Physics
Magnifiers
Magnifiers are optical devices that use lenses to make objects appear larger. They are commonly used in physics to study small objects or details that are not easily visible to the naked eye. By bending light rays, magnifiers can create an enlarged image of an object, allowing for closer examination and analysis.
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12 Key excerpts on "Magnifiers"
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
The result is f = 25 cm M − 1 = 25 cm 10 − 1 = 2.8 cm. Significance Note that a greater magnification is achieved by using a lens with a smaller focal length. We thus need to use a lens with radii of curvature that are less than a few centimeters and hold it very close to our eye. This is not very convenient. A compound microscope, explored in the following section, can overcome this drawback. 2.8 | Microscopes and Telescopes Learning Objectives By the end of this section, you will be able to: • Explain the physics behind the operation of microscopes and telescopes • Describe the image created by these instruments and calculate their magnifications Microscopes and telescopes are major instruments that have contributed hugely to our current understanding of the micro- and macroscopic worlds. The invention of these devices led to numerous discoveries in disciplines such as physics, astronomy, and biology, to name a few. In this section, we explain the basic physics that make these instruments work. 94 Chapter 2 | Geometric Optics and Image Formation This OpenStax book is available for free at http://cnx.org/content/col12067/1.4 Microscopes Although the eye is marvelous in its ability to see objects large and small, it obviously is limited in the smallest details it can detect. The desire to see beyond what is possible with the naked eye led to the use of optical instruments. We have seen that a simple convex lens can create a magnified image, but it is hard to get large magnification with such a lens. A magnification greater than 5 × is difficult without distorting the image. To get higher magnification, we can combine the simple magnifying glass with one or more additional lenses. In this section, we examine microscopes that enlarge the details that we cannot see with the naked eye. Microscopes were first developed in the early 1600s by eyeglass makers in The Netherlands and Denmark.
eBook - ePubLight and Optics
Principles and Practices
- Abdul Al-Azzawi(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
Figure 14.6 . The magnifying glass is a single converging lens. The lens held near the eye produces an image whose projected size on the retina is larger than the real size of the object (when compared to unaided eye). Maximum magnification of the object can be found by adjusting the distance between the lens and object. Varying this distance, one can find a clear image. The magnifying glass is considered a passive optical device. The magnifying glass is not only used to enlarge a fine object; it is also used in lens compensation, which is used in a compound microscope. In this arrangement, the magnifying glass is called the eyepiece, and the other lens near to an object is called the objective lens. The compound microscope instrument will be explained in detail in the next section. The primary function of magnifying glasses is to increase the angular size of the image while viewing with a relaxed eye.FIGURE 14.6 Simple magnifying lenses.FIGURE 14.7 (a) The object placed a distance from the eye. (b) The object placed closer to the eye.The apparent size of an object is determined by the size of its image on the retina. To an unaided eye, an object placed a distance from the eye creates an image covering part of the retina, as shown in Figure 14.7(a) . If the object comes closer to the eye, its image covers a larger part of the retina, as shown in Figure 14.7(b) . The greater the angle viewed, the larger the image appears.In Figure 14.8(a) the object is located at the near point, where it subtends an angle θ at the eye. In Figure 14.8(b) , a converging lens is used to form a virtual image that is larger and farther from the eye than the object. The image formation by converging lenses is widely explained in the lenses chapter. A lens used to enlarge an object is called a simple magnifier, or sometimes is called a magnifying glass. In Figure 14.8(b) a magnifier in front of the eye forms an image at the near point, with the angle θ′ subtended at the magnifier. The magnification power of the magnifier is defined by the ratio of the angle θ′(viewed with the magnifier) to the angle θ (viewed without the magnifier). This ratio is called the angular magnification Ma
