Diverging Lens

12 Key excerpts on "Diverging Lens"

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  eBook - PDF

  An Introduction to Physical Science

  • James Shipman, Jerry Wilson, Charles Higgins, Bo Lou, James Shipman(Authors)
  • 2020(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 184 Chapter 7 ● Optics and Wave Effects In general, there are two main types of lenses. A converging lens is thicker at the center than at the edges. A Diverging Lens is thinner at the center than at the edges. These two types and some of the possible shapes for each are illustrated in ●● Fig. 7.22. In general, we will investigate the spherical biconvex and biconcave lenses at the left of each group in the figure (bi- because they have similar spherical surfaces on both sides). Light passing through a lens is refracted twice, once at each surface. The lenses most commonly used are known as thin lenses. Thus, when constructing ray diagrams, the thickness of the lens can be neglected. The principal axis for a lens goes through the center of the lens (●● Fig. 7.23). Rays coming in parallel to the principal axis are refracted toward the principal axis by a converging lens. For a converging lens, the rays are focused at point F, the focal point. For a Diverging Lens, the rays are refracted away from the principal axis and appear to emanate from the focal point on the incident side of the lens. Ray Diagrams How lenses refract light to form images can be shown by drawing graphic ray diagrams similar to those applied to mirrors. 1. The first ray is drawn parallel to the principal axis and then refracted by the lens along a line drawn through a focal point of the lens. 2. The second ray is drawn through the center of the lens without a change in direction. The intersection of these rays locates the position of the image (tip of the image arrow). Examples of this procedure are shown in ●● Fig. 7.24. Only the focal points for the respective surfaces are shown—just focal points are needed. The lenses do have radii of curvature, but for spherical lenses, f Þ R/2 in contrast to f 5 R/2 for spherical mirrors.

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  Inquiry into Physics

  • Vern Ostdiek, Donald Bord(Authors)
  • 2017(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  The distance from the lens to the focal point is again called the focal length, but for a Diverging Lens it is given as a negative number, 215 centimeters, for example. If we reverse the process and send rays converging toward the focal point into the lens, they emerge parallel. For both types of lenses there are two focal points, one on each side. Clearly, if parallel light rays enter a converging lens from the right side in Figureuni00A09.45, they will converge to the focal point to the left of the lens. Whether a lens is diverging or converging can be determined quite easily: if it is thicker at the middle than at the edges, it is a converging lens; if it is thinner at the center, it is a Diverging Lens (Figure 9.44). 9.4a Image Formation The main use of lenses is to form images of things. First, let’s consider the ba- sics of image formation when a symmetric converging lens (see, for example, Figureuni00A09.44a left) is used. Our eyes, most cameras (both still and video), slide projectors, movie projectors, and overhead projectors all form images this way. Figure 9.45 illustrates how light radiating from an arrow, called the object, forms an image on the other side of the lens. One practical way of demonstrating this e e would be to point a flashlight at the arrow so that light would reflect off the arrow and pass through the lens. The image could be projected onto a piece of white paper placed at the proper location to the right of the lens. Although each point on the object has countless light rays spreading out from it in all directions, it is simpler to consider only three particular rays from a single point—the arrow’s tip. These rays, shown in Figureuni00A09.45, are called the principal rays. 1. The ray that is initially parallel to the optical axis passes through the fo- cal point (F ) on the other side of the lens. 2. The ray that passes through the focal point (F 9) on the same side of the lens as the object emerges parallel to the optical axis.

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  Physics

  • Fatih Gozuacik, Denise Pattison, Catherine Tabor(Authors)
  • 2020(Publication Date)
  • Openstax

    (Publisher)

