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# Experiment B11: Measuring focal length of lenses

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Introduction

11th February 2009

YMCA of Hong Kong Christian College

A-Level Physics Lab Report

Wong Hoi Sun 6Y34

Experiment B11: Measuring focal length of lenses (Done on 5th February 2009)

Objectives:

• To measure the focal length of a spherical convex lens by
(a) the “object & image distance method” and
(b) the “lens distance method”.
• To measure the focal length of a spherical concave lens by
(c) the “lenses-mirror method” and
(d) the “lenses combination method”.
• To identify the pros and cons of various methods.

Apparatus:

• Spherical convex lens with holder
• Spherical concave lens with holder
• Plane mirror
• Lamp housing
• White screen                1
• Metre rule                        2
• Tissue paper

Theory:

(Refer to pages.84-86 of “A-Level Practical Physics for TAS (Third Edition)”)

Procedure:

(Refer to pages 86-88 of “A-Level Practical Physics for TAS (Third Edition)”)

Experiment Results and Data Evaluation:

Method (a): Object & image distance method (for a convex lens)

Estimated focal length fx of the convex lens = 10 cm

 Object distance u/cm Image distance v/cm (1/u)/cm-1 (1/v)/cm-1 u < 2 fx 12 58 0.0833 0.0172 15 28.5 0.0667 0.0351 17 23.5 0.0588 0.0426 u≈ 2 fx 20 19 0.05 0.0526 u > 2 fx 30 15 0.0333 0.0667 40 13 0.025 0.0769 50 12 0.02 0.0833 Focal length fu of the convex lens calculated using (1/u)-intercept =

= 10 cm

Focal length fv of the convex lens calculated using (1/v)-intercept =

= 9.756 cm

Mean focal length f of the convex lens =

= 9.878 cm

Uncertainty of the mean focal length

Middle

13

28

9.870

s 5.8fx

58

46

12

34

9.517

s 6.2fx

62

49.5

12.5

37

9.980

s 6.6fx

66

54

12

42

9.818

Mean focal length f of the convex lens =

= 9.761 cm

Uncertainty

= −−−−−

= 0.154 cm

∴ Mean focal length f of the convex lens = (9.761 ± 0.154) cm

Method (c): Lenses-mirror method (for a concave lens)

 Image distance v/cm Separation between lenses t/cm Focal length f = v− t/cm u≈ 2fx 20 3 17 u≈ 1.9fx 21 5 16 u≈ 1.8fx 22 7 15 u≈ 1.7fx 23 9 14 u≈ 1.6fx 24 11 13

Mean focal length fof the concave lens =

= 15 cm

Uncertainty = −−−−−

= 1.2 cm

∴ Mean focal length fof the concave lens = (15 ± 1.2) cm

Method (d): Lenses combination method (for a concave lens)

Conclusion

Therefore, method (c): “Lenses-mirror method” should be used as its percentage error is the least.

In daily life, the above methods can be used.  For example, if people need to determine the focal length of the lens of a camera, they can use method (b): “Lens displacement method” to measure the focal length.  Cameras are made used of two convex lenses to make the light rays converge, so that photographs can be taken.  So, cameras have the apparatus needed for method (b).  To carry out this experiment, the experimentalist has to hold his camera far away from the object and adjust the focus, once the image is sharp, measure the distance between the camera and the object.  Then he needs to walk toward the object without adjusting the focus, once the image is sharp, measure the distance between the camera and the object again.  Repeat the measurement to obtain more pairs of distances, and then just follow the procedure.  The focal length of the lens of a camera then can be found by method (b): “Lens displacement method”.

Conclusion:

Method (a): “Object & image distance method” is suggested to measure the focal length of a spherical convex lens.  Method (c): “Lenses-mirror method” is suggested to measure the focal length of a spherical concave lens.

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