Physics
Lenses
Lenses are transparent devices that refract light, causing it to converge or diverge. They are commonly used in optics to focus, magnify, or reduce the size of images. Lenses can be classified into two main types: convex lenses, which converge light, and concave lenses, which diverge light.
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eBook - PDFLet 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)
Lenses and, to a lesser extent, mirrors are the central com-ponents of optical instruments. The most fundamental such instrument is the human eye, which brings the incoming light to a focus, performs a preliminary analysis of the signal, and then transmits the information to the brain. 60 Let There Be Light 2nd Edition 3.6 The eye The structure of the eye Light enters the eye through a thin transparent membrane called the cornea — the most powerful part of the lens system — where the main part of the bending of light occurs. Behind the cornea , the pliable crystalline lens — controlled by the ciliary mus-cles, adds fine-tuning to the focusing process to produce a sharp image on the retina , which is a photosensitive membrane and acts like an array of miniature photocells. These micro-scopic units (there are more than 100 million of them) are called rods and cones and respond to light by generating an electrical signal. This signal is carried to the brain by the optic nerve . The light passes through the pupil , an adjustable circu-lar opening in the centre of the iris which regulates the inten-sity of light entering the eye. The iris is beautifully pigmented and gives the eye its colour. Accommodation When the eye is relaxed, the lens is in its least rounded state. The focal length has its maximum value, suitable for distant viewing. The parallel beams of light from distant objects are focused on the retina, which is about 2 cm behind the lens. retina optic nerve lens iris cornea ciliary muscles t h e h u m a n e y e A relaxed eye focuses parallel light on the retina. 2 cm Light as a Ray: Refraction 61 When the muscles are relaxed in a normal eye, the power of the lens is P = 1/ f = 1/0.02 = 50 diopters. The eye ‘accommodates’ for close vision by tightening the ciliary muscles. This causes the pliable crystalline lens to become more rounded, decreasing the focal length and increasing the power of the lens.
eBook - PDF- Vern Ostdiek, Donald Bord(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
In this case, the emer- r r gent rays diverge outward as though they had originated from a point e e F 9 to the Optical axis Angle of incidence Angle of refraction Normal Glass Air F Figure 9.40 Refraction at a convex spherical surface showing the convergence of light rays. F is the focal point—that is, the point at which the light rays are concentrated after having passed through the surface. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 352 Chapter 9 Optics left of the interface. The ability to either bring together or spread apart light rays is the basic characteristic of Lenses, be they camera Lenses, telescope Lenses, or the Lenses in human eyes. Although the situation shown in Figureuni00A09.40 does occur in the eye, in most devices the light rays must enter and then leave the optical element (lens) that redirects them. Common Lenses have two refracting surfaces instead of one, with one surface typically in the shape of a segment of a sphere and the second either spherical as well or flat (planar). The effect on parallel light rays pass- ing through both surfaces is similar to that in the previous examples with one refracting surface. A converging lens causes parallel light rays to converge to a s s point, called the focal point of the lens ( t t Figure 9.42). The distance from the lens to the focal point is called the focal length of the lens. A more sharply curved lens has a shorter focal length. Conversely, if a tiny source of light is placed at the focal point, the rays that pass through the converging lens will emerge parallel to each other. This is the principle of reversibility again. F ' Optical axis Glass Air Figure 9.41 Refraction at a concave spherical surface showing the divergence of a beam of parallel light. F 9 is the focal point—that is, the point from which the rays appear to diverge after having passed through the surface.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
CHAPTER26 The Refraction of Light: Lenses and Optical Instruments PREVIEW In this chapter you will be introduced to one of the most useful properties of light: refraction at an interface between two transparent materials. Snell's law governs how much refraction occurs at an interface. You will learn to apply Snell's law to find how much the path of a light ray is bent in passing through an interface and how much the path of a light ray is displaced when passing through a pane of glass. A special case of Snell's law when the angle of incidence is sufficiently large leads to the phenomenon of total internal reflection at the interface. This phenomenon has importance in the transmission of light through optical fibers and is responsible for the brilliance of the light reflected from a diamond. The polarization of light by reflection from a boundary is discussed as well as the dispersion of light into its rainbow of colors when it is refracted through a prism Many applications of refraction involve Lenses. You will learn how Lenses refract light to form images of the object from which the light originated. In particular you will learn to calculate where the images will be formed, what kind of image is formed and the size of the image for the special case of thin Lenses. After treating thin Lenses separately, you will study thin Lenses in combinations. Two familiar applications of Lenses in combination are the microscope and the telescope which are also discussed along with the camera, the human eye, and the magnifying glass. QUICK REFERENCE Important Terms Interface The boundary between two materials. Refraction The change in the direction of travel of light as it passes from one material to another. Index of refraction The ratio of the speed oflight in a vacuum to the speed of light in a particular material. Apparent depth The depth of a submerged object as seen by someone not under the water.
