Converging Lens

11 Key excerpts on "Converging Lens"

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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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  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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  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

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

    (Publisher)

  The lens refracts the light rays more toward the principal axis before they enter the eye. Consequently, when the rays are refracted even more by the eye, they converge to form an image on the retina. Part c of the figure illustrates what the eye sees when it looks through the Converging Lens. The lens is designed so that the eye perceives the light to be coming from a virtual image located at the near point. Example 13 shows how the focal length of the Converging Lens is determined to correct for farsightedness. 26.11 Angular Magnification and the Magnifying Glass 761 the following describes what you see? (a) The Converging Lenses make the eyes appear smaller, and the diverging lenses make the eyes appear larger. (b) The Converging Lenses make the eyes appear larger, and the diverging lenses make the eyes appear smaller. (c) Both types of lenses make the eyes appear larger. (d) Both types of lenses make the eyes appear smaller. 26.11 Angular Magnification and the Magnifying Glass If you hold a penny at arm’s length, the penny looks larger than the moon. The reason is that the penny, being so close, forms a larger image on the retina of the eye than does the more distant moon. The brain interprets the larger image of the penny as arising from a larger object. The size of the image on the retina determines how large an object appears to be. However, the size of the image on the retina is difficult to measure. Alternatively, the angle  subtended by the image can be used as an indication of the image size. Figure 26.37 shows this alternative, which has the advantage that  is also the angle subtended by the object and, hence, can be measured more easily. The angle  is called the angular size of both the image and the object. The larger the angular size, the larger the image on the retina, and the larger the object appears to be.

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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)

  The con- verging lens (Fig. 38.28A) bends the rays so that they come together or converge at a point behind the lens. The point where they come together is the focal point F, and a real image of the distant object is formed there. The distance from the lens to the focal point is the focal length f. If you place a screen at F, you see the real image projected onto the screen. When parallel rays encounter a diverging lens (Fig. 38.28B), the refracted rays separate or diverge. Diverging rays never cross, so no real image forms. However, the diverging rays appear to originate from a point in front of the lens. This point is the focal point F of the lens. If you look through the back of the lens, you see a virtual image at the focal point. In the next two sections, we’ll explore the images produced by both types of lenses when the objects are not infinitely far away. Front Back A. Converging Lens B. Diverging lens f F Front Back f F Very distant object’s rays are parallel. Very distant object’s rays are parallel. FIGURE 38.28 A. When parallel rays are incident on a Converging Lens, they are bent toward one another and a real image forms at the focal point, sometimes called the real focal point. B. When parallel rays are incident on a diverging lens, they are bent away from one another and a virtual image forms at the focal point, sometimes called the virtual focal point. Convex Meniscus Lens EXAMPLE 38.7 A Figure 38.29 shows a convex meniscus lens and an object. If 0 r 1 0 5 6.50 cm and 0 r 2 0 5 8.50 cm, find the focal length and determine whether the lens is con- verging or diverging. The lens is made of glass with index of refraction n 5 1.55. h o r 1 c 1 c 2 Back Front Object 1 2 r 2 FIGURE 38.29 INTERPRET and ANTICIPATE The key to solving this problem is to apply the sign conventions correctly (Table 38.3). When we find the focal length using the lens maker’s equation, we can use the sign conventions again to determine whether the lens is converging or diverging.

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  The Filmmaker's Eye: The Language of the Lens

  The Power of Lenses and the Expressive Cinematic Image

  • Gustavo Mercado(Author)
  • 2019(Publication Date)
  • Routledge

    (Publisher)

  This means that all lenses, no matter how expensive or technologically advanced, inherently produce distorted images, an unavoidable compromise when captur-ing images that will be viewed on two-dimensional media. The most basic lens shapes are called positive , or Converging Lenses ((b), a biconvex lens), and negative , or diverging lenses ((c), a biconcave lens). Positive lenses focus light beams into a spot, and negative lenses spread light beams coming from a spot; since a single lens by itself cannot form a perfect im-age (things would look like they were shot through a cheap magnifying glass), all lenses designed for photography and filmmaking comprise an array of positive, negative, and a va -riety of other lenses of different shapes, thicknesses, sizes, materials, and coatings (chemical compounds designed to minimize reflections, improve light transmission, and con -trol color rendition), fixed together into groups and by them -selves inside a lens’ barrel. For example, figure 2 shows the internal construction of a Zeiss T2.8 21mm prime lens with 16 elements arranged into 1 3 groups. Even with all of these elements in place, most lenses cannot form optically flaw -less images, and will show imperfections called aberrations , generally defined as the failure of light rays to converge at one specific point on an image plane. A lens’ design is pri -marily aimed at reducing aberrations as much as possible given cost, function, and target market considerations. In theory, it would be possible to construct a lens with minimal 22 aberrations and optical compromises, but it would likely be extremely large and heavy, nearly impossible to mass pro-duce, and prohibitively expensive (to get an idea of what such a lens would cost, one needs to look no further than the “box lenses” used in professional broadcasting cameras, which cost almost a quarter of a million dollars).