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
THE PHYSICS OF . . . The telescope A telescope is an instrument for magnifying distant objects, such as stars and planets. Like a microscope, a telescope consists of an objective and an eyepiece (also called the ocular). When the objective is a lens, as is the case in this section, the telescope is referred to as a refracting telescope, since lenses utilise the refraction of light. * Usually the object being viewed is far away, so the light rays entering the telescope are nearly parallel, and the ‘first image’ is formed just beyond the focal point F o of the objective, as figure 26.41a illustrates. The first image is real and inverted. Unlike the first image in the compound microscope, however, this image is smaller than the object. If, as in part b of the drawing, the telescope is constructed so the first image lies just inside the focal point F e of the eyepiece, the eyepiece acts like a magnifying glass. It forms a final image that is greatly enlarged, virtual, and located near infinity. This final image can then be viewed with a fully relaxed eye. FIGURE 26.41 (a) An astronomical telescope is used to view distant objects. (Note the ‘break’ in the principal axis, between the object and the objective.) The objective produces a real, inverted first image. (b) The eyepiece magnifies the first image to produce the final image near infinity. Objective Distant object First image Eyepiece θ θ f o h i F o L (a) First image Final image (near ∞) θ′ h i F e f e (b) The angular magnification M of a telescope, like that of a magnifying glass or a microscope, is the angular size ′ subtended by the final image of the telescope divided by the reference angular size of the object. For an astronomical object, such as a planet, it is convenient to use as a reference the angular size of the object seen in the sky with the unaided eye.
eBook - PDF- Rudolf Kingslake(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
CHAPTER 1 1 Magnifying Instruments I. THE SIMPLE MAGNIFIER The apparent size of anything seen by the eye is expressed by the angle it subtends at the eye. Consequently, any device that increases angular subtense acts as a magnifier and makes objects look larger. The magnifying power (MP) of such a device is given by the ratio . __ angular subtense of the image seen through the instrument MP = angular subtense of the object viewed directly The denominator of this fraction needs some clarification, because merely bringing an object closer to the eye makes it appear larger. A myopic observer can often see a small object easily by simply remov-ing his spectacles and bringing the object close to his eye. For a simple magnifier or microscope, where an object can be placed at any desired distance from the eye, it is necessary to establish a conventional nearest distance of distinct vision at which the object is assumed to be viewed directly. This distance Fis generally taken to be 10 in., or 250 mm. We can now set up a general relation between the distances of object, image, and lens from the eye and obtain formulas for the magnifying power of the system. In Fig. 11.1, we see that if the object to be magnified is placed at a distance a beyond a simple thin magnify-ing lens and if the image seen by the eye is at a distance b from the lens, then if the eye is at a distance E from the lens, the magnifying power will be given by m „ image subtense h'/(E + b) mV MP == = == ( 1 ) object subtense h/V E + b 9 where m is the image magnification h'¡h = b/a. It is essential to distinguish between magnification and magnifying power. Magnifica-tion is the simple ratio of image size to object size. Magnifying power is the ratio of image subtense to object subtense (at the conventional 182 I. THE SIMPLE MAGNIFIER 183 Maqnified virtual image 4 FIG. 11.1. Magnifying power of a lens. distance V). Magnifying power thus involves object and image dis-tances as well as their sizes.
