Optics IntroReflectionReflection, continuedHall MirrorCurved mirrorsRefractionRefraction at a plane surfaceDriving AnalogyTotal Internal ReflectionRefraction in SuburbiaEven gets Total Internal Reflection RightReflections, Refractive offsetLet’s get focused…Cameras, in briefPositive LensesNegative LensesRaytracing made easierThin Lens BenefitsUsing the focus conditionTracing an arbitrary ray (positive lens)Tracing an arbitrary ray (negative lens)Image FormationNotes on Image FormationVirtual ImagesThe lens-maker’s formulaDeriving Gaussian Formula from RaysLenses map directions into displacementsTelescopeReflector/Refractor AnalogyParabolic ExampleCassegrain TelescopeCassegrain focusf-numbersf-numbers, comparedPupilsPupils within PupilsVignettingInfrared Cold StopRaytrace SimulationsAberrations: the real worldSpherical AberrationComaChromatic AberrationOptical Alignment TechniquesZemax ExamplesLab 4: RaytracingRaytracing AlgorithmReferences and AssignmentsOptics IntroOptics IntroGeometric OpticsGeometric OpticsRaytracingRaytracingWinter 2012UCSD: Physics 121; 20122ReflectionReflection•We describe the path of light as straight-line raysWe describe the path of light as straight-line rays–“geometrical optics” approach•Reflection off a flat surface follows a simple rule:Reflection off a flat surface follows a simple rule:–angle in (incidence) equals angle out–angles measured from surface “normal” (perpendicular)surface normalsameangleincident rayexit rayWinter 2012UCSD: Physics 121; 20123Reflection, continuedReflection, continued•Also consistent with “Also consistent with “principle of least timeprinciple of least time””–If going from point A to point B, reflecting off a mirror, the path traveled is also the most expedient (shortest) routeABtoo longshortest path;equal anglesWinter 2012UCSD: Physics 121; 20124Hall MirrorHall Mirror•Useful to think in terms of Useful to think in terms of imagesimages“image” you“real” youmirror onlyneeds to be half ashigh as you are tall. Yourimage will be twice as far from youas the mirror.Winter 2012UCSD: Physics 121; 20125Curved mirrorsCurved mirrors•What if the mirror isn’t flat?What if the mirror isn’t flat?–light still follows the same rules, with local surface normal•Parabolic mirrors have exact focusParabolic mirrors have exact focus–used in telescopes, backyard satellite dishes, etc.–also forms virtual imageWinter 2012UCSD: Physics 121; 20126RefractionRefraction•Light also goes Light also goes throughthrough some things some things–glass, water, eyeball, air•The presence of material slows light’s progressThe presence of material slows light’s progress–interactions with electrical properties of atoms•The “light slowing factor” is called the The “light slowing factor” is called the index of refractionindex of refraction–glass has n = 1.52, meaning that light travels about 1.5 times slower in glass than in vacuum–water has n = 1.33–air has n = 1.00028–vacuum is n = 1.00000 (speed of light at full capacity)Winter 2012UCSD: Physics 121; 20127n2 = 1.5n1 = 1.0ABRefraction at a plane surfaceRefraction at a plane surface•Light bends at interface between refractive indicesLight bends at interface between refractive indices–bends more the larger the difference in refractive index–can be effectively viewed as a “least time” behavior•get from A to B faster if you spend less time in the slow medium12Snell’s Law:n1sin1 = n2sin2Winter 2012UCSD: Physics 121; 20128Driving AnalogyDriving Analogy•Let’s say your house is 12 furlongs off the Let’s say your house is 12 furlongs off the roadroad in the in the middle of a huge field of middle of a huge field of dirtdirt–you can travel 5 furlongs per minute on the road, but only 3 furlongs per minute on the dirt•this means “refractive index” of the dirt is 5/3 = 1.667–Starting from point A, you want to find the quickest route:•straight across (AD)—don’t mess with the road•right-angle turnoff (ACD)—stay on road as long as possible•angled turnoff (ABD)—compromise between the twoA B CD (house)leg dist. t@5 t@3AB 5 1 —AC 16 3.2 —AD 20 — 6.67BD 15 — 5CD 12 — 4roaddirtAD: 6.67 minutesABD: 6.0 minutes: the optimal path is a “refracted” oneACD: 7.2 minutesNote: both right triangles in figure are 3-4-5Winter 2012UCSD: Physics 121; 20129Total Internal ReflectionTotal Internal Reflection•At critical angle, refraction no longer occursAt critical angle, refraction no longer occurs–thereafter, you get total internal reflectionn2sin2 = n1sin1  crit = sin1(n1/n2)–for glass, the critical internal angle is 42°–for water, it’s 49°–a ray within the higher index medium cannot escape at shallower angles (look at sky from underwater…)n2 = 1.5n1 = 1.042°incoming ray hugs surfaceWinter 2012UCSD: Physics 121; 201210Refraction in SuburbiaRefraction in Suburbia•Think of refraction as a pair of wheels on an axle Think of refraction as a pair of wheels on an axle going from sidewalk onto grassgoing from sidewalk onto grass–wheel moves slower in grass, so the direction changesNote that the wheelsmove faster (bigger space)on the sidewalk, slower(closer) in the grassWinter 2012UCSD: Physics 121; 201211Even gets Total Internal Reflection RightEven gets Total Internal Reflection Right•Moreover, this analogy is Moreover, this analogy is mathematically equivalentmathematically equivalent to the actual refraction phenomenonto the actual refraction phenomenon–can recover Snell’s law: n1sin1 = n2sin2Wheel that hits sidewalk starts to go faster,which turns the axle, until the upper wheel re-enters the grass and goes straight againWinter 2012UCSD: Physics 121; 201212n1 = 1.5 n2 = 1.0Reflections, Refractive offsetReflections, Refractive offset•Let’s consider a thick piece of glass (Let’s consider a thick piece of glass (nn = 1.5), and the = 1.5), and the light paths associated with itlight paths associated with it–reflection fraction = [(n1 – n2)/(n1 + n2)]2–using n1 = 1.5, n2 = 1.0 (air), R = (0.5/2.5)2 = 0.04 = 4%incoming ray(100%)96%92% transmitted0.16%4%4%8% reflected in tworeflections (front & back)image looks displaceddue to jogWinter 2012UCSD: Physics 121; 201213Let’s get focused…Let’s get focused…•Just as with mirrors, curved lenses follow same rules Just as with mirrors, curved lenses follow same rules as flat