  An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces. Note that rays from a light source placed at the focal point of a converging lens emerge parallel from the other side of the lens. You may have heard of the trick of using a converging lens to focus rays of sunlight to a point. Such a concentration of light energy can produce enough heat to ignite paper. Figure 16.26 shows a concave lens and the effect it has on rays of light that enter it parallel to its axis (the path taken by ray 2 in the figure is the axis of the lens). The concave lens is a Diverging Lens because it causes the light rays to bend away (diverge) from its axis. In this case, the lens has been shaped so all light rays entering it parallel to its axis appear to originate from the same point, F, defined to be the focal point of a Diverging Lens. The distance from the center of the lens to the focal point is again called the focal length, or “ƒ,” of the lens. Note that the focal length of a Diverging Lens is defined to be negative. An expanded view of the path of one ray through the lens is shown in Figure 16.26 to illustrate how the shape of the lens, together with the law of refraction, causes the ray to follow its particular path and diverge. Figure 16.26 Rays of light enter a concave, or diverging, lens parallel to its axis diverge and thus appear to originate from its focal point, F. The dashed lines are not rays; they indicate the directions from which the rays appear to come. The focal length, ƒ, of a Diverging Lens is negative. An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces. The power, P, of a lens is very easy to calculate. It is simply the reciprocal of the focal length, expressed in meters The units of power are diopters, D, which are expressed in reciprocal meters.

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  Let There Be Light: The Story Of Light From Atoms To Galaxies (2nd Edition)

  The Story of Light from Atoms to Galaxies

  • Alex Montwill, Ann Breslin(Authors)
  • 2013(Publication Date)
  • ICP

    (Publisher)

  Converging lens. image object O I Diverging Lens. focus 52 Let There Be Light 2nd Edition bring them to a focus on the other side. The lens does this by providing a number of paths of equal length in time . Light trav-els more slowly in glass than in air. The path along the straight line from O to I is actually made longer in time by slowing down the light as it passes through the thickest part of the lens. Rays going from O to I by one of the more roundabout routes have to traverse a smaller thickness of glass. Light rays are presented with these other routes which take the same time as the central route. The problem is to find the shape of the lens to ensure that the smaller width at any point off-axis exactly compensates for the extra length of the journey. Expensive lenses are complex in shape and may have many components, but it turns out that a single lens with spherical surfaces works quite well, particularly for rays close to the optic axis. The focal point of a converging lens is defined as the point at which incoming rays parallel to the axis are brought together at the other side of the lens. Conversely, a source of light at the focus will give rise to a beam of light parallel to the axis at the other side. 3.3 Objects and images: converging lenses Ray tracing through a thin lens A lens which is thicker in the middle than at the ends always acts as a converging lens, even when the curvature is convex Can we find the right shape? It turns out that spherical surfaces are pretty good. ? Light as a Ray: Refraction 53 on one side and concave on the other. It can also be shown that turning the lens around will not change its focusing properties. This means the focal length, f , of a lens is the same on both sides, regardless of its shape, and lenses may be designated by a single value of f which applies to either side of the lens. Principal rays (thin lenses) We can also draw rays which pass through certain selected points for lenses, as we did for mirrors.

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  Light and Optics

  Principles and Practices

  • Abdul Al-Azzawi(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  Figure 10.2 show some common shapes of lenses. Typical spherical lenses have two surfaces defined by two spheres. The surfaces can be convex, concave, or planar. Lenses are divided into two types: (a) converging and (b) diverging. Converging lenses have positive focal lengths and are thickest at the middle. Common shapes of converging lenses are (1) biconvex, (2) convex–concave, and (3) plano-convex. Diverging Lenses have negative focal lengths and are thickest at the edges. Common shapes of Diverging Lenses are (1) biconcave, (2) convex–concave, and (3) plano-concave.

  FIGURE 10.1 Converging and Diverging Lenses.

  FIGURE 10.2 Various shapes of lenses.

  Figure 10.3 illustrates the geometries of two common types of lenses: (a) a biconvex lens and (b) a biconcave lens. The type and thickness of the lens depends on the radius of curvatures R1 and R2 , and the distance between the centres of curvature.

  FIGURE 10.3 Two common types of lenses.

  The principle of operation for a lens forming an image is explained by the second law of light, the law of refraction. When light rays pass through a lens, they are bent or deviated from their original paths, according to the law of refraction. The theory of light refraction through an optical medium is presented in Chapter 7 , The Laws of Light. Refraction by a prism is addressed in Chapter 11 , Prisms.

