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Unformatted text preview: Image formation 4.3 • Images –real im age –virtual im age ObjectImage • A physical object is usually obser ved by reflected light that diverges from the object. • An optical system (m irrors or lenses) can produce an image of the object by redirecting the light. – Real Image – Virtual Image • Image formation by mirrors, ray tracing –plane m irror –convex m irror –concave m irror •Mirror equation Real Image diver gi ng convergi ng diver gi ng diver gi ng Virtual Image Optica l Syste m div er g ing Objec t Optica l Syste m real Ima ge Objec t virtua l Image Light passes through the real im age Film at the position of the real im age is exposed. Light does not pass through the virtual im age Film at the position of the virtual im age is not exposed. Image formed by a plane mirror. Each point on the im age can be determ ined by tracing 2 rays from the object. O l l ‘ O’ objec t ima ge P P’ mirror Ray trac ing – Trace the light rays comi ng from the o bjec t ref lec ting of f the mirror (angle of i ncidence e qua l the a ngle of ref lec tion) The reflec ted rays appear to come from a virt ual ima ge. A virt ua l i mage is formed by a pla ne mirror at a dista nce l ’ be hi nd the mirror. l ‘ = l 1 A mirror reverses front and back Parabolic Mirrors The z direction is revers ed i n the mirror ima ge. The direction of rotatio n of a spi nning to p is revers ed. Yo ur ri ght hand is the mirror i mage of yo ur lef t hand. Paralle l rays reflec ted by a parabo lic mirror are foc used at a poi nt, ca lled the Focal Poi nt Parabolic Reflector Spherical mirrors • Spherical mirrors can be used ot form im ages • Spherical mirrors are m uch easi er to fabric ate than parabolic m irrors • A spherical m irror is an approxim ation of a parabolic mirror for sm all curvatures. (i.e. for paraxi al rays –close to parall el to the optic axis. • Spherical mirrors can be convex or concave Parabolic mirrors can be used to foc us i ncomi ng paralle l rays to a s ma ll area or to direct rays diverging from a s ma ll area into paralle l rays. Ray tracing with spherical mirrors 1. 2. 3. 4. A ray parallel to the mirror axis reflects through the focal point, F. A ray passing through the focal point reflects parallel to the mirror axis A ray striking the center of the mirror reflects symmetrically around the mirror axis A ray that passes through the center of curvature C reflects and passes back through itself The position of the image can be determined from two rays from the object. • Mirror axi s C C • F • F • W hen object distance > C, F The im age is real, invert ed, reduced Conc ave Mirror 2 Images formed by a concave mirror Concave mirrors Sim ulation of im age form ation with concave m irrors http://micro.magnet.fsu.edu/primer/java/scienceopticsu/mirrors/concave.html O > C Real Invert ed Reduc ed C > O > F Real Invert ed Enlarged F > O Virtual Upright Enlarged Question What im age of yourself do you see when you m ove toward a concave m irror? 3 Convex Mirror Convex Mirror • • • virtual, upright, reduc ed • Im age is virtual, upright, reduced virtual, upright, reduc ed Convex mirror Sim ulation of im age form ation with convex m irrors http://micro.ma gnet.fsu.e du/pri mer/java/scienceopticsu/mirrors/convex.ht ml Question Describe how your image would appear as you approach a convex m irror? 4 Mirror Equation
ℓ O • f I 1 1 1 += l l ' f ℓ’ f is positive if the light from infinity goes through the focal point. f positive for concave mirrors, f negative for convex mirrors The image distance ℓ’ is positive if the light goes through the image ℓ’ positive real image ℓ’ negative – virtual image Mirror equation. Special cases 1 1 1 += l l ' f
W hen f > 0
concave m irror Magnification ℓ O h h’ l = in f inity l ' = f l ' = 2f • f I ℓ’ Real Image h ' l ' =h l l = 2f l = f M = l ' = inf inity M is negative if the image is inverted. 5 Question A boy stands 2.0 m in front of a conc ave m irror with a foc al length of 0.50 m. Find the position of the im age. Find the m agnification. Is the im age upright or inverted? Question At what two distances could you place an object from a 10 cm focal l ength concave m irror in order to get an im age 2 tim es the size of the object? Question W hen viewed from the earth the m oon subt ends an angl e of 0.5 degrees. How large an im age of the m oon will be form ed by the 3.6 m diam eter Haw aiian tel escope which has a foc al length of 8.5 m. 6 ...
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