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# Focal Length of a convergin lens

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Introduction

Focal length of a converging lens

Aim: To find the radius of curvature and the focal length of a converging lens by experimental method

Hypothesis:

The relationship between u, v, and the focal length f for a converging lens is =  where f is the focal length of the lens, u is the distance between the object to the lens and v is distance between the images to the lens.

Variables:

 Independent Controlled Dependent Different types of lens usedDistance between the candle and the lens Experiment conducted at a dark roomSame projection screen used Focal length of the lens and the distance between the image and the lens

Materials:

 Item Quantity Accuracy Candle & Matches 1 - Converging lenses 5 - Screen 1 - Distance marker 1 Δl ±0.05cm

Diagram:

Method:

1. First of all, set up the apparatus up as shown in the diagram, so that the lengths u and v are equal and so that the image of the candle appears in focus on the screen.
2. Record the lengths u and v
3. Move the candle away from the lens by 5 cm more and adjust the screen distance (v), until the image is one again in focus. Record u and v in the table

Middle

20.620

10.310

0,1096

0,012012

40

14

20.408

10.204

0,0036

1,3E-05

45

13.4

20.834

10.417

0,2166

0,046916

50

13.2

19.240

9.620

-0,5804

0,336864

55

12.4

20.202

10.101

-0,0994

0,00988

60

12.2

20.202

10.101

-0,0994

0,00988

Mean ( ) 10.2004

Σ (x-)2

0,596472

Standard deviation: = =

The focal length : 10.2004 ± 0.257439

Percentage error:

Table7. Table of u vs v

 U (the initial position) Δl ±0.05 cm V (the image produced) Δl ±0.05 cm Radius of curvature (R) Frequency (f)   Hz (x-) (x-)2 15 27.5 19.418 9.709 -0,5325 0,283556 20 22/5 21.276 10.638 0,3965 0,157212 25 18.1 21.052 10.526 0,2845 0,08094 30 15.2 20.202 10.101 -0,1405 0,01974 35 14.5 20.618 10.309 0,0675 0,004556 40 14 20.834 10.417 0,1755 0,0308 45 13.3 20.618 10.309 0,0675 0,004556 50 12.8 20.408 10.204 -0,0375 0,001406 55 12.3 20.202 10.101 -0,1405 0,01974 60 12.2 20.202 10.101 -0,1405 0,01974 Mean ( ) 10.2415 Σ (x-)2 0,622248

Standard deviation: = =

The focal length: 10.2415 ± 0.262942

Percentage error:

Table8. Table of u vs v

 U (the initial position) Δl ±0.05 cm V (the image produced) Δl ±0.05 cm Radius of curvature (R) Frequency (f)   Hz

Conclusion

The results in this experiment were quiet pleasing because the percentage error of different types of converging lens in focal length was less than 10%. From the table, the biggest percentage error was 7.2%. Although there wasn’t perfect result which has 0%, our results can be said as excellent rather than other group. However, slight differences were still seen on the results. This is thought to be caused by inaccurate measurements on the distance marker and also on the screen’s image (whether the image is certainly focused or not)

There are several improvements can be made upon this experiment. One such improvement was that it is best to firstly agree upon what will focused images look like on the screen because in some cases, even though the image is not quite focused, the image is considered as being focused and therefore, the measurements might be affected. Another possible improvement was to also run the experiment on a constantly dark room so that it is easier to keep track on the candle light.

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

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