Focal Length

9 Key excerpts on "Focal Length"

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  Cinematography: Theory and Practice

  Image Making for Cinematographers and Directors

  • Blain Brown(Author)
  • 2016(Publication Date)
  • Routledge

    (Publisher)

  Refractive index is defined as the relative speed at which light moves through a material with respect to its speed in a vacuum. When light passes from a less dense medium such as air to a more dense medium, such as glass, the speed of the wave decreases. Conversely, when light passes from a more dense medium to a less dense medium, the speed of the wave increases. The angle of refracted light is dependent upon both the angle of incidence and the composition of the material into which it is entering. “Normal” is defined as a line perpendicular to the boundary between two substances.

  FOCAL LENGTH AND ANGLE OF VIEW

  The Focal Length of the lens is the distance between the optical center of the lens and the image sensor when the subject is in focus; it is usually stated in millimeters such as 18 mm, 50 mm, or 100 mm (Figure 14.3 ). For zoom lenses, both the minimum and maximum Focal Lengths are stated, for example, 18—80 mm (Figure 14.2 ).

  The angle of view is the visible extent of the scene captured by the image sensor, stated as an angle. Wide angles of view capture greater areas, small angles smaller areas (Figure 14.6 ). Changing the Focal Length changes the angle of view. The shorter the Focal Length (such as 18 mm), the wider the angle of view and the greater the area seen. The longer the Focal Length (100 mm, for example), the smaller the angle and the larger the subject appears to be. The angle-of-view is also affected by the size of the sensor or film format. The smaller the sensor size, the greater the angle of view will be for the same Focal Length. The difference between two formats (sensor sizes) is called the crop factor. Charts and calculators are available online to help you determine what the angle of view will be for a particular combination of lens Focal Length and sensor size. As we will see, sensor size also affects depth-of-field—a larger sensor (or film format) will have less depth-of-field for the same Focal Length and aperture setting.

  Figure 14.3. A prime lens

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  The Lens

  A Practical Guide for the Creative Photographer

  • NK Guy(Author)
  • 2012(Publication Date)
  • Rocky Nook

    (Publisher)

  The field of view can be described as horizontal degrees, vertical degrees, or diagonal degrees of coverage. Typically, the diagonal field of view is used. This photo of a flowering water lily in the Waterlily House, Kew Gardens, England, was taken with a 300mm lens on a 1.6x subframe camera. This accounts for its very narrow field of view.

  2.6 Focal Length

  Every lens has an optical property called the Focal Length , which is measured in millimeters. The Focal Length is key to how much of a scene a lens can view.

  If a lens has a very short Focal Length, then it’s a wide angle lens. A lens with a really long Focal Length is a telephoto lens.

  So why is the Focal Length used rather than the angle of view? The amount of a scene that a lens can view, assuming the lens is focusing on infinity, actually depends on two basic factors:

  The Focal Length of the lens, which determines the amount of the scene projected onto the image area

  The size of the image area: the film or digital sensor chip

  And since the image area is a property of the camera and not the lens, it won’t be marked on the lens.

  WHY ARE CERTAIN Focal LengthS POPULAR?

  The answer is due mostly to tradition and convenience. There’s no real technical reason why lenses have to be, say, 28mm, 50mm, or 85mm. And some companies do buck the trends. For example, Pentax Limited lenses have un-orthodox Focal Lengths like 40mm, 43mm, and 77mm.

  But for the sake of convenience, most makers tend to produce lenses with similar popular Focal Lengths.

  A British-built Austin Mini parked on a Paris street. By standing close to the car and using a wide-angle lens I was able to get the roof of the vehicle to dominate the foreground of the shot. Paris, France. 17mm full frame. f /10, 1/200 sec. ISO 100.

  A very long telephoto lens makes the distant moon seem very close to the prosaic sublunary scene below. Earthshine, the reflected light of the Earth on the dark side of the crescent moon, is just visible. Death Valley National Park, CA, USA. 280mm full frame. f /5.6, 0.8 sec. ISO 800.

  Pentax has always enjoyed being different. Its standard prime lens has a Focal Length of 55mm, and not 50mm like almost every other manufacturer.

  The Focal Length of a lens isn’t the same thing as its physical length. Very long telephoto lenses tend to be physically longer, but at shorter Focal Lengths it’s not such a straightforward relationship.

