111Lec. 7: Ch. 2 - Geometrical Optics1. Shadows2. Reflection3. Refraction4. DispersionWe are hereRead Chapter 3, skip 3.3C and skip 3.5DSkip solar power, pp. 104 – 106. 5. Mirages, sun dogs, etc.We only covered the first 44 vugraphs. 22DispersionDispersion: refraction (bending) of different colors by different amounts. Light bulbSpectrum Prism33Index n varies with colorwavelength n (index of refraction)300 nm (UV) 1.486 (bent more)500 nm 1.462700 nm (deep red) 1.455 (bent less)Quartz glass4Prisms demonstrate refraction and dispersion4Reflection at a transparent surface occurs because the n values are different. Only a few percent of the light is reflected this way.55Rainbows: dispersion by water raindrops180 degree rainbow is possible. Double rainbow is possible. Both together is very rare. 66How we see a rainbowbigraindropsSun(behind you)this ray not seenthis ray not seenthese rays are seen7RaindropDispersion occurs here during refraction white lightcomes inReflectionsDispersion occurs here during refraction A spectrum ofcolors comes outPink Floyd is slightly wrong. The colors are spread inside the prism as well as outside. The colors start to spread inside the raindrop. Animated slide88How we see two rainbowssuntwo total internal reflectionstwo total internal reflections91010Waterfall droplets create rainbows1111121212Lec. 7: Ch. 2 - Geometrical Optics1. Shadows2. Reflection3. Refraction4. DispersionWe are here5. Mirages, sun dogs, etc.1313Fogbow(sun behind you) (sun if front of you)22 degrees, center to edgeCircles around the Moon also occur. 141422 degree haloYou only see the purple rays1515Sun pillar and sun dogs1616What is a mirage?A mirage is an image (often upside down) caused by heated air refracting rays. n falls from 1.003 at room temperature to 1.002 when the temperature goes up 100 C.1717Inferior mirage (image below the object)sky appears to be on the groundThe ray bends from the low n material toward the high n material.1818Superior mirage (image above the object)19192020The green flash from dispersion at sunset is rare!Pekka Parvianen212121Lec. 6: Ch. 3 - Geometrical Optics1. Virtual images (review)2. Spherical mirrors3. Spherical lenses4. Aberrations of lensesWe are hereWe are here2222objectvirtual imageVirtual image: (p. 73)The light appears to come from the virtual image, but in fact does not come from there, it comes from a lens or mirror.Real image: (p. 84)The light comes to you from a real image. You may need a screen to see it.a real image:23Mirrors and lenses23We will study these two cases. A positive lens is thicker in the middle. A negative lens is thicker at the edge. 24Mirrors can be plane, convex or concave24Convex traffic safety mirror,similar to anti-shoplifting mirror. Objects may be closer than they appear.25Mirrors can be plane, convex or concave25Concave solar concentrator2626Lec. 7: Ch. 3 - Geometrical Optics26261. Virtual images (review)2. Spherical mirrors3. Spherical lenses4. Aberrations of lensesWe are hereWe are herehttp://en.wikipedia.org/wiki/Lens_%28optics%292727Curved MirrorsFirst, a little geometry review:This line segment (from center of circle)......is perpendicular (or normal) to this tangent.We use a circle to represent a spherical surface.2828• Ray aimed toward center of sphere comes straight back (specular reflection with normal incidence)• What about other rays?All rays aimed at the center C come straight back out.C is also called “center of curvature.”CRays reflecting from a convex (spherical) mirrorRay reflects at the surfaceThis is rule 2.2929θrθi• Specular reflection• Find where incoming ray hits mirror surface• Find surface normal at that point• 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?No light is actually back here3030• 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?This is rule 1.3131• Easy rule 3 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 behind and halfway to the centerRule 3 is rule 1 “backwards.”CFWhat about rays aimed at the focus?(This is the previous rule, backwards)32321. 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 mirrors3333Ray tracing: convex mirrorusing the 3 rules CFQuestions:• Is the image real or virtual?• Is the image larger or smallerthan the object?• Is the image right-side-up or upside-down?Demo with vugraph machine and pensHint: start the rays moving toward the mirror andthese rays must contain the arrow head. 3434Ray 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?objectimage3535Ray through the center reflects straight back at its sourceCRays reflecting from concave (cavity) mirrorsRule 2 applied to concave mirrors3636• All incoming parallel rays reflect and go through the focus, about half way from center to mirrorCFIncoming parallel rays reflect through the focus FAs usual, this rule 1 works backwards: incoming rays that go through the focus reflect back parallel (to the C-F axis) and this is rule 3. .This is rule 1.3737CFRays through focus reflect back parallel to C-F axis.38381. 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 mirrors3939CFConcave mirrors are very usefullight beam emitter(flashlight)light collectoror solar oven4040Ray tracing: concave mirror object outside centerCFDemo with vugraph machine and pensHint: start the rays