ERHS PHYSICS Chapter 18.2 Notes: LIGHT
Notes: Chapter 18.2 Lenses Types of lenses Convex lenses Thicker at the center than at the edges. • These are converging lenses. • We consider lenses we study here to be thin lenses, in which case all refractions occur on a plane, called the principal plane, that passes through the center of the lens. • Convex lenses can form real images • Have a positive focal length Converging lenses follow these three rules of refraction: • Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens • Any incident ray traveling through a focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. • An incident ray which passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens. Concave lenses Thinner at the center than at the edges. • These are diverging lenses. • Concave lenses form ONLY virtual images • Have a negative focal length Diverging lenses follow these three rules of refraction: • Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel away from the focal point on the same side of the lens • Any incident ray traveling toward a focal point on the opposite side of the lens will refract through the lens and travel parallel to the principal axis. • An incident ray which passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens. Definitions and Concepts Lenses have curved surfaces, or a very large number of flat surfaces located at slightly different angles. (i.e., Fresnel lens) Converging lenses (positive lenses) are thicker at the center than at the edges. Diverging lenses (negative lenses) are thicker at the edges than at the center. (Only thin, single lenses are dealt with in this course. Note as well that the terms concave and convex, as applied to lenses, can be misleading. A meniscus lens has both a concave and a convex surface, but the thickness at the centre compared with the edges determines if it behaves as a converging or a diverging lens.) The optical center of the lens is located at its geometric centre. The principal axis is a construction line drawn perpendicular to the lens, through the optical centre. Rays parallel to the principal axis will converge when passing through a converging lens, and diverge when passing through a diverging lens. The principal focus (F) is a point on the principal axis where light comes to a focus (for a converging lens) or appears to be diverging from (for a diverging lens). Two foci exist, equidistant on either side of the lens, since light behaves the same way when travelling in either direction (Principle of Reversibility). The two foci, F and F' are called the primary principal focus and the secondary principal focus, respectively. F, sometimes also referred to as the primary focal point, is shown on the right side of a converging lens, and on the left side of a diverging lens, while F', the secondary focal point is shown on the opposite side of each respective lens.) Ray diagrams are used to show rays passing through a lens. Ray diagrams can be useful in determining the characteristics of an image formed by a lens. By convention, incident rays are shown travelling from left to right on ray diagrams. A dotted line is usually drawn through the lens at the optical center, perpendicular to the principal axis. Ray diagrams should always be drawn and labelled neatly, accurately, and to some appropriate scale. The focal length is the distance between the principal focus and the optical centre of the lens. The focal plane is an imaginary plane perpendicular to the principal axis at the focal point. Parallel rays will converge through a converging lens somewhere on the focal plane. Incident light rays are refracted twice by a lens; once at each boundary. Partial reflection may also occur. (In optical systems, partial reflection is undesirable. It can be minimized by using optical lens coatings. Coated lenses provide superior image quality.) To simplify matters on ray diagrams, incident rays can be shown to refract at the construction line passing through the optical centre of the lens. For a thin lens this leads to a reasonably close approximation because the lateral displacement is quite small. Light rays that have travelled over a large distance are effectively parallel. Lenses can form either real or virtual images. The rules for drawing ray diagrams for converging and diverging lenses can be used to determine the characteristics of an image formed by a lens. Lens equations can be used to determine the characteristics of an image. Refer to page 381 for lens equations. A diverging lens always forms an erect, virtual image which is diminished in size. It is located closer to the lens than the object, between the principal focal point and the lens. To correct for spherical aberration in lenses, achromatic lenses can be used. (Spherical aberration in lenses can be corrected by using aspheric lenses, or by using thin lens combinations which cancel out aberrations. Achromatic lenses, designed to correct for chromatic aberration at some wavelengths, can also help to reduce spherical aberration.) Lens defects are called aberrations. They hinder the quality of the image formed in an optical system. Lenses are used in many different kinds of practical applications. (Several should be studied.) An optical system may use a combination of mirrors, lenses, prisms, and other kinds of optical devices. An image formed by one component in an optical system can serve as an object for a different component. The image characteristics formed by converging lenses depend on the location of the object. This table summarizes the characteristics of images found in a converging mirror based onthe location of the object. Image Characteristics Object location Magnification Attitude Type Position near infinity 0 inverted real at F beyond 2F > -1 inverted real between F & 2F at 2F -1 inverted real at 2F between 2F and F < -1 inverted real beyond 2F between F and O > +1 erect virtual same side as object at F undefined       Rules for Drawing Ray Diagrams for Converging and Diverging Lenses (Parenthetical remarks refer specifically to diverging lenses) An incident ray that is parallel to the principal axis is refracted such that it passes through (or appears to have originated from) the principal focus (F). An incident ray passing through (or heading toward) the secondary principal focus (F') is refracted such that it travels parallel to the principal axis. An incident ray passing through the optical centre of the lens continues to travel in a straight line. Images formed by a converging lens     Characteristics of the Image a) Distant object Real Inverted Smaller than object At F b) Object at 2F Real Inverted Same size At 2F c) Object between 2F ans F Real Inverted Larger than object Beyond 2F d) Object at F No image Refracted rays are parallel e) Object between F and lens Virtual Erect Larger than object Behind the object on the same side of the lens Image formed by a diverging lens e) Object at F Characteristics of the image regardless of object postion Virtual Erect Smaller than object Between object and lens Glossary of Terms Interactive simulation of ray diagrams Homework: Set#3: chapter 18, questions 10-12, problems 35-39 Activities: use the Ray Box and Optics kit to study the properties of both converging and diverging lenses.