  To study light refraction in a biconvex lens, two prisms can be placed base to base to approximate the convex lens operation, as shown in Figure 10.4(a) . Parallel light rays that pass through the prisms are deviated so that the various rays intersect. They do not intersect or focus at a single point. However, if the surfaces of the prisms are curved rather than flat, then it becomes a converging lens, as shown in Figure 10.4(b) . The converging lens brings incoming parallel rays of light to a single point F, called the focal point, at the principal axis. Because the refracted light rays pass through F, the focal point is real. This type of lens is often called a converging or convex lens.

  FIGURE 10.4 The principle of the converging lens.

  FIGURE 10.5 The principle of the Diverging Lens.

  Similarly, a biconcave lens can be approximated by two prisms with their apexes together, as shown in Figure 10.5(a) . Parallel light rays that pass through the prisms are spread outward, but these diverging rays cannot be projected back to a single point. However, if the surfaces of the prisms are curved rather than flat, then it becomes a Diverging Lens, as shown in Figure 10.5(b) . The diverging rays appear to originate from a single point on the incident side of the lens. The focal point F is not real; it is virtual because the rays do not actually pass through F

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  Physics for Scientists and Engineers

  Foundations and Connections, Extended Version with Modern Physics

  • Debora Katz(Author)
  • 2016(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Ray 2 is parallel to the optical axis. For a converg- ing lens, ray 2’s refraction passes through the focal point on the back of the lens. For a Diverging Lens, ray 2’s refraction is bent away from the optical axis. When you extend the refracted ray backward, it passes through the focal point on the front of the lens. Notice that you draw the bend in the ray only where it strikes the vertical line through the middle of the lens. For a converging lens, ray 3 passes through the focal point on the front of the lens. For a Diverging Lens, ray 3 is aimed at the focal point on the back of the lens. For both lenses, the refracted ray is parallel to the optical axis. PRIMARY RAYS FOR THIN LENSES Tool 38-6 Images Formed by Diverging Lenses We can use ray diagrams to find the position, orientation, and magnification of a Diverging Lens when an object is at some finite distance from it. The location of an object relative to the focal point of a Diverging Lens does not matter. Figure 38.31 shows an object at some arbitrary distance in front of a Diverging Lens along with the three primary rays. The three refracted rays that result do not cross behind the lens, so no real image is formed. However, if you look through the lens from the back, the RAY DIAGRAMS Tool Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 38-6 Images Formed by Diverging Lenses 1239 Unless otherwise noted, all content on this page is © Cengage Learning. three rays entering your eye can be traced to a point in front of the lens. The resulting image is upright, in front of the lens, virtual, and smaller than the object. Let’s connect our ray diagram (Fig. 38.31) to the thin-lens equation (Eq. 38.5). The focal length is negative because the lens is diverging, and the object distance is positive because the object is real and in front of the lens.

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  Let There Be Light

  The Story of Light from Atoms to Galaxies

  • Ann Breslin, Alex Montwill(Authors)
  • 2013(Publication Date)
  • ICP

    (Publisher)

  longer in time by slowing down the light as it passes through the thickest part of the lens. Rays going from O to I by one of the more roundabout routes have to traverse a smaller thickness of glass. Light rays are presented with these other routes which take the same time as the central route.

  The problem is to find the shape of the lens to ensure that the smaller width at any point off-axis exactly compensates for the extra length of the journey.

  Expensive lenses are complex in shape and may have many components, but it turns out that a single lens with spherical surfaces works quite well, particularly for rays close to the optic axis. The focal point of a converging lens is defined as the point at which incoming rays parallel to the axis are brought together at the other side of the lens. Conversely, a source of light at the focus will give rise to a beam of light parallel to the axis at the other side.

  3.3 Objects and images: converging lenses

  Ray tracing through a thin lens

  A lens which is thicker in the middle than at the ends always acts as a converging lens, even when the curvature is convex on one side and concave on the other. It can also be shown that turning the lens around will not change its focusing properties. This means the focal length, f, of a lens is the same on both sides, regardless of its shape, and lenses may be designated by a single value of f which applies to either side of the lens.

  Principal rays (thin lenses)

  We can also draw rays which pass through certain selected points for lenses, as we did for mirrors. There are just three such rays.