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  University Physics Volume 3

  • William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
  • 2016(Publication Date)
  • Openstax

    (Publisher)

  This value is extremely close to the lens’s focal distance. Now let us consider the case of a distant object. Let us say that we would like to take a picture of a person standing about 5 m from us. Using the thin-lens equation again, we obtain the image distance of 5.005 mm. The farther the object is from the lens, the closer the image distance is to the focal distance. At the limiting case of an infinitely distant object, we obtain the image distance exactly equal to the focal distance of the lens. As you can see, the difference between the image distance for a selfie and the image distance for a distant object is just about 0.05 mm or 50 microns. Even a short object distance such as the length of your hand is two orders of magnitude larger than the lens’s Focal Length, resulting in minute variations of the image distance. (The 50-micron difference is smaller than the thickness of an average sheet of paper.) Such a small difference can be easily accommodated by the same detector, positioned at the focal distance of the lens. Image analysis software can help improve image quality. Conventional point-and-shoot cameras often use a movable lens to change the lens-to-image distance. Complex lenses of 90 Chapter 2 | Geometric Optics and Image Formation This OpenStax book is available for free at http://cnx.org/content/col12067/1.4 the more expensive mirror reflex cameras allow for superb quality photographic images. The optics of these camera lenses is beyond the scope of this textbook. 2.7 | The Simple Magnifier Learning Objectives By the end of this section, you will be able to: • Understand the optics of a simple magnifier • Characterize the image created by a simple magnifier The apparent size of an object perceived by the eye depends on the angle the object subtends from the eye. As shown in Figure 2.36, the object at A subtends a larger angle from the eye than when it is position at point B.

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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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  The Science of Imaging

  • Graham Saxby(Author)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  u v f N 1 N 2 F F´ Figure 4.3 Gauss points in a thick (compound) lens. The Focal Length f and image distance v are measured from the rear nodal point N 2 and the object distance u is measured from the front nodal point N 1 . F is the rear and F ′ the front principal focus, and F ′ N 1 = FN 2 . Two other points, the principal points, coincide with N 1 and N 2 if the lens is wholly in air. P X P E F 2 F 1 S Figure 4.4 Entrance and exit pupils for a simple triplet lens with converging front component. The entrance pupil P E and the exit pupil P X are virtual images of the stop S as seen from the front and rear focal points F 1 and F 2 , respectively, and in this case are both larger than the stop itself. The Science of Imaging, Second Edition: An Introduction 52 Telephoto Lenses Going back to the lens laws, it is plain that when u , the object distance, is large, v , the image distance, will be approximately equal to f , the Focal Length. The formula for magnification then simplifies to M ≈ f/u i.e., the image scale is directly proportional to the Focal Length of the lens. So if you want to be around to be able to impress your friends with a full-frame shot of a charging rhinoceros, you need to use a lens of at least 400-mm Focal Length (a long-focus lens ) rather than the usual 35- or 50-mm prime lens. Now, a 400-mm lens of conventional design is a cumbersome object, not the kind of thing one would want to carry on safari. But the Focal Length is measured, not from the back of the lens, but from the rear nodal plane. If the lens designer can coax this plane out in front of the lens, you will be able to carry around a physically short lens, but with a long Focal Length—by definition, a telephoto lens . The basic principle of a telephoto lens is that of the Galilean telescope (about which more is discussed in Chapter 17). Figure 4.5a shows how the addition of a nega-tive lens increases the Focal Length of the combination.

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  Optical System Design

  • Rudolf Kingslake(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  III. DEPTH OF FOCUS AND DEPTH OF HELD The two terms depth of focus and depth of field are liable to be confused, and they are generally defined in the following manner. Assuming that the lens is free from all aberrations, there will be a 266 15. PHOTOGRAPHIC OPTICS certain plane in the object space that is precisely conjugate to the film plane in the image space. This is known as the focused plane in the object. Because the observer's eyes have a limited acuity, there will be a small amount of tolerable blur in a photograph that the average observer will be unable to distinguish from sharp imagery. Thus a point object may be imaged as a small circle of confusion on the film before the observer can detect that the image is not perfectly sharp. The depth of focus of a lens is the distance along the lens axis in the image space from the plane of sharp definition to the place where the image of a point source just reaches this permissible circle of confu-sion. Similarly, the depth of field ofa lens is the corresponding distance of an object point from the focused plane in the object space before its image reaches the permissible circle of confusion in the film plane. To make these matters more specific, it is clear that the depth of focus is obviously equal to the product of the diameter c' of the permissible circle of confusion on the film and the F-number TV of the lens. This distance is the same whether the image is just within or just beyond the film plane. In the object space things are more complicated because objects lying beyond the focused plane may at times extend to infinity before their image becomes significantly out of focus on the film, whereas near objects soon reach a limit to their acceptable distance from the focused plane.

