111Lec. 8: Ch. 3 - Geometrical Optics1. Virtual images (review)2. Spherical mirrors3. Spherical lenses4. Aberrations of lensesWe are hereHomework is due Tuesday next week. Next week: Concept questions Tues. and Thurs. Next Thursday: Exam review Tuesday, Sept. 28: Exam 1 Read: Ch. 4.1 and 4.2. We covered about 31 of these viewgraphs.Web 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• http://micro.magnet.fsu.edu/primer/java/mirrors/convex.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.html2223• Convex spherical mirror object outside only• Concave spherical mirror, object outside center• Concave spherical mirror, object between center and focus• Concave spherical mirror, object between focus and mirrorFor each case, you can now answer: Image larger? Virtual? Where? What good is it?AND you can answer these question by ray tracing with three simple rulesReview: We now have several distinct cases for mirror ray tracing4On to lenses: first, review refractionairn=1 (nearly)v = c (nearly)glass, e.g.n=1.5v = c/n < cRays bend toward normal when entering slower medium (larger n),away from normal when entering faster medium (smaller n).35Soldiers in mud analogy (challenge: where does this analogy break down?)pavement(soldiers go fast)deep mud (soldiers march slower through deep mud)“fronts”“rays” (perpendicular to fronts)As soldiers slow down, space between them narrowsA trick to remember which way rays bend6Ray tracing with lensesn>1Rays entering “slower” material bend toward normalRays entering “faster” material bend away from normaln=1Brute force ray tracing:1. As long as ray stays in same medium, it goes straight.2. At each interface to a different medium, use Snell’s law to calculate how it will bend. Go back to 1.This gets tedious!47FFThin convex (converging) lensfocifocal length81) A ray parallel to the axis is deflected through the focus on the other side2) A ray through the center of the lens continues undeviated3) A ray coming from the focus on one side goes out parallel to the axis on the otherF’FThe ray might have to be extended to find the image1233Thin convex lens: three easy rules for ray tracingfocifocal length12359Note light-focusing property of convex (converging) lensa good light collector or solar oven; can also fry ants with sunlight, but please don’t do that unless you’re going to eat them10Note light-dispersing property of convex lensThe “backwards” light collector:create a collimated light beam611Ray Tracingfoci (focuses?)Where will this ray go?12Ray TracingWhere will this ray go?Suppose it’s emitted from this objectfoci (focuses?)713Ray TracingWhere will this ray go?Suppose it’s emitted from this objectfoci (focuses?)We know where these 3 rays go, using the simple ray rules14Ray TracingWe know where these 3 rays go, using the simple ray rulesAmazing property of this lens: all rays from the tip of the object will converge to the same point815Ray TracingWhere will this ray go?Suppose it’s emitted from this objectWe know where these 3 rays go, using the simple ray rulesAmazing property of this lens: all rays from the object will converge to the same point16F’FFor diverging lens focal length defined to be negative (of the distance between focus and lens)Thin concave (diverging) lensGuess how this ray will be bent:917F’FFor diverging lens focal length defined to be negativeThin concave (diverging) lens181) A ray parallel to the axis is deflected as if it came from the focus2) A ray through the center of the lens continues undeviated3) A ray aimed at the focus on the other side comes out parallelF’FRay might have to be extended123For diverging lens focal length defined to be negativeThin concave (diverging) lens: three easy ray rules1019F’F1Difference between convex (converging) and concave (diverging) lensesF’F1(Rule 3, the backwards version of rule 1, also differs)20Ray tracing a convex lens: object inside focus1121Ray tracing a convex lens: object inside focusThe image appears larger (and farther away) than the object.This is a magnifying glass. {Demo}(Remember: a magnifying glass is a convex lens.)Aside: near-sighted people need concave/diverging lenses; can a marooned myopic start a fire with his eye-glasses?Web 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• http://micro.magnet.fsu.edu/primer/java/mirrors/convex.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.html2222Can demo some of these in lecture if there is time.1223Lec. 8: Ch. 3 - Geometrical Optics1. Virtual images2. Spherical mirrors, ray tracing3. Spherical lenses, ray tracingThin lens approximation3 formulas4. Aberrations of lensesWe are here23Some 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 or focal length:the distance from the mirror (or lens) to the focal point (a length), usually you are told what it is. This is a property of the lens.• Paraxial ray:a ray of light coming into the mirror parallel to the axis (a line)2413Thin lens approximationLight is refracted at the two glass-air surfaces but we pretend that there is