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  (c) The Diverging Lens is designed to form a virtual image at the far point of the nearsighted eye. 26.10 The Human Eye 759 Farsightedness BIO THE PHYSICS OF . . . farsightedness. A farsighted (hyperopic) person can usu- ally see distant objects clearly, but cannot focus on those nearby. Whereas the near point of a young and normal eye is located about 25 cm from the eye, the near point of a farsighted eye may be considerably farther away than that, perhaps as far as several hundred centimeters. When a far- sighted eye tries to focus on a book held closer than the near point, it accommodates and shortens its focal length as much as it can. However, even at its shortest, the focal length is longer than it should be. Therefore, the light rays from the book would form a sharp image behind the retina if they could do so, as Figure 26.36a suggests. In reality, no light passes through the retina, but a blurred image does form on it. EXAMPLE 12 Eyeglasses for the Nearsighted Person A nearsighted person has a far point located only 521 cm from the eye. Assuming that eyeglasses are to be worn 2 cm in front of the eye, find the focal length needed for the Diverging Lenses of the glasses so the person can see distant objects. Reasoning In Figure 26.35c the far point is 521 cm away from the eye. Since the glasses are worn 2 cm from the eye, the far point is 519 cm to the left of the Diverging Lens. The image distance, then, is −519 cm, the negative sign indicating that the image is a virtual image formed to the left of the lens. The object is assumed to be infinitely far from the diverg- ing lens. The thin-lens equation can be used to find the focal length of the eyeglasses. We expect the focal length to be negative, since the lens is a Diverging Lens. Problem-Solving Insight Eyeglasses are worn about 2 cm from the eyes. Be sure, if necessary, to take this 2 cm into account when determining the object and image distances (d o and d i ) that are used in the thin-lens equation.

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  Seeing the Light

  Optics in Nature, Photography, Color, Vision, and Holography (Updated Edition)

  • Joan G. Thomas, David Falk, Dieter Drill, David Stork(Authors)
  • 2021(Publication Date)
  • Echo Point Books & Media

    (Publisher)

  Fig. 3.22 ). Focusing lenses are quite old. The early ones were glass spheres filled with water. The Greek comic playwright Aristophanes suggested that burning glasses could be used to annul promissory notes by melting the letters off the wax notes.

  FIGURE 3.21

  A converging lens, consisting of two converging surfaces. (a) Rays parallel to the axis are focused at F′. (b) Rays originating at F are also made to converge and emerge parallel to the axis.

  A converging lens also has a first focal point, F, in front of the lens (Fig. 3.21b ). All rays originating at F and passing through the lens will emerge parallel to the axis. To see that this must be true, notice that Figure 3.21b is simply Figure 3.21a flipped around, with the arrows on the rays reversed.

  We can make a Diverging Lens by combining the two diverging surfaces of Figures 3.20c and d . In Figure 3.23a , we see that the incident rays parallel to the axis are made to diverge. To an eye on the right- hand side of the lens, these divergent rays will appear to be coming from their point of intersection (when extended backward). We again label this point F′ and call it the second focal point. For the Diverging Lens, then, F′ lies in front of the lens (the reverse of a converging lens, where parallel incident rays actually go through F′).

  FIGURE 3.22

  Flipping Figure 3.23a over and reversing the arrows (Fig. 3.23b ) shows that the first focal point, F, of a Diverging Lens lies behind the lens. All rays aimed at F that hit the lens emerge parallel to the axis.

  FIGURE 3.23

  A Diverging Lens, consisting of two diverging surfaces. (a) Rays parallel to the axis seem to come from F′ after they pass through the lens. (b) Rays converging toward F

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  Physics for Scientists and Engineers with Modern Physics

