11Lec. 7: Ch. 3 - Geometrical Optics1. Virtual images (review)2. Spherical mirrors3. Spherical lenses4. Aberrations of lensesWe are hereSkip 3.3c anamorphic art. We are herehttp://en.wikipedia.org/wiki/Lens_%28optics%292Review: plane mirrors, specular reflection• Equal angle rule• Similar triangles are useful• Ray tracing a mirrorXobject= XimageImage point is on the normal(mirror might need an extension)θrθiNormalMirrorXobjectXimageExtension23Basics: What is an object? What is an image?XobjectXimageExtension=4Basics: What is an object? What is an image?XobjectXimageExtension=In this context, an object is a point that emits light rays in a range of directions:35Why do we make this definition?How does the “eye”know the object is here?and not here?6The eye can sense (to some extent) the angle of incoming raysHow does the “eye”know the object is here?and not here?(Caution: I’m not really talking about depth perception here (wait for Ch. 8), but this is related to one form of depth perception, c.f. accommodation.)The eye effectively traces nearby rays back toward their intersection; it “sees”an image at that intersection.47How does the eye make sense of all those light rays?It’s often easier to think in terms of objects than individual light rays.You are not aware of all those rays, but rather of 3 points of light:8What is an image?XobjectXimageExtension=59What is an image?XobjectXimageExtension=In this context, an image is a point from which light rays emerge in a range of directions: (the image doesn’t necessarily emit or produce the light)10Real vs. Virtual ImagesThe (stationary) eye can’t distinguish between the above cases; the rays entering the eye are exactly the same. But a person could run over and put a piece of paper where the image is and determine whether it’s real or virtual.magic,invisible,ray machineThis is a virtual image. The light rays didn’t actually intersect at (or pass through) the image, but the eye sees the image all the same (the eye is rather amazing).magic,invisible,ray machineThis is a real image. The light rays actually intersect at (or pass through) the image.611Curved MirrorsFirst, a little geometry review:This line segment (from center of circle)......is perpendicular (or normal) to this tangent.12• Ray aimed toward center of sphere comes straight back (specularreflection with normal incidence)• What about other rays?All rays aimed at the center C come straight back out.CRays reflecting from a convex (spherical) mirror713θrθi• Specular reflection• Find where incoming ray hits mirror surface• Find surface normal at that point (along line from center--remember geometry review?)• Angle of incidence = angle of reflection• Reflection (of parallel ray) looks like it’s coming from F -- turns out this is true for all parallel rays.The focus is halfway to the centerCFWhat happens to all rays that come in parallel?14• Easy rule for parallel incoming rays (parallel to the line between F and C): they are reflected as if they came from F.Focal point = focus is behind the surfaceThe focus is halfway to the centerCFWhat happens to all rays that come in parallel?815• Easy rule for rays aimed at focus:• An incoming ray aimed at F gets reflected back parallel (to the C-F axis).Focal point = focus is behind the surfaceThe focus is halfway to the centerCFWhat about rays aimed at the focus?(This is the previous rule, backwards)161. All rays incident parallel to the C-F axis are reflected so that they appear to be coming from the focal point F2. All rays that (when extended) pass through the center C are reflected back on themselves.3. All rays that (when extended) pass through the focal point F are reflected back parallel to the axis2CF13Three easy rules for convex, spherical mirrors917Ray tracing: convex mirrorCFQuestions:• Is the image real or virtual?• Is the image larger or smaller than the object?• Is the image right-side-up or upside-down?18Ray tracing: convex mirrorCFQuestions:• Is the image real or virtual?• Is the image larger or smaller than the object?• Is the image right-side-up or upside-down?• How could a mirror be useful when used like this?1019Ray through the center reflects straight back at its sourceCRays reflecting from concave (cavity) mirrors20• All (incoming parallel) rays reflect and go through the focus, about half way from center to mirrorCFIncoming parallel rays reflect through focusAs usual, this rule works backwards: incoming rays that go through the focus reflect back parallel (to the C-F axis).1121CFRays through focus reflect back parallel to C-F axis.22CFConcave mirrors are very usefullight beam emitter(flashlight)light collectoror solar oven12231. All rays incident parallel to the C-F axis are reflected through the focal point F2. All rays that pass through the center C are reflected back on themselves.3. All rays that pass through the focal point F are reflected back parallel to the axis213CFThree easy rules for concave, spherical mirrors24Ray tracing: concave mirrorobject outside centerCF1325Ray tracing: concave mirrorobject outside centerCFQuestions:• Is the image real or virtual?• Is the image larger or smaller than the object?• Is the image right-side-up or upside-down?• How could a mirror be useful when used like this?26Ray tracing: concave mirrorobject between center and focusCFQuestions:• Is the image real or virtual?• Is the image larger or smaller than the object?• Is the image right-side-up or upside-down?• How could a mirror be useful when used like this?1427Ray tracing: concave mirrorobject between focus and mirrorCF28Ray tracing: concave mirrorobject between focus and mirrorCFQuestions:• Is the image real or virtual?• Is the image larger or smaller than the object?• Is the image right-side-up or upside-down?• How could a mirror be useful when used like this?1529ray tracing applet30• Convex spherical mirror• 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 rulesWe now have many distinct cases1631On 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