1Lec. 8: Ch. 3 - Geometrical Optics1. Virtual images2. Spherical mirrors, ray tracing3. Spherical lenses, ray tracingThin lens approximation3 formulas4. Aberrations of lensesWe did this1Preview:Tue., Feb. 9, Ch. 4, Camera, clicker questionsThurs., Feb. 11, Exam review, HW 4 dueTue., Feb. 16, Exam in classThurs., Feb 18, no HW dueReview ray tracing: convex and concave mirrorsConvex mirror: Concave mirror:(alternatively, arrow could be closer to mirror than F) Demo: blackboard optics3 rays:1. Start parallel to axis, thenbends thru an F2. Thru C, no bend3. Starts bent thru an F,becomes parallel 2Review ray tracing: convex and concave lensesConvex lens as a magnifier:(alternatively, could be a projection lens) Concave lens:(demagnifier) Demo: lenses and vugraf projector3 rays:1. Start parallel to axis, then bends thru an F2. Thru the middle, no bend3. Starts bent thru an F, becomes parallel 3Review: Ray tracings (1 to 4)4Review: Ray tracings (5 and 6) 5Review: Rules for mirror ray tracing• Rule 1 for mirrors: All incident rays parallel to the axis are reflected so that they appear to have come from the focal point F.• We also see that a ray coming in along a radius will have a zeroangle with the normal (it IS a normal), so its reflected back on itself.• Rule 2 for mirrors: Incident rays coming toward the center of curvature, C, are reflected back onto themselves.• Notice that if I turn the reflected ray around, so that it is an incoming ray, it goes out parallel to the axis (turn around the paraxial ray so it goes out). Let’s call this rule 3:• Rule 3 for mirrors: Incident rays headed for F are reflected so that they are parallel to the axis. This is simply rule 1 with the rays turned around so the outgoing ray is the incoming ray and vice versa.6Review: Rules for ray tracing lenses• Rule 1. A ray parallel to the axis is deflected through F' (or as though it came from F'). Hint: In either case, the point F' will be on the ruler edge.• Rule 2. A ray through the center of the lens is not bent.• Rule 3. A ray from F (extension may be necessary) is deflected parallel to the axis.Rule 3 is rule 1 with a reversed path, just like for mirrors. You may have to extend the edge of the lens or the rays to apply the rules. 78Lec. 8: Ch. 3 - Geometrical Optics1. Virtual images2. Spherical mirrors, ray tracing3. Spherical lenses, ray tracingThin lens approximation3 formulas4. Aberrations of lensesWe are here8Some definitions• Radius of curvature (for a curved mirror):the radius of the sphere the mirror is "cut from," (a distance).• Center of curvature for a mirror, C:the center of the sphere mentioned above (a place).• Focal point, F:the point or points where rays appear to converge (a place)• Focal distance:the distance from the mirror (or lens) to the focal point (a length)• Paraxial ray:a ray of light coming into the mirror parallel to the axis (a line)9Thin lens approximationLight is refracted at the two glass-air surfaces but we pretend that there is one bend at the midplane of the lens.Distances XOand XIare measured from the midplane.10Object distance, image distance, focal length11XiXoF1212Lec. 8: Ch. 3 - Geometrical Optics1. Virtual images (review)2. Spherical mirrors3. Spherical lensesThin lens approximationFormulasMagnificationAdding lensesImage distance4. Aberrations of lensesWe are here12Magnification formulaS0= object height Si= image heightNote the similar triangles. 13Distances below the horizontal axis are defined as negative.Demo: big mama lens and bulbImage distance equationFXXIO111=+F = focal lengthXO= object distanceXI= image distanceUsually, F is given.OIXFX111−=14Distant objects: Let Xobe very large, say 1,000,000 meters. Then 1/Xo= 0.000001, which is very small. You can ignore it. Then FXI11≅For distant objects, the image is at the focal point(ask a burnt ant)Demo: find focal length of lensesWhat is lens power (or diopters)?Lens power: D = 1/FUnits of D are 1/meters, also called dioptersEyeglass lenses are measured in diopters. Example: D = 2/m = what focal length?F = 1/D = 1/(2/m) = (1/2) m = 0.5 m How thin lenses addFtot= final focal lengthF1= focal length lens 1F2= focal length lens 2Diverging lenses (concave) have negative focal lengthsThis is the same as adding powers: Dtot= D1+ D216Demo: put together some lensesCompound Lenses• Can have less aberration.• A modern lens can have 16 elements and can “zoom”. 17“stop”Reduces aberrationImage planeFresnel LensUsed in lighthouses 18Fresnel stage lightLighthouse lens19http://sandiartfullyyours.com/NewFiles/lighthouse3/images/Ponce%20Fresnell.jpgConcave mirror gadgets20Auto headlightSolar cooker2121Lec. 8: Ch. 3 - Geometrical Optics1. Virtual images (review)2. Spherical mirrors3. Spherical lenses3 formulas4. Aberrations of lensesWe are here21Aberrations• Field curvature• Off-axis aberration• Spherical aberration• Distortion• Chromatic aberration22Aberration: field curvature23Image does not lie in one planeOff axis aberrationEdges of images are less clear. 24Demo with lens and bulbSpherical aberrationRays at the edge focus closer to the mirror25Demo with lens, not mirrorAberrations: Distortion26Demo with overhead and small lensesChromatic Aberration27Demo with lens and bulbWeb tutorials with Java Applets• Useful web links on curved mirrors• http://micro.magnet.fsu.edu/primer/java/mirrors/concavemirrors/index.html• http://micro.magnet.fsu.edu/primer/java/mirrors/convexmirrors/index.html• http://micro.magnet.fsu.edu/primer/java/mirrors/concave.html• Useful web links on lenses• http://micro.magnet.fsu.edu/primer/lightandcolor/lenseshome.html• http://micro.magnet.fsu.edu/primer/java/lenses/simplethinlens/index.html• http://micro.magnet.fsu.edu/primer/java/lenses/converginglenses/index.html• http://micro.magnet.fsu.edu/primer/java/lenses/diverginglenses/index.html• http://micro.magnet.fsu.edu/primer/java/components/perfectlens/index.html•