4/8/2016 Images Review & Summary Real and Virtual Images An image is a reproduction of an object via light. If the image can form on a surface, it is a real image and can exist even if no observer is present. If the image requires the visual system of an observer, it is a virtual image. Image Formation Spherical mirrors, spherical refracting surfaces, and thin lenses can form images of a source of light—the object—by redirecting rays emerging from the source. The image occurs where the redirected rays cross (forming a real image) or where backward extensions of those rays cross (forming a virtual image). If the rays are sufficiently close to the central axis through the spherical mirror, refracting surface, or thin lens, we have the following relations between the object distance p (which is positive) and the image distance i (which is positive for real images and negative for virtual images): 1. Spherical Mirror: (34-4, 34-3) where f is the mirror's focal length and r is its radius of curvature. A plane mirror is a special case for which , so that . Real images form on the side of a mirror where the object is located, and virtual images form on the opposite side. 2. Spherical Refracting Surface: (34-8) where n1 is the index of refraction of the material where the object is located, n2 is the index of refraction of the material on the other side of the refracting surface, and r is the radius of curvature of the surface. When the object faces a convex refracting surface, the radius r is positive. When it faces a concave surface, r is negative. Real images form on the side of a refracting surface that is opposite the object, and virtual images form on the same side as the object. 3. Thin Lens: (34-9, 34-10) where f is the lens's focal length, n is the index of refraction of the lens material, and r1 and r2 are the radii of curvature of the two sides of the lens, which are spherical surfaces. A convex lens surface that faces the object has a positive radius of curvature; a concave lens surface that faces the object has a negative radius of curvature. Real images form on the side of a lens that is opposite the object, and virtual images form on the same side as the object. Lateral Magnification The lateral magnification m produced by a spherical mirror or a thin lens is (34-6) The magnitude of m is given by http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c34/aGFsbGlkYXk5NzgxMTE4MjMwNzI1YzM0LXNlYy0wMDQwLnhmb3Jt.enc?co… 1/2 4/8/2016 Images (34-5) where h and are the heights (measured perpendicular to the central axis) of the object and image, respectively. Optical Instruments Three optical instruments that extend human vision are: 1. The simple magnifying lens, which produces an angular magnification mθ given by (34-12) where f is the focal length of the magnifying lens. The distance of is a traditionally chosen value that is a bit more than the typical near point for someone 20 years old. 2. The compound microscope, which produces an overall magnification M given by (34-14) where m is the lateral magnification produced by the objective, mθ is the angular magnification produced by the eyepiece, s is the tube length, and fob and fey are the focal lengths of the objective and eyepiece, respectively. 3. The refracting telescope, which produces an angular magnification mθ given by (34-15) Copyright © 2014 John Wiley & Sons, Inc. All rights reserved. http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c34/aGFsbGlkYXk5NzgxMTE4MjMwNzI1YzM0LXNlYy0wMDQwLnhmb3Jt.enc?co… 2/2.