1 Mirrors & Lenses 23.1 Flat Mirrors (also called plane ... - Physics

Mirrors & Lenses23.1 Flat Mirrors (also called plane mirrors)An object viewed using a flat mirrorappears to be located behind the mirror,because to the observer the diverging raysfrom the source appear to come frombehind the mirror.The images reflected in flat mirrors have the following properties:The image distance q behind the mirrorequals the object distance p from themirrorThe image height h’ equals the objectheight h so that the lateral magnificationimage heightM !object height = h"h = 1The image has an apparent left-rightreversalThe image is virtual, not real!Real Image – where the light ray actually come to a focus – you can actually see theobject projected on a screen placed at that locationVirtual Image – no light rays actually come directly from a virtual image, they just appearto the eye to do so. (When you see yourself in the mirror, are you actually located behindit as you appear?)To figure out what happens: draw rays, use law of reflection, use geometry1

Example: “I can see myself” – how high must the mirror be for the man to see all ofhimself?23.2 Images Formed by Spherical MirrorsSpherical Mirror:Principle Axis: OCIVCenter of Curvature CRadius of Curvature RLight rays converge to a real image atimage point IWhere is the image formed? What is its height? – Draw two rays: one hitting V and theother passing through C:tan! = h p = " h#q( note sign convention)M = h#h = " q pafter some algebra ( see textbook)1p + 1 q = 2 R2

For p ! "q ! R 2. We give thislocation a special name & designation : thefocal point f = R 2. With this designationwe can re-write the concave sphericalmirror equation as: 1 p + 1 q = 1 fNote, however, that truly spherical mirrorsdo not bring all rays to focus at the samelocation!Spherical Aberration – this is the problemthe Hubble Space Telescope had when firstlaunched.23.3 Convex Mirrors (diverging mirrors) and Sign ConventionsIs the entry for Image location q correct?3

Example: Problem #6A spherical Christmas tree ornament is 6.00 cm in diameter. What is the magnification ofan object placed 10.0 cm away from the ornament?4

Example: Problem #11A 2.00-cm-high object is placed 3.00 cm in front of a concave mirror. If the image is 5.00cm high and virtual, what is the focal length of the mirror?Example: Problem #16A convex spherical mirror with a radius of curvature of 10.0 cm produces a virtual imageone-third the size of the real object. Where is the object?23.5 Atmospheric Refraction (read)23.6 Thin LensesNote: a convex-concave lenses issometimes referred to as a meniscus. It isthe shape used for most eyeglasses.Using the same sign convention for thin lenses:5

M = h!h = " q p1p + 1 q = 1 fSame as for mirrors!(This is the thin lensequation)If you are on a computer with Java installed go here and play with the mirrors & lenses.If it doesn’t fire up after a few seconds, go down to “8” and hit the start button. Theselittle applets will give you a “feel” for what happens. Also try this converging lens anddiverging lens applets. Simpler & prettier (but no mirrors).6

Example: Problem #32A convex lens of focal length 15.0 cm is used as a magnifying glass. At what distancefrom a postage stamp should you hold this lens to get a magnification of +2.00?Example: Problem #36An object’s distance from a converging lens is ten times the focal length. How far is theimage from the focal point? Express the answer as a fraction of the focal length.Multiple LensesThis is more complicated, but straightforward if you follow these rules:1. Do the first lens as if the others weren’t there.2. Use the image formed by this lens as the object of the next lens3. Repeat this process for all the lenses in the system4. The total magnification is just the product of the individual magnifications ofeach lens.See Example 23.9 of the bookExample: Problem #41Two converging lenses, each of focal length 15.0 cm, are placed 40.0 cm apart, and anobject is placed 30.0 cm in front of the first. Where is the final image formed, and what isthe magnification of the system?Microscope: Object very close to F 0 makes a real inverted larger image. This image isthen viewed & magnified further using the eyepiece.7

Telescope: Object near infinity forms a real inverted smaller image near the focal point.Eyepiece is used to magnify this image.The angular magnification (how much bigger it looks) is just m = f of e. To get differentmagnifications, just change eyepieces!Most large telescopes use a concave mirrorinstead of a lens to form the image.8