eBook - ePub- Jeremy Sanderson(Author)
- 2019(Publication Date)
- Wiley(Publisher)
Figure 3.11 shows how an object placed at the reference viewing distance forms a 1x image on the retina. The same 1x image is formed if a lens with a focal length of 250 mm is used to view the object. If a lens of shorter focal length is used, a magnified image is formed.Source: Reproduced with permission from Carl Zeiss Ltd.Figure 3.11The reference viewing distance How the reference viewing distance is used to calculate the magnification of a simple lens. See the text and also Box 3.2 for further explanation.For optical instruments with an eyepiece, or for a single lens forming a virtual image, the linear dimension of the image cannot be given since in these cases magnification is an angular measure and the image size is proportional to the tangent of the angle subtended by the object at the focal point of the lens (See the comments on magnification in Note 1, in the Notes section of the front matter). By convention, for magnifying glasses, telescopes and microscope eyepieces, where the size of the object is a linear dimension and the apparent size is an angle, the magnification is the ratio between the apparent (angular) size as seen in the eyepiece and the angular size of the object when placed at the reference viewing distance of 25 cm from the eye (as if observed by a ‘normal’ unaided eye). The formulae given in Box 3.2 show how to calculate the power of a magnifying glass.Magnifiers are limited by having short working distances between the object and magnifying lens and also small depths of field. Loupes are used by jewellers, watchmakers, surgeons and dentists for intricate work. Simple hand loupes generally magnify a maximum of 10x.3.9 The Compound Microscope
A compound microscope is one in which the image of the object is presented to the eye by a combination of objective and eyepiece. The advantage of a compound lens system, rather than a single simple lens magnifier, is that much higher magnifications can be achieved. To obtain high magnification with a single-lens magnifier, the lens itself must be placed close to the eye (Figure 3.12
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
In other words, an optical instrument magnifies the angular size of the object. The angular magnification (or magnifying power) M is the angular 844 CHAPTER 26 The Refraction of Light: Lenses and Optical Instruments size θʹ of the final image produced by the instrument divided by a reference angular size θ. The reference angular size is the angular size of the object when seen without the instrument. Angular magnification M = Angular size of final image produced by optical instrument ________________ Reference angular size of object seen without optical instrument = θ ′ _ θ (26.9) A magnifying glass is the simplest device that provides angular magnification. In this case, the reference angular size θ is chosen to be the angular size of the object when placed at the near point of the eye and seen without the magnifying glass. Since an object cannot be brought closer than the near point and still produce a sharp image on the retina, θ represents the largest angular size obtainable without the magnifying glass. Figure 26.41a indicates that the reference angular size is θ ≈ h o /N, where N is the distance from the eye to the near point. To compute θʹ, recall from Section 26.7 and Figure 26.28 that a magnifying glass is usually a single converging lens, with the object located between the focal point of the lens and the lens. In this situation, Figure 26.41b indicates that the lens produces a virtual image that is enlarged and upright with respect to the object. Assuming that the eye is next to the magnifying glass, the angular size θʹ seen by the eye is θʹ ≈ h o /d o , where d o is the object distance.
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
Greater magnification can be achieved by combining two lenses in a device called a compound microscope shown in Figure 35.43a. It consists of one lens, the objective, that has a very short focal length f o , 1 cm and a second lens, the eyepiece, that has a focal length f e of a few centimeters. The two lenses are separated by a distance L that is much greater than either f o or f e . The object, which is placed just outside the focal point of the objective, forms a real, inverted image at I 1 , and this image is located at or close to the focal point of the eyepiece. The eyepiece, which serves as a simple magnifier, produces at I 2 a virtual, enlarged image of I 1 . The lateral magnification M 1 of the first image is 2q 1 / p 1 . Notice from Figure 35.43a that q 1 is approximately equal to L and that the object is very close to the focal point of the objective: p 1 < f o . Therefore, the lateral magnification by the objective is M o < 2 L f o The angular magnification by the eyepiece for an object (corresponding to the image at I 1 ) placed at the focal point of the eyepiece is, from Equation 35.25, m e 5 25 cm f e The overall magnification of the image formed by a compound microscope is defined as the product of the lateral and angular magnifications: M 5 M o m e 5 2 L f o S 25 cm f e D (35.26) The negative sign indicates that the image is inverted. The microscope has extended human vision to the point where we can view pre- viously unknown details of incredibly small objects. The capabilities of this instru- ment have steadily increased with improved techniques for precision grinding of lenses. A question often asked about microscopes is, “If one were extremely patient and careful, would it be possible to construct a microscope that would enable the human eye to see an atom?” The answer is no, as long as light is used to illuminate the object.
