mirrors and lensesan important pointwe saw…the flat mirrorquestionray diagramsconcave mirrorsconcave mirrors: an object outside Fexampleexampledemo: the virtual pigexampleconvex mirrors with p < |f|Mirrors: an overviewlon-capaLenseslensmakers equationexampleexample 2example 3questionconverging lens p>flens equationexampleexamplequestionlenses, an overviewspherical aberrations: Hubble space telescope chromatic aberrationstwo lensesmirrors and lensesPHY232Remco [email protected] W109 – cyclotron buildinghttp://www.nscl.msu.edu/~zegers/phy232.htmlPHY232 - Remco Zegers - Mirrors and lenses 2an important point¾ objects do not emit rays of light that get ‘seen’ by your eye. Light (from a bulb or the sun) gets reflected off the object towards your eye.PHY232 - Remco Zegers - Mirrors and lenses 3we saw…¾ that light can be reflected or refracted at boundaries between material with a different index of refraction.¾ by shaping the surfaces of the boundaries we can make devices that can focus or otherwise alter an image.¾ Here we focus on mirrors and lenses for which the properties can be described well by a few equations.PHY232 - Remco Zegers - Mirrors and lenses 4the flat mirror¾ in the previous chapter we already saw flat mirrors.¾ The distance from the object to the mirror the object distance p¾ The distance from the image to the mirror is the image distance q¾ in case of a flat mirror, an observer sees a virtual image, meaning that the rays do not actually come from it.¾ the image size (h’ ) is the same as the object size (h), meaning that the magnification h’/h=1¾ the image is not invertedp qNOTE: a virtual imagecannot be projected on a screen but is ‘visible’ bythe eye or another opticalinstrument.PHY232 - Remco Zegers - Mirrors and lenses 5question¾ You are standing in front (say 1 m) of a mirror that is less high than your height. Is there a chance that you can still see your complete image?¾ a) yes b) noPHY232 - Remco Zegers - Mirrors and lenses 6ray diagrams¾ to understand the properties of optical elements we use ray diagrams, in which we draw the most important elements and parameters to understand the elementspqhh’PHY232 - Remco Zegers - Mirrors and lenses 7concave mirrorsCC: center of mirror curvaturea light ray passing through the center of curvature will be reflected back upon itself because it strikes the mirror normally to the surface.F: focal pointFa light ray traveling parallel to the central axis of the mirrorwill be reflected to the focal point F, with FM=CM/2The distance FM is called the focal length f.MPHY232 - Remco Zegers - Mirrors and lenses 8concave mirrors: an object outside FOFstep 1: draw the ray from the top of the object parallel to the central axis and its reflection (through F).step 2: draw the ray from the top of the object through F and itsreflection (parallel to the central axis)step 3: note that a ray from the bottom of the object just reflects back.the image of the top of the object is located where the reflected rays meetconstruct the image IIPHY232 - Remco Zegers - Mirrors and lenses 9concave mirrors: an object outside FOFIThe image is:a) inverted (upside down)b) real (light rays pass through it)c) smaller than the objectPHY232 - Remco Zegers - Mirrors and lenses 10concave mirrors: an object outside FOFIdistance object-mirror: pdistance image-mirror: qdistance focal point-mirror: fmirror equation: 1/p + 1/q = 1/fgiven p,f this equation can be used to calculate qmagnification: M=-q/pcan be used to calculate magnification.• if negative: the image is inverted• if smaller than 1, object is demagnifiedPHY232 - Remco Zegers - Mirrors and lenses 11example¾ An object is placed 12 cm in front of a a concave mirror with focal length 5 cm. What are: ¾ a) the location of the image¾ b) the magnificationPHY232 - Remco Zegers - Mirrors and lenses 12concave mirrors: an object inside FOFstep 1: draw the ray from the top of the object parallel to the central axis and its reflection (through F).step 3: note that a ray from the bottom of the object just reflects back.step 2: draw the ray from the top of the object through F and itsreflection (parallel to the central axis)Ithe image of the top of the object is located where the reflected rays meet: in this you must draw virtual rays on the other side of the lenscreate the imagethe image is:a) not invertedb) virtualc) magnifiedPHY232 - Remco Zegers - Mirrors and lenses 13concave mirrors: an object inside FOF Ithe image is:a) not invertedb) virtualc) magnifiedThe lens equation and equation for magnification are stillvalid. However, since the image is now on the otherside of the mirror, its sign should be negativePHY232 - Remco Zegers - Mirrors and lenses 14example¾ an object is placed 2 cm in front of a lens with a focal length of 5 cm. What are the a) image distance and b) the magnification?PHY232 - Remco Zegers - Mirrors and lenses 15demo: the virtual pigPHY232 - Remco Zegers - Mirrors and lenses 16step 2: draw the ray from the top of the object through F and itsreflection (parallel to the central axis)convex mirrors: an object outside F (p>|f|)OFstep 3: note that a ray from the bottom of the object just reflects back.the image of the top of the object is located where the reflected rays meetconstruct the image IIstep 1: draw the ray from the top of the object parallel to the central axis and its reflection (through F).F is now located on the otherside of the mirrorPHY232 - Remco Zegers - Mirrors and lenses 17convex mirrors: an object outside F (p>|f|)OFIF is now located on the otherside of the mirrorthe image is:a) not invertedb) virtualc) demagnifiedThe lens/mirror equation and equation for magnification are still valid. However, since the image and focal point are now on the other side of the mirror, their signs should be negativePHY232 - Remco Zegers - Mirrors and lenses 18example¾ an object with a height of 3 cm is placed 6 cm in front of a convex mirror, with f=-3 cm. What are a) the image distance and b) the magnification?PHY232 - Remco Zegers - Mirrors and lenses 19convex mirrors with p < |f|¾ the situation is exactly the same as for the situation with p > |f|. The demagnification will be different though…OFIFPHY232 - Remco Zegers - Mirrors and lenses 20Mirrors: an overview¾ mirror equation 1/p + 1/q = 1/f ¾ f=R/2 where R is the radius of the mirror¾ magnification: M=-q/p type p? image image directionMqf+
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