Physics
Focal Points
Focal points are specific points in space where light rays converge or from which they appear to diverge after passing through a lens or reflecting from a curved mirror. In the context of physics, these points are crucial for understanding the behavior of light and the formation of images in optical systems. Understanding focal points is essential for various applications, including photography, microscopy, and astronomy.
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6 Key excerpts on "Focal Points"
eBook - PDF- Vern Ostdiek, Donald Bord(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
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. uni25D7 Physics To Go 9.10 Look around your home, office, or dorm room for a simple, hand-held magnifying lens. Stand under an overhead light, and holding the lens in one hand, project the image of the source onto your other hand. Move the lens up or down to produce a clearly focused image (not just a blur of light) on your palm. Now estimate the distance from the lens to the image. Congratulations! You’ve just found the focal length of the lens. This same technique works for any converging lens as long as the source is a good deal farther from the lens than its focal length. Project the image on a white index card or a piece of white paper instead of your hand. Describe the image of the source produced by the lens. Focal length Focal length Focal point Focal point Figure 9.42 Converging lenses focusing parallel light rays at their Focal Points. A more sharply curved lens has a shorter focal length. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 9.4 Lenses and Imagesuni00A0 353 A diverging lens causes parallel light rays to diverge after passing through it. s s These emergent rays appear to be radiating from a point on the other side of the lens. This point is the focal point of the diverging lens (Figure 9.43). 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.
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Fundamentals & Applications, Second Edition
- Rolf R. Hainich, Oliver Bimber(Authors)
- 2016(Publication Date)
- A K Peters/CRC Press(Publisher)
The plane that is perpendicular to the optical axis and on which the front focal point is located is called the front focal plane. Thus, parallel rays on one side of the lens are mapped to the focal point on the other side. Nonparallel rays (i.e., belonging to object or image points that are closer than infinity) do not map to the focal point. But light rays that cross these points from the same angle always cross on the opposite focal plane. The focal length of a spherical lens can be computed as: 1 f = (η 2 − 1) 1 r 1 − 1 r 2 + (η 2 − 1) 2 η 2 t r 1 r 2 (3.23) where r 1 and r 2 are the two radii, and t is the central thickness. The behavior of converging lenses is similar to the behavior of concave mirrors, but reversed. 3.4.2.3 Diverging Lenses With diverging lenses, objects at infinity create virtual images at the focal plane (Figure 3.19(right)). Real objects always create virtual images, independent of their location. The behavior of diverging lenses is similar to the behavior of convex mirrors, but reversed. Principles of Optics 71 3.4.2.4 Plane Parallel and Curved Parallel Lenses Objects behind a thick glass plate appear slightly enlarged because of refraction, an effect that is increased if the glass is curved toward the observer. This fact is important for the design of cathode ray tubes with their very thick front panels. 3.4.2.5 Varifocal Lenses Varifocal in this context does not address zoom lenses for photographic equipment, which are built of several complex (rigid) lens groups that are moved forward and backward to change focal length. Instead, varifocal lenses are lenses that can change their surface shape. This is more difficult to achieve than with mirrors, and is usually confined to very small lenses. They are also sometimes referred to as liquid lenses. Varifocal microlenses can, for example, be built by enclosing a conducting aqueous solu- tion (e.g., a salt solution) and a nonconductive oil (e.g., silicon oil) in a small cavity.
- Andrei D. Polyanin, Alexei Chernoutsan(Authors)
- 2010(Publication Date)
- CRC Press(Publisher)
An image is the point of intersection of ray transmitted through an optical system. Images are real (the rays converge after leaving the system) and virtual (emergent rays diverge from the virtual point of intersection of their virtual continuations). The system of reflecting and refracting spherical (and plane) surfaces perpendicular to an axis forms the image of a point source by rays incident at small angles to the axis ( paraxial approximation ). The system axis is called the principal optic axis . The point of convergence of rays parallel to the axis is called the focus of the system ; the plane perpendicular to the axis and drawn through the focus is called the focal plane . Like the images, the foci can be real and apparent. Additionally, one introduces the notion of “apparent source” denoting the point of intersection of imaginary continuations of the converging rays incident on the system. In what follows, we use the important property of images: the optical path lengths of all rays from the source to the image are the same; that is, the optical system does not change the path difference of rays. The basic elements of optical systems are the simple optical systems: plane and spherical mirrors, plane and spherical refracting surfaces, and thin lenses. The image formed by each of these elements is the source for the subsequent element. When considering a simple system, one counts all the distances from the point of intersection of this system with the principal optical axis. The distance from this point to the source is denoted by s , the distance to the image, by s ′ , and the distance to the focus, P5.1. G EOMETRIC O PTICS . R ADIOMETRY 537 by f ( focal distance ). To real sources, images, and foci there correspond positive values, to apparent sources, negative values. Below are formulas relating s , s ′ , and f for simple optical systems. 1) Spherical mirror of radius R : 1 s + 1 s ′ = 1 f .