eBook - PDF- 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.
eBook - PDF- Graham Saxby(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
47 4 Chapter Lens Principles A Model for the Geometry of Camera Lenses Although there are a number of models describing the behavior of light, the one used by lens designers is the simplest, namely the ray model. Before there were computers, the designing of a new lens was a complicated business involving months of laborious ray tracing. Today, designers can optimize a lens design in a few minutes using an off-the-shelf computer program. The variables to juggle are the refractive indices of the components; the color dispersions of the glasses; the number of components and their curvature, thickness, and separation; and the position of the stop. This all represented a heavy meal for the old-time designer equipped with only a slide-rule and a set of tables of glass types. But to a mod-ern computer they signify no more than a light breakfast. The result still doesn’t predict everything about the performance of the final lens; this demands a more sophisticated model, as we will see in Chapter 6. However, a simple ray model is sufficient to describe how a lens forms an image, and to explain why it is necessary to have more than one element in a camera lens. To begin with we will look at the properties of a simple convex lens. The Simple Lens The most basic ray model for a lens makes a number of assumptions: 1. The thickness of the lens can be ignored. 2. The lens aperture is small compared with the focal length. 3. The refractive index of the material is the same for all wavelengths. The geometrical optics of a simple or “thin” lens was established by Sir Isaac Newton, and for this reason is usually known as Newtonian optics . The Lens Laws The Newtonian lens laws consist of three basic principles concerning a simple lens. The first gives the relationship between the distances of the object and its image from the lens. The positions of the object and the image (which is inverted) are together termed conjugate foci (Figure 4.1).
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
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. 35.4 Images Formed by Thin Lenses 943 (Fig. 35.27c), the image is always virtual and upright, regardless of where the object is placed, like the image in a door peephole. These geometric constructions are reasonably accurate only if the distance between the rays and the principal axis is much less than the radii of the lens surfaces. Refraction occurs only at the surfaces of the lens. The uniform material inside the lens simply propagates the light, but does not affect the direction in which it travels. A certain lens design takes advantage of this behavior to produce the Fresnel lens, a powerful lens without great thickness. Because only the surface curvature is important in the refracting qualities of the lens, material in the middle of a Fresnel lens is removed as shown in the cross sections of Lenses in Figure 35.28. Because the edges of the curved segments cause some distortion, Fresnel Lenses are generally used only in situations in which image quality is less important than reduction of weight. A classroom overhead projector often uses a Fresnel lens; the circular edges between segments of the lens can be seen by looking closely at the light projected onto a screen. 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.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
26.5 The Dispersion of Light: Prisms and Rainbows A glass prism can spread a beam of sunlight into a spectrum of colors because the index of refraction of the glass depends on the wavelength of the light. Thus, a prism bends the refracted rays corresponding to different colors by different amounts. The spreading of light into its color components is known as dispersion. The dispersion of light by water droplets in the air leads to the formation of rainbows. A prism will not bend a light ray at all, neither up nor down, if the surrounding fluid has the same refractive index as the material from which the prism is made, a condition known as index matching. 26.6 Lenses 26.7 The Formation of Images by Lenses Converging Lenses and diverging Lenses de- pend on the phenomenon of refraction in forming an image. With a converging lens, paraxial rays that are parallel to the principal axis are focused to a point on the axis by the lens. This point is called the focal point of the lens, and its distance from the lens is the focal length f. Paraxial light rays that are parallel to the principal axis of a diverging lens appear to originate from its focal point after passing through the lens. The distance of this point from the lens is the focal length f. The image produced by a converging or a diverging lens can be located via a technique known as ray tracing, which utilizes the three rays outlined in the Reasoning Strategy given in Section 26.7. The nature of the image formed by a converging lens depends on where the object is situated relative to the lens. When the object is located at a distance from the lens that is greater than twice the focal length, the image is real, inverted, and smaller than the object. When the object is located at a distance from the lens that is between the focal length and twice the focal length, the image is real, inverted, and larger than the object.
