### Converging Lenses

```Alex Yepez and Adam Ferguson
1.
2.
3.
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.
1.
2.
3.
As object distance increases, image
distance decreases.
As object distance increases, image
height decreases.
As object height increases, image height
increases.
Image height
Lens
Light Source
Screen
Image distance
Air track with
distance
markings
Object
distance
Object height
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
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%
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 %
1. The precision in measuring image height
was limited by our tools and setup.
1/di = (-1.021)*(1/do) + 5.103 1/m
1/di = (-1)*(1/do) + (1/f)
1/di + 1/do = 1/f
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
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
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%
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%
hi = (.7847)*ho
hi = [f/(do – f)]*ho
```