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  Physics for Scientists and Engineers with Modern Physics

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

    (Publisher)

  ● Ray 3 (red) is drawn through the center of the lens and continues in a straight line. For the Converging Lens in Figure 35.27a, where the object is to the left of the focal point ( p . f ), the image is real and inverted and the lens acts like a video projector. When the object is between the focal point and the lens ( p , f ) as in Figure 35.27b, the image is virtual and upright. In that case, the lens acts as a mag- nifying glass, which we study in more detail in Section 35.6. For a diverging lens Plano- convex Convex- concave Biconvex Biconcave Convex- concave Plano- concave a b Figure 35.26 Various lens shapes. (a) Converging Lenses have a positive focal length and are thickest at the middle. (b) Diverging lenses have a negative focal length and are thickest at the edges. a c b O F 1 Front I 1 2 3 I Front Back Back O 1 3 2 O Front Back I 1 3 2 F 2 F 1 F 2 F 2 F 1 When the object is in front of and outside the focal point of a Converging Lens, the image is real, inverted, and on the back side of the lens. When the object is between the focal point and a Converging Lens, the image is virtual, upright, larger than the object, and on the front side of the lens. When an object is anywhere in front of a diverging lens, the image is virtual, upright, smaller than the object, and on the front side of the lens. Figure 35.27 Ray diagrams for locating the image formed by a thin lens. Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

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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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  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)

  While you have the projection lens out, you may want to measure its focal length. You can then measure the lens’ diameter and compute its f-number, which you can check against the manufacturer’s marking.

  SUMMARY

  An eye that has too strong a lens system (myopic) requires a diverging (negative power) eyeglass lens, which puts the far point properly at infinity. A hyperopic eye requires a converging lens to move the near point back to the normal 25 cm. Bifocal lenses have two parts, each a lens of different focal length. Astigmatism in vision (unequal focal lengths along different meridians) is corrected by lenses having a cylindrical component. A magnifying glass (Converging Lens) forms a virtual image, at a point on which you can focus, of a much closer object. The eyepiece of a compound microscope acts like a magnifying glass for the real image formed by the objective lens. Scanning microscopes link a scanning electronic display with a scanning spot of illumination. Telescopes accept parallel light and produce a parallel beam at a different direction. Refracting astronomical telescopes produce an inverted image. Terrestrial telescopes provide erect images by means of a prism system or by a diverging eyepiece (Galilean telescope). Reflecting telescopes use concave mirrors to collect and focus light. Catadioptric telescopes (such as the Schmidt telescope) combine reflecting and refracting elements. A schlieren system uses a knife edge at the focal point to block undeviated light, while permitting light that has been bent to strike the screen. Otherwise invisible objects are thereby made visible. A field lens preserves the field of view, making the image uniformly illuminated (without vignetting) while not changing the image-forming properties of the system, an important consideration in projectors, enlargers, and most optical instruments.

  PROBLEMS

  P1

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  Physics, Student Study Guide

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

    (Publisher)

  Accommodation The process by which the focal length of the eye is automatically adjusted, so that objects at different distances can be made to produce focused images on the retina. Near point The point nearest the eye at which an object can be placed and still produce a sharp image on the retina. Far point The location of the farthest object on which the fully relaxed eye can focus. Nearsightedness (myopia) A condition in which the eye can focus on nearby objects, but not on distant ones. The condition can be corrected through the use of glasses made from diverging lenses. Farsightedness (hyperopia) A condition in which the eye can focus on distant objects, but not on nearby ones. The condition can be correctec;l through the use of glasses made from Converging Lenses. Refractive power A figure of merit of a lens measured in diopters and given by 1/f, where f is the focal length of the lens in meters. Angular size The angle an object subtends at the eye of the viewer. Angular magnification The ratio of the fmal angular size produced by an optical instrument to the reference angular size of the object. Magnifying glass A single Converging Lens that fonns an enlarged, upright, and virtual image of an object which is placed at or inside the focal point of the lens. Compound microscope A device consisting of an objective lens and an eyepiece lens which produces an enlarged, inverted, and virtual image of an object. Astronomical telescope A device which magnifies distant objects with the aid of objective and eyepiece lenses. It produces a final image which is inverted and virtual. Spherical aberration An effect in which rays from the outer edge of a spherical lens are not focused at the same point as rays that pass through the center of the lens, thus causing images to be blurred. Chromatic aberration An undesirable lens effect arising when a lens focuses different colors at different points.

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  Introduction to Optics

  • Frank L. Pedrotti, Leno M. Pedrotti, Leno S. Pedrotti(Authors)
  • 2017(Publication Date)
  • Cambridge University Press

    (Publisher)

  In Figure 2-29, the line image formed is the result of an object point “at infinity,” which produces parallel rays at the lens. In Figure 2-31, the object point O is near the lens, producing diverging rays of light incident on the lens. Still, if the lens is thin, focusing occurs along the vertical sections, as shown. Rays 1 and 3, in the left vertical section of Figure 2-31, focus at A ; rays 2 and 4 in the right vertical section focus at B . However, no focusing oc-curs for rays 1, 5, and 2 along the horizontal section. Because of the diver-gence of the rays entering the lens, however, the length of the focused line image AB is no longer equal to the effective length CL of the lens. The di-vergence of the extreme rays at each end of the lens now determines an image that is longer than the length of the lens. The image length AB can be found from a simple, geometrical argument that is apparent in Figure 2-32a, a view of the central horizontal section in Figure 2-31 as seen from above. If the effective length of the cylindrical lens is CL , then by similar triangles it follows that AB CL = s + s ¿ s (a) (b) F Axis Point image Lens F Axis Point image Lens Vertical fan of rays Horizontal fan of rays Figure 2-27 Parallel rays of light focused by a spherical lens. Because of its axis of symme-try relative to rotation about an axis through its center, the lens treats (a) vertical and (b) horizontal fans of rays similarly, producing in each case a point image at the same location. Each ray refracts twice through the lens, once at each surface. For simplicity, only one re-fraction is shown. 6 To be more precise, we are speaking of a plano-convex or plano-concave cylindrical lens as shown in Figure 2-28. Generally speaking, both surfaces of the lens might be cylindrical. In such a case, the behavior of the lens as a whole, due to the addition of the powers of the two surfaces, may not re-duce to that of the simple plano-convex or plano-concave lens described here.

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