  • Raymond Serway, John Jewett(Authors)
  • 2018(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  They then continue past that point, diverging before they finally reach the retina and causing blurred vision (Fig. 35.39a). Nearsightedness can be corrected with a Diverging Lens as shown in Figure 35.39b. The lens refracts the rays away from the principal axis before they enter the eye, allowing them to focus on the retina. A number of people have difficulties with color blindness. Some individuals are dichromats, meaning that they only have functioning cones for two of the three colors in Figure 35.37. Another type of color blindness occurs in people who are anomalous trichromats. For these individuals, the range of sensitivity of, most often, red- and green-sensitive cones has shifted so that there is more overlap between the red and green curves in Figure 35.37. This makes it difficult to distinguish red and green. A new type of glasses offers some relief for anomalous trichromats. The glasses are designed to filter out the wavelength regions in which the curves in Fig- ure 35.37 are crossing, allowing the individual to see three distinct wavelength regions. Many people trying these new glasses report remarkable improvement in their perception of colors. Optometrists and ophthalmologists usually prescribe lenses 1 measured in diopters: the power P of a lens in diopters equals the inverse of the focal length in meters: P 5 1/ f. For example, a converging lens of focal length 120 cm has a power of 15.0 diopters, and a Diverging Lens of focal length 240 cm has a power of 22.5 diopters. Q UICK QUIZ 35.7 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 1 The word lens comes from lentil, the name of an Italian legume.

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  Dynamic Fields and Waves

  • A Norton(Author)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  virtual image.

  Figure 3.52  When an object is positioned a distance less than the focal length from a converging lens, the emergent rays are still diverging; the image I is said to be virtual

  Q3.5

      In all three cases 1/v + 1/u = 1/f

  (a)  Here, the object is a distance/in front of the lens; hence u = +f. The lens equation reduces to 1/v + 1/f= 1/f, or 1/v = 0. It therefore follows that v = 1/zero = infinity: the image is at infinity, so the output beam is parallel.

  (b)  The input beam is parallel: u = ∞. The lens equation becomes 1/v + 1/∞ = 1/f. As 1/∞ equals zero, so 1/v = 1/f, or v = f. The image is real (v is positive since f is positive) and a distance/beyond the lens.

  (c)  Again, 1/u = l/∞ = zero. Hence 1/v + zero = 1/f, so v = f. But remember that in this case/is negative (it’s a Diverging Lens), so that v will be negative. Hence, the image will be a distance f from the lens, but it will be a virtual image located in front of the lens.

  Q3.6

      Your sketch should look something like Figure 3.53 . The Diverging Lens, being concave in shape, delays the wavefront less at its centre than at its perimeter. The emergent wavefronts, therefore, will acquire a curvature that makes them appear to have diverged from the focal point F to the left of the lens.

  Figure 3.53  A Diverging Lens converts plane wavefronts into diverging spherical wavefronts.

  Q3.7

      As you already know, the image will be real and in the same plane as the object; however, as you can see from Figure 3.54

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  Physics, Student Study Guide

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  A nearsighted (myopic) person can only focus clearly on nearby objects but not on distant ones. For such a person, the far point of the fully relaxed eye is not at infmity, but may be only a few meters away. The image of a distant object falls in front of the retina, as shown in the figure at the top of the next page, thus causing the image to be out of focus. To correct this, a Diverging Lens is used to refocus the light back on the retina. Nearsightedness (myopia) can be corrected using a Diverging Lens as shown in the figure below. The Diverging Lens acts to produce a virtual image at the far point of the unaided myopic eye. Thus, instead of the eye trying to focus at infmity, it will focus on a virtual image located at the far point of the eye. 346 THE REFRACTION OF LIGHT: LENSES AND OPTICAL INSTRUMENTS Distant object Distant object Example 10 Use of a Diverging Lens to correct nearsightedness Image formed in front of retina Image formed on retina A nearsighted person is diagnosed to have a far point located only 350 em from his eyes. Determine the focal length of contact lenses that will enable him to see distant objects clearly. The virtual image formed by the Diverging Lens is located at the far point of the eye. Since contact lenses are placed right against the eyes, di = - 350 em, the negative sign indicating a virtual image. Since the object is far away, the object distance is taken to be infinity, that is, d 0 = oo. The thin-lens equation (26.6) then gives => f = - 350 em. Note that the focal length is negative since it is a Diverging Lens. A farsighted (hyperopic) person can usually see distant objects clearly, but cannot focus on those nearby. Whereas the near point of a "normal" eye is located about 25 em from the eye, the near point of the farsighted eye may be much farther away. As shown in the figure below, an object located inside the near point of a hyperopic eye will be focused behind the retina, thus producing a blurred image.

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