Converging Lenses

1. Converging Lenses Alex Yepez and Adam Ferguson

2. Purpose Determine 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.

3. Hypothesis As object distance increases, image distance decreases. As object distance increases, image height decreases. As object height increases, image height increases.

4. Setup

5. Equipment Lens Image height Light Source Object height Screen Image distance Object distance Air track with distance markings

6. Image Distance vs. Object Distance & Image Height vs. Object Distance

10. Mathematical Analysis:1/Image Distance vs. 1/Object Distance 1. 1/Image Distance  1/di; 1/Object Distance  1/do 2. Y = mx + b 3. 1/di = k*(1/do) + b 4. K = [∆ (1/di)]/[∆ (1/do)] 5. K = -1.021 6. B = 5.103 1/m 7. 1/di = (-1.021)*(1/do) + 5.103 1/m

11. Error Analysis: Error CalculationMagnitude of Slope of 1/Image Distance vs. 1/Object Distance Accepted value = 1 Experimental value = magnitude of slope of graph Experimental value = 1.021 Absolute Error = |Experimental value – accepted value| Absolute Error = |1.021 – 1| Absolute Error = .021 Relative Error = Absolute error/Accepted value Relative Error = .021/1 Relative Error = .021 Relative Error = 2.1%

12. Error Analysis: Error CalculationY-intercept of 1/Image Distance vs. 1/Object Distance Accepted value = 1/Focal Distance Accepted value = 1/.194 m Accepted value = 5.15 1/m Experimental value = Y-intercept of graph Experimental value = 5.103 1/m Absolute Error = |Experimental value – accepted value| Absolute Error = |5.103 1/m – 5.15 1/m| Absolute Error = .047 1/m Relative Error = Absolute error/Accepted value Relative Error = (.047 1/m)/(5.15 1/m) Relative Error = .0091 Relative Error = .91 %

13. Error Analysis: Sources of Error 1. The precision in measuring image height was limited by our tools and setup.

14. Mathematical Model 1/di = (-1.021)*(1/do) + 5.103 1/m 1/di = (-1)*(1/do) + (1/f) 1/di+ 1/do = 1/f

18. Image Height vs. Object Height

21. Mathematical Analysis: Image Height vs. Object Height (1.5 FL) 1. Image Height  hi; Object Height  ho 2. hi ho 3. hi= k*ho 4. K = ∆hi/∆ho 5. K = 2.051 6. hi= (2.051)*ho

22. Mathematical Analysis: Image Height vs. Object Height (2.5 FL) 1. Image Height  hi; Object Height  ho 2. hi ho 3. hi= k*ho 4. K = ∆hi/∆ho 5. K = .7847 6. hi= (.7847)*ho

23. Error 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 = 1.83 Experimental value = Slope of graph Experimental value = 2.051 Absolute Error = |Accepted value – Experimental value| Absolute Error = |1.83 – 2.051| Absolute Error = .221 Relative Error = Absolute error/Accepted value Relative Error = .221/1.83 Relative Error = .121 Relative Error = 12.1%

24. 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 = .634 Experimental value = Slope of graph Experimental value = .7847 Absolute Error = |Accepted value – Experimental value| Absolute Error = |.634 – .7847| Absolute Error = .1507 Relative Error = Absolute error/Accepted value Relative Error = .1507/.634 Relative Error = .238 Relative Error = 23.8%

25. Mathematical Model hi= (.7847)*ho hi= [f/(do – f)]*ho

26. Ray Diagram