Converging Lenses

Converging LensesAlex Yepez and Adam FergusonPurposeDetermine the relationship between object distance and image distance.Determine the relationship between object distance and image height.Determine the relationship between object height and image height.HypothesisAs object distance increases, image distance decreases.As object distance increases, image height decreases.As object height increases, image height increases.Setup

EquipmentObject distanceImage distanceScreenLensLight SourceObject heightImage heightAir track with distance markingsImage Distance vs. Object Distance & Image Height vs. Object Distance

Mathematical Analysis:1/Image Distance vs. 1/Object Distance 1. 1/Image Distance 1/di; 1/Object Distance 1/do2. Y = mx + b3. 1/di = k*(1/do) + b4. K = [ (1/di)]/[ (1/do)]5. K = -1.0216. B = 5.103 1/m7. 1/di = (-1.021)*(1/do) + 5.103 1/mError Analysis: Error CalculationMagnitude of Slope of 1/Image Distance vs. 1/Object DistanceAccepted value = 1Experimental value = magnitude of slope of graphExperimental value = 1.021Absolute Error = |Experimental value accepted value|Absolute Error = |1.021 1|Absolute Error = .021Relative Error = Absolute error/Accepted valueRelative Error = .021/1Relative Error = .021Relative Error = 2.1%

Error Analysis: Error CalculationY-intercept of 1/Image Distance vs. 1/Object DistanceAccepted value = 1/Focal DistanceAccepted value = 1/.194 mAccepted value = 5.15 1/mExperimental value = Y-intercept of graphExperimental value = 5.103 1/mAbsolute Error = |Experimental value accepted value|Absolute Error = |5.103 1/m 5.15 1/m|Absolute Error = .047 1/mRelative Error = Absolute error/Accepted valueRelative Error = (.047 1/m)/(5.15 1/m)Relative Error = .0091Relative Error = .91 %

Error Analysis: Sources of Error1. The precision in measuring image height was limited by our tools and setup.Mathematical Model1/di = (-1.021)*(1/do) + 5.103 1/m1/di = (-1)*(1/do) + (1/f)1/di + 1/do = 1/f

Image Height vs. Object Height

Mathematical Analysis: Image Height vs. Object Height (1.5 FL)1. Image Height hi; Object Height ho2. hi ho3. hi = k*ho4. K = hi/ho5. K = 2.0516. hi = (2.051)*hoMathematical Analysis: Image Height vs. Object Height (2.5 FL)1. Image Height hi; Object Height ho2. hi ho3. hi = k*ho4. K = hi/ho5. K = .78476. hi = (.7847)*hoError Analysis: Error Calculations:Image Height vs. Object Height (1.5 FL)Accepted value = f/(do f)Accepted value = (.194 m)/(.300 m - .194 m)Accepted value = 1.83Experimental value = Slope of graphExperimental value = 2.051Absolute Error = |Accepted value Experimental value|Absolute Error = |1.83 2.051|Absolute Error = .221Relative Error = Absolute error/Accepted valueRelative Error = .221/1.83Relative Error = .121Relative Error = 12.1%Error Analysis: Error Calculations:Image Height vs. Object Height (2.5 FL)Accepted value = f/(do f)Accepted value = (.194 m)/(.500 m - .194 m)Accepted value = .634Experimental value = Slope of graphExperimental value = .7847Absolute Error = |Accepted value Experimental value|Absolute Error = |.634 .7847|Absolute Error = .1507Relative Error = Absolute error/Accepted valueRelative Error = .1507/.634Relative Error = .238Relative Error = 23.8%Mathematical Modelhi = (.7847)*hohi = [f/(do f)]*ho

Ray Diagram