- James Stewart(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
Optical Systems 12 In this chapter a number of optical systems are discussed. The systems are selected to illustrate useful optical principles and also to present some designs that might be incorporated as subsystems in engineering projects. Some problems can occur with aperture stops when optical systems are assembled from subsystems or developed by modification of existing systems. It is worth emphasizing that there can be only one pupil in a system, and the insertion of additional stops can lead to surprising observations, such as vignett ing of images. The optical design of optical systems is discussed by Kingslake (1983) and Smith (1990) among others. For mechanical design of optical systems see O’Shea (1988) and Yoder (1992). 12.1. EYEPIECES AND Magnifiers An eyepiece (or ocular) is used to inspect a final image formed by an optical system. A magnifier, on the other hand, is used to inspect a small object. It is the function of both of them to form an image in a position where it can be viewed by the observer’s eye. The lens of the eye transfers the image to the retina of the eye. The eyepiece has an additional task. It should place an image of the pupil of the optical system on the iris of the eye, in order to not interfere with the field of view. The optical characteristics of eyepieces and Magnifiers 169 170 Chapter 12 were reviewed by Rosin (1965); eyepieces for telescopes were described by Sidgwick (1980). The magnification of a magnifier is not well defined. As given by Rosin (1965), the magnification is ( 12 . 1 ) w here/is the focal length of the magnifier, s is the so-called distance of distinct vision which is commonly taken to be 250 mm, although it varies with individual eyes. Z is the reciprocal of the distance between the eye and the image it is viewing. If the image is at infinity, Z = 0 and M = s/f But, if the image is at the distance of distinct vision Z = /s and M = (s/f + 1).
eBook - PDFHow Things Work
The Physics of Everyday Life
- Louis A. Bloomfield(Author)
- 2016(Publication Date)
- Wiley(Publisher)
M any of the devices around us perform useful tasks by manipulating light, charge, or both. The techniques of optics deal with light and allow cameras to record images of the objects in front of them, our eyes to observe those objects directly, and eyeglasses and magnifying glasses to help us see details we’d miss with our eyes alone. The techniques of electronics deal with charge and permit an audio player’s memory to store sound information, its computer to retrieve that information, and its amplifier and headphones to re-create the sound at the push of a button. Optical tools such as lenses and prisms have been around for hundreds of years, and electronic devices such as resistors, capacitors, and inductors also have a long history. Advances of modern technology, however, have accelerated developments in both fields. The invention of lasers has sped the growth of the optics industry and the invention of transistors has revolutionized the world of electronics. Rapid progress in both fields, optics and electronics, has brought them closer together and has given birth to the combined field of optoelectronics. There is even hope that one day com- puters will be as much optical devices as they are electronic. Magnifying Glass Camera There are many household devices that manipulate light, and one of the most familiar is a magnifying glass. A magni- fying glass bends light rays toward one another as they pass through it. In this chapter, we’ll see how a simple converging lens of this sort can magnify an object or cast its image onto a light-sensitive surface. For the moment, we’ll use it to cast the image of a window onto a wall. Take a magnifying glass to a room with a bright window and turn off the lights. Hold the magnifying glass near the wall opposite the window and move the glass ACTIVE LEARNING EXPERIMENTS 392 14 Optics and Electronics Courtesy Lou Bloomfield
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
The resulting optical instrument is called a compound microscope. The magnifying glass is called the eyepiece of the microscope, and the additional lens is called the objective. If f 0 is the focal length of the objective, fe the focal length of the eyepiece, and L the distance between the objective and eyepiece, the angular magnification of the compound microscope is given by (26.11) Example 15 The objective of a compound microscope has a focal length of 5.0 mm, while that of the eyepiece is 1.8 em. If the two lenses are separated by 25.0 em, determine the angular magnification if a person with normal vision is using the microscope (that is, N = 25 em). M:= (25. 0 em - 1. 