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  Physics

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

    (Publisher)

  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. If the Focal Length is negative, as it is for the diverging lens in Figure 16.26 , then the power is also negative. In some circumstances, a lens forms an image at an obvious location, such as when a movie projector casts an image onto a screen. In other cases, the image location is less obvious. Where, for example, is the image formed by eyeglasses? We use ray 16.15 16.3 • Lenses 499 tracing for thin lenses to illustrate how they form images, and we develop equations to describe the image-formation quantitatively. These are the rules for ray tracing: 1. A ray entering a converging lens parallel to its axis passes through the focal point, F, of the lens on the other side 2. A ray entering a diverging lens parallel to its axis seems to come from the focal point, F, on the side of the entering ray 3. A ray passing through the center of either a converging or a diverging lens does not change direction 4. A ray entering a converging lens through its focal point exits parallel to its axis 5. A ray that enters a diverging lens by heading toward the focal point on the opposite side exits parallel to the axis Consider an object some distance away from a converging lens, as shown in Figure 16.27 . To find the location and size of the image formed, we trace the paths of select light rays originating from one point on the object. In this example, the originating point is the top of a woman’s head. Figure 16.27 shows three rays from the top of the object that can be traced using the ray- tracing rules just listed.

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  Introduction to Optics

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

    (Publisher)

  If the Focal Length of the lens representing the eyepiece is 4 cm, determine the Focal Length of the other. 3-26 A level telescope contains a graticule —a circular glass on which a scale has been etched—in the common focal plane of objective and eyepiece so that it is seen in focus with a 10 * M = 12.5 a 1 f 1 + 1 f 2 b 1 100 s, distant object. If the telescope is focused on a telephone pole 30 m away, how much of the post falls between mil-limeter marks on the graticule? The Focal Length of the ob-jective is 20 cm. 3-27 A pair of binoculars is marked The Focal Length of the objective is 14 cm, and the diameter of the field lens of the eyepiece is 1.8 cm. Determine (a) the angular magni-fication of a distant object, (b) the Focal Length of the ocular, (c) the diameter of the exit pupil, (d) the eye relief, and (e) the field of view in terms of feet at 1000 yd. 3-28 a. Show that when the final image is not viewed at infinity, the angular magnification of an astronomical telescope may be expressed by where is the linear magnification of the ocular and is the distance from the ocular to the final image. b. For such a telescope using two converging lenses with Focal Lengths of 30 cm and 4 cm, find the angular magni-fication when the image is viewed at infinity and when the image is viewed at a near point of 25 cm. 3-29 The moon subtends an angle of 0.5° at the objective lens of an astronomical telescope.The Focal Lengths of the objective and ocular lenses are 20 cm and 5 cm, respectively. Find the diameter of the image of the moon viewed through the tele-scope at near point of 25 cm. 3-30 An opera glass uses an objective and eyepiece with Focal Lengths of and respectively. Determine the length (lens separation) of the instrument and its magnify-ing power for a viewer whose eyes are focused (a) for infin-ity and (b) for a near point of 30 cm.

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  Physics for Scientists and Engineers with Modern Physics

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

    (Publisher)

  Q UICK QUIZ 35.6 What is the Focal Length of a pane of window glass? (a) zero (b) infinity (c) the thickness of the glass (d) impossible to determine Figure 35.28 A side view of the construction of a Fresnel lens. (a) The thick lens refracts a light ray as shown. (b) Lens material in the bulk of the lens is cut away, leaving only the material close to the curved surface. (c) The small pieces of remaining material are moved to the left to form a flat surface on the left of the Fresnel lens with ridges on the right surface. From a front view, these ridges would be circular in shape. This new lens refracts light in the same way as the lens in (a). (d) A Fresnel lens used in a lighthouse shows several segments with the ridges discussed in (c). a c d b Example 35.8 Images Formed by a Converging Lens 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. S O L U T I O N Conceptualize Because the lens is converging, the Focal Length is positive (see Table 35.3). We expect the possibilities of both real and virtual images. Categorize Because the object distance is larger than the Focal Length, we expect the image to be real. The ray diagram for this situation is shown in Figure 35.29a. Analyze Because Equation 35.18 for lenses is identical to q 5 f p p 2 f 5 (10.0 cm)(30.0 cm) 30.0 cm 2 10.0 cm 5 115.0 cm Equation 35.6 for mirrors, we can use Equation 35.7 for lenses: continued a b O F 1 F 2 I 15.0 cm 30.0 cm 10.0 cm O F 2 I, F 1 10.0 cm 5.00 cm 10.0 cm The object is farther from the lens than the focal point. The object is closer to the lens than the focal point. Figure 35.29 (Example 35.8) An image is formed by a converging lens. Kent Weakley/Shutterstock Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

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