

142 If you can't see the image above, please install Shockwave Flash Player. If this active figure can t auto-play, please click right button, then click play : The Compound Microscope A simple magnifier provides only limited assistance in inspecting minute details of an object. Greater magnification can be achieved by combining two lenses in a compound microscope. It consists of one lens, called the objective (left), with a very short focal length and a second lens, the eyepiece (right), with a focal length of a few centimeters. Use this animation to explore and understand how a compound microscope works. 142

143 Magnifications of the Compound Microscope The lateral magnification by the objective is M 0 L / f 0 The angular magnification by the eyepiece of the microscope is m e = 25 cm / f e The overall magnification of the microscope is the product of the individual magnifications. M L 25 cm M 0 me f 0 f e (36.26) Section

144 Other Considerations with a Microscope The ability of an optical microscope to view an object depends on the size of the object relative to the wavelength of the light used to observe it. For example, you could not observe an atom (d 0.1 nm) with visible light (l 500 nm). Section

145 Telescopes Telescopes are designed to aid in viewing distant objects. Two fundamental types of telescopes Refracting telescopes use a combination of lenses to form an image. Reflecting telescopes use a curved mirror and a lens to form an image. Telescopes can be analyzed by considering them to be two optical elements in a row. The image of the first element becomes the object of the second element. Section

146 Refracting Telescope The two lenses are arranged so that the objective forms a real, inverted image of a distant object. The image is formed at the focal point of the eyepiece. p is essentially infinity The two lenses are separated by the distance f 0 + f e which corresponds to the length of the tube. The eyepiece forms an enlarged, inverted image of the first image. Section

147 Refracting Telescope, cont. 147

148 If you can't see the image above, please install Shockwave Flash Player. If this active figure can t auto-play, please click right button, then click play : The Refracting Telescope Like the compound microscope that we saw in Active Figure 36.41, the refracting telescope in this animation has an objective and an eyepiece. Because the object is essentially at infinity, the point at which the image forms is the focal point of the objective. Use this animation to explore the workings of a refracting telescope. 148

149 Angular Magnification of a Telescope The angular magnification depends on the focal lengths of the objective and eyepiece. m f0 0 fe The negative sign indicates the image is inverted. Angular magnification is particularly important for observing nearby objects. Nearby objects would include the sun or the moon. Very distant objects still appear as a small point of light. (36.27) Section

150 Disadvantages of Refracting Telescopes Large diameters are needed to study distant objects. Large lenses are difficult and expensive to manufacture. The weight of large lenses leads to sagging which produces aberrations. Section

151 Reflecting Telescope Helps overcome some of the disadvantages of refracting telescopes Replaces the objective lens with a mirror The mirror is often parabolic to overcome spherical aberrations. In addition, the light never passes through glass. Except the eyepiece Reduced chromatic aberrations Allows for support and eliminates sagging Section

152 Reflecting Telescope, Newtonian Focus The incoming rays are reflected from the mirror and converge toward point A. At A, an image would be formed. A small flat mirror, M, reflects the light toward an opening in the side and it passes into an eyepiece. This occurs before the image is formed at A. Section

153 Reflecting Telescope, Newtonian Focus 153

154 Examples of Telescopes Reflecting Telescopes Largest in the world are the 10-m diameter Keck telescopes on Mauna Kea in Hawaii Each contains 36 hexagonally shaped, computer-controlled mirrors that work together to form a large reflecting surface. Telescopes with different mirrors working together can result in an effective diameter up to 30 m. Section

155 Examples of Telescopes, cont. Refracting Telescopes Largest in the world is Yerkes Observatory in Williams Bay, Wisconsin Has a diameter of 1 m Section

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