8 em)(25 em) = (0.50 em)(l.8 em) -640 Note that when the eyepiece is used alone, the angular magnification would be M = (N/fe) + 1 = 15. The compound microscope therefore represents an improvement in angular magnification by a factor of 640/15 = 43 over that of the magnifying glass alone. 350 THE REFRACTION OF LIGHT: LENSES AND OPTICAL INSTRUMENTS 26.13 The Telescope A telescope is an instnunent for magnifying distant objects, such as stars and planets. A telescope consists of an objective lens and an eyepiece. The "first image" is formed by the objective lens and is real, inverted, and smaller than the object. If this first image falls inside the focal point of the eyepiece, the eyepiece acts like a magrufying glass. It forms a fmal image that is virtual, enlarged, and located near infinity. This fmal image can then be viewed with a fully relaxed eye. The angular magnification of a telescope can be written as: (26.12) Example 16 A refracting telescope has an objective and an eyepiece that have refractive powers of 1.25 diopters and 250 diopters, respectively. Find the angular magnification of the telescope. To find the angular magnification we first need the focal lengths of the objective and eyepiece.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
When the objective is a lens, as is the case in this section, the telescope is referred to as a refracting telescope, since lenses utilize the refraction of light.* Usually the object being viewed is far away, so the light rays entering the telescope are nearly parallel, and the “first image” is formed just beyond the focal point F o of the objective, as Figure 26.41a illustrates. The first image is real and inverted. Unlike the first image in the compound microscope, however, this image is smaller than the object. If, as in part b of the drawing, the telescope is constructed so the first image lies just inside the focal point F e of the eyepiece, the eyepiece acts like a magnifying glass. It forms a final *Another type of telescope utilizes a mirror instead of a lens for the objective and is called a reflecting telescope. 752 Chapter 26 | The Refraction of Light: Lenses and Optical Instruments image that is greatly enlarged, virtual, and located near infinity. This final image can then be viewed with a fully relaxed eye. The angular magnification M of a telescope, like that of a magnifying glass or a mi- croscope, is the angular size u9 subtended by the final image of the telescope divided by the reference angular size u of the object. For an astronomical object, such as a planet, it is convenient to use as a reference the angular size of the object seen in the sky with the unaided eye. Since the object is far away, the angular size seen by the unaided eye is nearly the same as the angle u subtended at the objective of the telescope in Figure 26.41a. Moreover, u is also the angle subtended by the first image, so u < 2h i /f o , where h i is the height of the first image and f o is the focal length of the objective. A minus sign has been inserted into this equation because the first image is inverted relative to the object and the image height h i is a negative number.
- Gerhard Wanner(Author)
- 2022(Publication Date)
- Wiley-VCH(Publisher)
Total magnification = scale number of the lens x eyepiece magnification In modern microscopes, there is an intermediate stage: a tube lens is added to support the objective. The objective lens creates an image at an “infinite” distance; the tube lens with its focal length (e.g. f = 164.5 mm) then forms the inter- mediate image from these parallel beams (Figure 2.4.1). The ocular again serves as a mag- nifying glass to make this small intermediate image appear even more magnified to the eye. Figure 2.3.2 In 1665, Robert Hooke (1635–1703) used a compound microscope, which he improved, to study cork cells and introduced the term “cellula” (cell) into biology. A B Figure 2.3.1 An object is viewed with two lenses (A + B) spaced apart. The magnifications multiply, and the image is “upside down.” 2.4 Optics and resolution 11 2.4.1 Resolution determines what is visible When observing small objects under the microscope, the incident light is deflected (diffracted) by these objects from its original direction. This deflection becomes stronger as the structures become smaller. To obtain sharp images of small structures, the objective lens must “collect” as much of this dif- fracted light as possible. This works especially well if the lens captures a large solid angle. The term aperture (= opening; lat. apertus = open, opened) describes this property. The fundamental relationship between resolution, wavelength, and aperture angle was first described in detail in a pioneering work by Ernst Abbe (Figure 2.4.1.1). The “numerical aperture” is a measure of the solid angle that an objective lens “overlooks.” This for- mula applies when there is air (refractive index n < 1) between the objective and the object.
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