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Review Final Set of Labs & Formal Report Session 6 Physics 2CL Summer 2009 Outline • Review the last set of labs • Review formal write-up • Review error/uncertainty analysis Last set of labs • Choose 2 of remaining 4 • Topics include: – Microwaves: refraction & interference – Magnetic fields: RC integrator, force balance – Laser: interference, diffraction – Human eye: lens equation, lens in series Exp. 4 –Microwave refraction and interference • Measure n for wax • Make use of refraction and reflection Refraction n1 sin θ1 = n2 sin θ2 Uncertainties • What is uncertainty of n1 ? n1 sin θ1 = n2 sin θ2 n1 = n2 sin θ2/ sin θ1 εn12 = ε(sin θ2)2 + ε(sin θ1)2 δ(sin θ2) = [δ(sin θ2)/δθ2]δθ2 δ(sin θ2) = cos θ2 δθ2 ε(sin θ2) = cos θ2 δθ2/sin θ2 Exp. 4 – total internal reflection total internal reflection : sin θC = n2/n1 Interference Theory constructive φ = 0o φ = 0o λ φ = 360o Interference Theory destructive φ = 180o Exp. 4 –Interference apparatus 2d = mλ (for max) Exp. 5 – Magnetic Fields • Basic RC integration circuit • Measure value for magnetic field – Flipped coil – Current balance An RC Integrating Circuit Why? Flip Coil Integrating Circuit Total change in B upon thrusting loop into field is B itself Flipped coil Decay through Circuit Current balance Measure magnetic force Forces on current loop Exp 6 – Laser diffraction & interference • Use light from visible range • λ is relatively small so objects are similarly small • Lithography • Basic ideas for X-ray diffraction Diffraction & Interference • Extension of ideas in experiment 4 • Make use of interference leading to diffraction d sin θ = nλ Single Slit Diffraction Pattern Multi-Slit Interference Single slit envelope Interference between slits Exp. 7 – Lenses & Human Eye • Model for lens of the human eye • Detection of blind spot Lenses Converging lens Diverging lens Thins Lens equation Combination of lens Exp. 7 Objectives Convergent and divergent lenses Verify thin lens equation Power of lens Accomodation Glasses Check of Blind Spot Formal Report • • • • • • 5 pages Title page Introduction Theory Experiment Results Title page – Title page • • • • Experiment title Name, institution Date Abstract – 150 word limit – Succinct summary of results and significance Introduction • Overall description • Background • Objectives Theory • Review theory – give references • Predictions • Diagrams Experiment • • • • Apparatus - diagrams Procedure Make clear all tools Easily understood Results • Raw data – Tables – Graphs – organization • Analysis of data – Sample and clear calculations – Uncertainty analysis – Tables, graphs – units Discussion • Summarize data • Quantitative comparison with theory • Discuss in terms of δ, σ, and t analyses Summary of propagation formulae summation q = x+ y−z δq = (δx) 2 + (δy ) 2 + (δz ) 2 q = x× y ÷ z multiplication εq = (εx) 2 + (εy ) 2 + (εz ) 2 q = Bx constants δq = B δx εq = εx Number measurements Distributions 4 3 2 ±1σ 1 68 % ±2σ 95 % 0 69.4 69.6 69.8 70.0 70.2 70.4 height (inches) 1 G X ,σ ( x) = exp(− ( x − x) 2 2σ 2 ) σ 2π Number measurements Distributions 4 a 3 2 b 1 0 69.4 69.6 69.8 70.0 70.2 70.4 height (inches) b 1 G X ,σ ( x) = exp(− ( x − x) 2 2σ 2 ) a σ 2π ∫ Remember • Lab Writeup • Read next week’s lab description, do prelab • Homework 6 due with last lab (Taylor 8.1, 8.6, 8.10)