PowerPoint PresentationSlide 2Slide 3Slide 4Law of ReflectionDrawing NormalsFermat’s PrincipleTwo light rays 1 and 2 taking different paths between points A and B and reflecting off a vertical mirrorSlide 9Slide 10Slide 11JAVA APPLETWhat allows you to see various colors when white light passes through a prismHow does a Rainbow work?Dispersion: Different wavelengths have different velocities and therefore different indices of refraction. This leads to different refractive angles for different wavelengths. Thus the light is dispersed. The frequency dose not change when n changes.Why is light totally reflected inside a fiber optics cable? Internal reflectionFiber CableCorner Reflector?Show Total Internal reflection simulatorSlide 20Inverse Mirage BendSlide 23Polarization by Reflection Brewsters LawPlane Mirrors Where is the image formedPlane mirrorsSlide 27Slide 28Slide 29Slide 30Rules for drawing images for mirrorsSlide 32Concept Simulator/IllustrationsSpherical refracting surfacesApply this equation to Thin Lenses where the thickness is small compared to object distance, image distance, and radius of curvature. Neglect thickness.Slide 36Sign ConventionRules for drawing rays to locate images from a lensExample of drawing images24(b). Given a lens with a focal length f = 5 cm and object distance p = +10 cm, find the following: i and m. Is the image real or virtual? Upright or inverted? Draw 3 rays.Slide 41Slide 42Slide 43Slide 44Optical InstrumentsLecture 14 Images Chapter 34•Law of Reflection•Dispersion•Snell’s Law•Brewsters AnglePreliminary topics before mirrors and lenses•Law of Reflection•Dispersion•Snell’s Law•Brewsters AngleGeometrical Optics:Study of reflection and refraction of light from surfacesThe ray approximation states that light travels in straight linesuntil it is reflected or refracted and then travels in straight lines again.The wavelength of light must be small compared to the size ofthe objects or else diffractive effects occur.Law of Reflection1ABθI= θRθiθrMirrorDrawing NormalsFermat’s PrincipleUsing Fermat’s Principle you can prove theReflection law. It states that the path taken by light when traveling from one point to another is the path that takes the shortesttime compared to nearby paths.Two light rays 1 and 2 taking different paths between points A and B and reflecting off a vertical mirror12ABPlane Mirror Use calculus - method of minimizationt =1C( h12+y2+ h22+(w−y)2)dtdy=2yh12+y2+−2(w−y)h22+(w−y)2)=0yh12+y2=(w−y)h22+(w−y)2)sinθI = sinθRθI= θRWrite down time as a function of yand set the derivative to 0.Law of Refraction: Snells Law € n1sinθ1= n2sinθ2n1n2How do we prove it?1v1sinθ1=1v2sinθ2Air 1.0Glass 1.33t =(1v1h12+y2+1v2h22+(w−y)2)dtdy=01v1sinθI= 1v2sinθRn1sinθI=n2 sinθRJAVA APPLETShow Fermat’s principle simulatorWhat allows you to see various colors when white light passes through a prismDispersionHow does a Rainbow work?Dispersion: Different wavelengths have different velocities and therefore different indices of refraction. This leads to differentrefractive angles for different wavelengths. Thus the light is dispersed.The frequency dose not change when n changes.v =fλλ changes when medium changesf does not change when medium changesWhy is light totally reflected inside a fiber optics cable? Internal reflection€ n1sinθ1= n2sinθ2€ (1.33)sinθ1= (1.00)sin90 =1.00When θ1≥sin−111.33≥48.75 deglight won't get out of the materialFiber CableSame hereCorner Reflector?Show Total Internal reflection simulatorHalliday, Resnick, Walker: Fundamentals of Physics, 7th Edition - Student Companion SiteWhat causes a Mirage1.061.091.081.071.071.081.09skyeyeHot road causes gradient in the index of refraction that increasesas you increase the distance from the roadIndex of refractionInverse Mirage Bend47. In the figure, a 2.00-m-long vertical pole extends from the bottom of a swimming pool to a point 50.0 cm above the water. What is the length of the shadow of the pole on the level bottom of the pool?Consider a ray that grazes the top of the pole, as shown in the diagram below. Here 1 = 35o, l1 = 0.50 m, and l2 = 1.50 m.21l2l1L xairwatershadowx is given by x = l1tan1 = (0.50m)tan35o = 0.35 m.The length of the shadow is x + L.L is given byL=l2tan 2Use Snells Law to find  Snells Law ExampleAccording to the law of refraction, n2sin2 = n1sin1. We take n1 = 1 and n2 = 1.33oon55.2533.135sinsinsinsin12112=⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛=−−θθL is given by.72.055.25tan)50.1(tan22mmlLo=== θThe length of the shadow is L+x.L+x = 0.35m + 0.72 m = 1.07 m.21l2l1L xairwatershadowCalculation of LPolarization by Reflection Brewsters Law(1.)sinθB=nsinθrθB+θr=90 we get 100% polarized reflected wavesin θB=nsin(90−θB) =ncosθBθB=tan−1n Brewsters LawPlane Mirrors Where is the image formedMirrors and LensesPlane mirrorsNormalAngle ofincidenceAngle of reflectioni = - pReal sideVirtual sideVirtual imageeyeObject distance = - image distanceImage size = Object sizeProblem: Two plane mirrors make an angle of 90o. How many images are there for an object placed between them? objecteye123 mirrormirrorProblem: Two plan mirrors make an angle of 60o. Find all images for a point object on the bisector.object245,631mirrormirror eyepocketAssuming no spinAssuming an elastic collisionNo cushion deformationddUsing the Law of Reflection to make a bank shotWhat happens if we bend the mirror?i = - p magnification = 1Concave mirror.Image gets magnified.Field of view is diminishedConvex mirror.Image is reduced.Field of view increased.Rules for drawing images for mirrors• Initial parallel ray reflects through focal point.•Ray that passes in initially through focal point reflects parallel from mirror•Ray reflects from C the radius of curvature of mirror reflects along itself.• Ray that reflects from mirror at little point c is reflected symmetrically1p+1i=1fm=−ipConcept Simulator/IllustrationsHalliday, Resnick, Walker: Fundamentals of Physics, 7th Edition - Student Companion SiteSpherical refracting surfacesn1p+n2i=n2−n1rUsing Snell’s Law and assuming small Angles between the rays with the central axis, we get the following formula:Apply this equation to Thin Lenses where the thickness is small compared to object distance, image distance, and radius of curvature. Neglect thickness.Converging lensDiverging lensThin Lens