DOC PREVIEW
UVA PHYS 632 - Lecture 14 Images Chapter 34

This preview shows page 1-2-3-21-22-23-43-44-45 out of 45 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Lecture 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 refractionof 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 Reflection1AB!I=!R!i!rMirrorDrawing NormalsFermat’s PrincipleUsing Fermat’s Principle you can prove theReflection law. It states that the path taken by light when traveling from one point toanother is the path that takes the shortesttime compared to nearby paths.Two light rays 1 and 2 taking different pathsbetween points A and B and reflecting off avertical 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)sin"I = sin"R!I=!RWrite down time as a function of yand set the derivative to 0.Law of Refraction: Snells Law  n1sin!1= n2sin!2n1n2How do we prove it?1v1sin!1=1v2sin!2Air 1.0Glass 1.33t = (1v1h12+ y2+1v2h22+ (w ! y)2)dtdy= 01v1sin"I= 1v2sin"Rn1sin!I= n2 sin!RJAVA APPLETShow Fermat’s principle simulatorWhat allows you to see various colors whenwhite light passes through a prismDispersionHow does a Rainbow work?Dispersion: Different wavelengths have different velocities andtherefore 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 = f!! changes when medium changesf does not change when medium changesWhy is light totally reflected inside a fiberoptics cable? Internal reflection n1sin!1= n2sin!2 (1.33)sin!1= (1.00)sin90 = 1.00When !1" sin#111.33" 48.75 deglight won't get out of the materialFiber CableSame hereCorner Reflector?Show Total Internal reflectionsimulatorHalliday, Resnick, Walker: Fundamentals of Physics, 7thEdition - 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 bottomof a swimming pool to a point 50.0 cm above the water. What is thelength of the shadow of the pole on the level bottom of the pool?Consider a ray that grazes the top of thepole, 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 !2 Snells Law ExampleAccording to the law of refraction, n2sin!2 =n1sin!1. We take n1 = 1 and n2 = 1.33oon55.2533.135sinsinsinsin12112=!!"#$$%&=!!"#$$%&=''((L is given by.72.055.25tan)50.1(tan22mmlLo===!The 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.)sin!B= n sin!r!B+!r= 90 we get 100% polarized reflected wavesin !B= n sin(90 "!B) = n cos!B!B= 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. Howmany images are there for an object placed betweenthem?objecteye123mirrormirrorProblem: Two plan mirrors make an angle of 60o. Find allimages for a point object on the bisector.object245,631mirrormirroreyepocketAssuming no spinAssuming an elastic collisionNo cushion deformationddUsing the Law of Reflection tomake 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, 7thEdition - 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 issmall compared to object distance, image distance, andradius of curvature. Neglect thickness.Converging lensDiverging lensThin Lens Equation 1f=1p+1iLensmaker Equation 1f= (n !1)(1r1!1r2)What is the sign convention?Lateral Magnification for a Lensm = !ipSign ConventionpVirtual side - VReal side - RiLightReal object - distance p is pos on V side (Incident rays are diverging)Radius of curvature is pos on R side.Real image - distance is pos on R side.Virtual object - distance is neg on R side. Incident rays are converging)Radius of curvature is neg on the V side.Virtual image- distance is neg on the V side. r2r1Rules for drawing rays to locate images froma lens•A ray initially parallel to the central axis will pass through the focal point.•A ray that initially passes through the focal point will emerge from the lens parallel to the central axis.• A ray that is directed towards the center of the lens will go straightthrough the lens undeflected.Example 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.pfi111!= m =! y y= "ip 1i=15!110= +110Image is real, inverted.. .F1F2pVirtual sideReal side m = !1010= !1 i = +10 cmExample24(e). Given a lens with the properties (lengths in cm) r1 = +30, r2 =-30, p = +10, and n = 1.5, find the following: f, i and m. Is the imagereal or virtual? Upright or inverted? Draw 3 rays.( )!!"#$$%&''=211111rrnf( )30130130115.11=!"#$%&'''=fcmf 30=pfi111!=1511013011!=!=icmi 15!= m =! y y= "ip m = !!1510= +1.5Image is virtual,upright.Virtual sideReal sider1. .F1F2pr227. A converging lens with a focal


View Full Document

UVA PHYS 632 - Lecture 14 Images Chapter 34

Download Lecture 14 Images Chapter 34
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lecture 14 Images Chapter 34 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lecture 14 Images Chapter 34 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?