Final Exam information

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1 Fial Exam iformatio Wedesday, Jue 6, 2012, 9:30 am - 11:18 am Locatio: i recitatio room Comprehesive (covers all course material) 35 multiple-choice questios --> 175 poits Closed book ad otes Make up your ow equatio sheet (same rules as midterm)

2 26.2 Sell s Law ad the Refractio of Light Because light from the chest is refracted away from the ormal whe the light eters the air, the apparet depth of the image is less tha the actual depth. Simpler case -- look directly above the object. Apparet depth, observer directly above object & d' = d $ % 1 -- medium of object 2 -- medium of observer 2 1 #! "

3 26.2 Sell s Law ad the Refractio of Light Example. O the Iside Lookig Out A swimmer is uder water ad lookig up at the surface. Someoe holds a coi i the air, directly above the swimmer s eyes at a distace of 50 cm above the water. Fid the apparet height of the coi as see by the swimmer (assume = 1.33 for water). Use the equatio d' = & d $ % 2 1 #! " I this case, d will be the apparet height of the coi, d is the actual height above the water, 1 = 1.00 for air (object), ad 2 = 1.33 for water (the observer), d = (50)(1.33/1.00) = 66.5 cm è greater tha the actual height

4 26.2 Sell s Law ad the Refractio of Light THE DISPLACEMENT OF LIGHT BY A SLAB OF MATERIAL Whe a ray of light passes through a pae of glass that has parallel surfaces ad is surrouded by air, the emerget ray is parallel to the icidet ray, θ 3 = θ 1, but is displaced from it. 1 st iterface: 1 si θ 1 = 2 si θ 2 2 d iterface: 2 si θ 2 = 1 si θ 3 è 1 si θ 1 = 1 si θ 3 è θ 3 = θ 1

5 26.3 Total Iteral Reflectio Whe light passes from a medium of larger refractive idex ito oe of smaller refractive idex, the refracted ray beds away from the ormal. 1 si θ 1 = 2 si θ 2 siθ 2 c = > 1 Critical agle 1 2 For this water/air iterface: 1 si θ c = 2 si 90 o ê For θ 1 > θ c the ray is totally reflected si θ c = 1.00/1.33 = è θ c = 48.8 o

6 26.3 Total Iteral Reflectio Example. Total Iteral Reflectio A beam of light is propagatig through diamod ad strikes the diamod-air iterface at a agle of icidece of 28 degrees. (a) Will part of the beam eter the air or will there be total iteral reflectio? (b) Repeat part (a) assumig that the diamod is surrouded by water.

7 26.3 Total Iteral Reflectio Icidet agle i diamod = θ 1 = 28 o (a) Diamod i air: θ c = si 1 & $ % 2 1 #! " = si 1 & $ % #! " = 24.4 θ 1 > θ c è ray is totally reflected back ito the diamod (b) Diamod i water: θ c = si 1 & $ % 2 1 #! " = si 1 & $ % #! " = 33.3 θ 1 < θ c è some light is reflected back ito the diamod ad some light is trasmitted ito the water

8 26.3 Total Iteral Reflectio Coceptual Example. The Sparkle of a Diamod The diamod is famous for its sparkle because the light comig from it glitters as the diamod is moved about. Why does a diamod exhibit such brilliace? Why does it lose much of its brilliace whe placed uder water? As see i the last example, θ c is relatively small for the diamod i air so much of the light icidet o its back surface reflects back through the top of the diamod, makig it sparkle. I water θ c is larger so less light is reflected through the top, reducig its sparkle.

9 26.3 Total Iteral Reflectio Total iteral reflectio at a glass-air iterface. Sice = 1.5 for glass, at a glass-air iterface the critical agle is si θ c = 2 / 1 = 1.00/1.5 = è θ c = 42 o This ca be used to tur a ray of light through a agle of 90 o or 180 o with total iteral reflectio usig a prism of glass ad keepig θ 1 = 45 o è useful i the desig of optical istrumets. Two prisms, each reflectig the light twice by total iteral reflectio, are Sometimes used i bioculars to produce a lateral displacemet of a light ray.

10 26.3 Total Iteral Reflectio Total iteral reflectio i optical fibers. Light ca travel with little loss i a curved optical fiber made of glass or plastic ( light pipe ) because the light is totally reflected wheever it strikes the core-claddig Iterface ad sice the absorptio of light by the core itself is small. Usig optical fibers, light ca be piped from oe place to aother for may applicatios, e.g. telecommuicatios.

11 Example. A optical fiber cosists of a core made of flit glass ( flit = 1.667) surrouded by a claddig made of crow glass ( crow = 1.523). A ray of light i air eters the fiber at a agle θ 1 with respect to the ormal. What is θ 1 if this light also strikes the core-claddig iterface at a agle that just barely exceeds the critical agle?

12 claddig = crow = core = flit = Strategy: fid θ c usig the kow core ad claddig fid θ 2 usig θ c ad geometry fid θ 1 from θ 2, core ad Sell s Law si θ c = claddig / core = 1.523/1.667 = è θ c = o From figure, sice right triagle è θ 2 = 90 o - θ c = 90 o o = o Usig Sell s Law at the air-core iterface è air si θ 1 = core si θ 2 (1.000) si θ 1 = (1.667) si o è si θ 1 = è θ 1 = o

13 26.6 Leses Covergig ad divergig leses. Leses refract light i such a way that a image of the light source is formed. With a covergig les, paraxial rays that are parallel to the pricipal axis coverge to the focal poit, F. The focal legth, f, is the distace betwee F ad the les. Two prisms ca bed light toward the pricipal axis actig like a crude covergig les but caot create a sharp focus.

14 26.6 Leses With a divergig les, paraxial rays that are parallel to the pricipal axis appear to origiate from the focal poit, F. The focal legth, f, is the distace betwee F ad the les. Two prisms ca bed light away from the pricipal axis actig like a crude divergig les, but the apparet focus is ot sharp.

15 26.6 Leses Covergig ad divergig les come i a variety of shapes depedig o their applicatio. We will assume that the thickess of a les is small compared with its focal legth è Thi Les Approximatio