eBook - PDF- John Matolyak, Ajawad Haija(Authors)
- 2013(Publication Date)
- CRC Press(Publisher)
This is a way to create paraxial rays, namely place the light source at the focal point of a converging lens. This property is exploited in both the headlights and tail lights of automobiles. Figure 20.13 shows paraxial rays refracted by a double-concave lens. The rays diverge after refraction, but if extended backward, appear to an observer to originate from a point, which is the focal point. Note that for paraxial rays, real light energy passes through the focal point of a convex lens but not through (F) of a concave lens. F f FIGURE 20.12 All paraxial rays pass through the focal point of the lens after refraction. 373 Geometrical Optics © 2010 Taylor & Francis Group, LLC If the source of light (the object) is close, not far from the lens, an image is formed (Figure 20.14). As with mirrors, the location of the image, formed by lenses, can be found either graphically or analytically. Graphically, the properties of several select rays allow the determination of image location and size. In Figure 20.14, ray one is paraxial and passes through (F) after refraction. Ray two passes through the center of the lens at the principal axis and is essentially undeflected for a thin lens. Ray three is chosen to pass through the focal point before refraction. After refraction, ray three is paraxial. These three specifically chosen rays intersect in a plane, the image plane , and form an image of the object. If the diagram is drawn to scale, the image distance (s i ) and size (h i ) can be measured off the diagram. Analytically, the image location and size can be determined from an equation relating (s i ) to (s 0 ) and (f). To derive the equation, consider the parameters in Figure 20.14 both before and after refraction. tan h s h s 0 0 i i α = = or h h s s i 0 i 0 = . (20.16) f F FIGURE 20.13 Paraxial rays appear to originate and converge from the focal point of a concave lens, when viewed from downstream.
eBook - PDF- W.T. Welford(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
CHAPTER 2 Some Basic Ideas in Geometrical Optics 2.1 The Concepts of Geometrical Optics Geometrical optics is used as the basic tool in designing almost any optical system, image forming or not. We use the intuitive ideas of a ray of light, roughly defined as the path along which light energy travels, together with surfaces that reflect or transmit the light. When light is reflected from a smooth surface it obeys the well-known law of reflection, which states that the incident and reflected rays make equal angles with the normal to the surface and that both rays and the normal lie in one plane. When light is transmitted, the ray direction is changed according to the law of refraction, Snell's law. This law states that the sine of the angle between the normal and the incident ray bears a constant ratio to the sine of the angle between the normal and the refracted ray; again, all three directions are coplanar. A major part of the design and analysis of concentrators involves ray tracing, i.e., following the paths of rays through a system of reflecting and refracting surfaces. This is a well-known process in conventional lens design but the requirements are somewhat different for concentrators, so it will be convenient to state and develop the methods ab initio. In conventional lens design the reflecting or refract-ing surfaces involved are almost always portions of spheres, and the 9 10 2 Some Basic Ideas in Geometrical Optics centers of the spheres lie on one straight line (axisymmetric optical system), so that special methods that take advantage of the simplicity of the forms of the surfaces and the symmetry can be used. Nonimaging concentrators do not, in general, have spherical surfaces. In fact, sometimes there is no explicit analytical form for the surfaces, although usually there is an axis or a plane of symmetry.
eBook - PDF- Richard L. Myers(Author)
- 2005(Publication Date)
- Greenwood(Publisher)
In communications technology, a light source such as a laser is used to transmit informa- tion through fiber cables packed in bundles. In this manner, large amounts of information are transmitted. In addition to the vast amounts of information optical fibers carry, they are also relatively free from the electri- cal interference associated with traditional metal wires. Another major application of optical fibers is in medicine. Endoscopes are optical fibers used to examine the interior of the body. For example, in arthroscopy, they are used to examine joints such as the knee, and surgery performed with the aid of these scopes is termed arthroscopic surgery. A colonoscopy uses optical fibers to exam- ine and remove polyps in the colon. Just as mirrors are used for reflection, lenses are based largely on the refractive properties of light. A lens is typically a thin piece of glass or other transparent material such as plastic that has the ability to redi- rect light rays to form an image. Lenses that cause incident parallel light rays to converge through a focal point are called converg- ing or convex (also referred to as positive) lenses. Diverging or concave (negative) lenses cause incident parallel light rays to diverge from a focal point. Similar to mir- rors, lenses are characterized by a focal point, focal length, principal axis, and center of curvature (Figure 9.12). Ray tracing similar to that employed for mirrors can be used to locate and describe images produced from lenses. Parallel inci- dent rays (those parallel to the principal axis) are refracted through the focal point on the opposite side they enter for converging lenses. For a diverging lens, parallel incident rays are refracted as though they originate from the focal point on the incident side. Rays drawn from the object through the focal point will refract from the lens parallel to the principal axis.
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