No longer available |Learn morePhysics for Scientists and Engineers
Foundations and Connections, Extended Version with Modern Physics
- Debora Katz(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
We modeled the microscope as a system of two thin converging Lenses. However, like modern camera Lenses, each lens of a modern microscope usually consists of several optical elements. CASE STUDY The Refracting Telescope A microscope provides a greatly enlarged image of a small close object. Contrast this to an astronomical telescope, which provides an image of a large distant object. The main job of the telescope is to gather more light than you could with your unaided eyes. Both microscopes and refracting telescopes are made of two converging Lenses, but the arrangement of these Lenses determines which instru- ment results. Figure 38.46A shows the major components of a refracting telescope. As in a microscope, the lens closer to the object is the objective and the lens closer to your eye is the eyepiece. An object examined through a telescope is far away, so rays from the object are parallel and come together at the focal point of the objec- tive lens (Fig. 38.46B). The image formed at the focal point is very small. The second lens—the eyepiece—magnifies that image. The image produced by the objective becomes the object for the eyepiece, which produces an enlarged virtual image. Ideally, the image you see through the eyepiece is at infinity so that your ciliary muscles can relax, which means the image produced by the objective should be at the focal point of the eyepiece. So the distance between the objective lens and the eyepiece should be the sum of their focal lengths: f o 1 f e in Figure 38.46B. f o f e f e F e F e F o Eyepiece Objective Eyepiece Objective Parallel rays from object at ∞ u o u o u e I 1 I 2 h A. B. FIGURE 38.46 A. A refracting telescope has two Lenses. B. A ray diagram for an astronomical telescope. I 1 is the image produced by the objective; it is the object of the eyepiece. I 2 is the image that you observe through the eyepiece. Copyright 2017 Cengage Learning. All Rights Reserved.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
760 CHAPTER 26 The Refraction of Light: Lenses and Optical Instruments The Refractive Power of a Lens—The Diopter The extent to which rays of light are refracted by a lens depends on its focal length. However, optometrists who prescribe correctional Lenses and opticians who make the Lenses do not specify the focal length directly in prescriptions. Instead, they use the concept of refractive power to describe the extent to which a lens refracts light: Refractive power of a lens (in diopters) = 1 f (in meters) (26.8) The refractive power is measured in units of diopters. One diopter is 1 m −1 . Equation 26.8 shows that a converging lens has a refractive power of 1 diopter if it focuses parallel light rays to a focal point 1 m beyond the lens. If a lens refracts parallel rays even more and converges them to a focal point only 0.25 m beyond the lens, the lens has four times more refractive power, or 4 diopters. Since a converging lens has a positive focal length and a diverging lens has a negative focal length, the refractive power of a converging lens is positive and that of a diverging lens is negative. Thus, the eyeglasses in Example 12 would be described in an optom- etrist’s prescription in the following way: Refractive power = 1/(−5.19 m) = −0.193 diopters. The contact Lenses in Example 13 would be described in a similar fashion: Refractive power = 1/(0.284 m) = 3.52 diopters. Check Your Understanding (The answers are given at the end of the book.) 21. Two people who wear glasses are camping. One is nearsighted, and the other is farsighted. Whose glasses may be useful in starting a fire by concentrating the sun’s rays into a small region at the focal point of the lens used in the glasses? 22. Suppose that a person with a near point of 26 cm is standing in front of a plane mirror. How close can he stand to the mirror and still see himself in focus? 23.
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.
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)
CHAPTER 26 The refraction of light: Lenses and optical instruments 759 FIGURE 26.43 (a) In a converging lens, spherical aberration prevents light rays parallel to the principal axis from converging to a common point. (b) Spherical aberration can be reduced by allowing only rays near the principal axis to pass through the lens. The refracted rays now converge more nearly to a single focal point F. Circle of least confusion (a) (b) F Variable-aperture diaphragm Chromatic aberration also causes blurred images. It arises because the index of refraction of the material from which the lens is made varies with wavelength. Section 26.5 discusses how this variation leads to the phenomenon of dispersion, in which different colours refract by different amounts. Figure 26.44a shows sunlight incident on a converging lens, in which the light spreads into its colour spectrum because of dispersion. For clarity, however, the picture shows only the colours at the opposite ends of the visible spectrum — red and violet. Violet is refracted more than red, so the violet ray crosses the principal axis closer to the lens than does the red ray. Thus, the focal length of the lens is shorter for violet than for red, with intermediate values of the focal length corresponding to the colours in between. As a result of chromatic aberration, an undesirable colour fringe surrounds the image. FIGURE 26.44 (a) Chromatic aberration arises when different colours are focused at different points along the principal axis: F V = focal point for violet light, F R = focal point for red light. (b) A converging and a diverging lens in tandem can be designed to bring different colours more nearly to the same focal point F. F V F R Red Sunlight Violet (a) (b) F Red Sunlight Violet Chromatic aberration can be greatly reduced by using a compound lens, such as the combination of a converging lens and a diverging lens shown in figure 26.44b.
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