P5.1.2.4 - LD Didactic
LD
Physics
Leaflets
Optics
Geometrical optics
Laws of imaging
P5.1.2.4
Verifying the imaging laws with
a collecting lens
Objects of the experiment
g Experimental verification of the lens equation.
g Experimental verification of the imaging law.
Principles
The focal length of lenses can be determined by a variety of
means. The basis for the different procedures are the laws of
imaging.
An image of an object is formed on a translucent screen by a
convex lens of focal length f. The lens equation
1 1 1
= +
f g b
(I)
Is verified by altering the object distance g and measuring the
image distance b.
Apparatus
1 Lamp, 6 V/30 W ................................................. 450 51
1 Lamp housing .................................................... 450 60
1 Aspherical condenser ........................................ 460 20
1 Transformer ....................................................... 521 210
1 Lens f = +50 mm ................................................ 460 02
1 Lens f = +100 mm .............................................. 460 03
1 Set of two transparencies .................................. 461 66
1 Translucent screen ............................................ 441 53
1 Small optical bench............................................ 460 43
1 Stand base, V-shape, 20 cm.............................. 300 02
3 Leybold multiclamp ............................................ 301 01
1 Steel tape measure, 2 m.................................... 311 77
The relationship between the object size G and the image
size B and the object distance g and image distance b is
derived.
Setup
Bi 0205
- Set up the lamp with the aspherical condenser and the
translucent screen on optical bench as depicted in Fig. 1.
- Set up the translucent screen at the opposite end of the
optical bench.
- Position a lens with a clamp between the lamp and the
translucent screen.
Fig. 1: Schematic diagram of the basic experimental setup.
LD Didactic GmbH . Leyboldstrasse 1 . D-50354 Huerth / Germany . Phone: (02233) 604-0 . Fax: (02233) 604-222 . e-mail: info@ld-didactic.de
©by LD Didactic GmbH
Printed in the Federal Republic of Germany
Technical alterations reserved
P5.1.2.4
LD Physics leaflets
-2-
Carrying out the experiment
2. Experimental verification of the imaging law
The experiment should be performed in a darkened room.
The object of size G before the collecting lens is imaged on
the screen. The relationship between the image size B and
the object size G is given by the imaging law
- Measure the object size on the transparency and insert it
in the diaphragm holder of the lamp.
- Position the lens f = +100 mm 25 cm apart from the lamp.
- Form a sharp image on the screen (shift the lens slightly)
- Measure the object distance g (distance between lens and
object) and the image distance b (distance between lens
and image on screen).
- Measure the image size B.
- Repeat the experiment with object distances smaller, equal
to or greater than twice the focal length.
Repeat the experiment for the lens f = +50 mm.
B b
=
G g
the linear magnification β is:
β=
B
G
Supplementary information
Equation (I) can be used to determine the focal length f of a
collecting lens. For further methods see experiments P5.1.2.1
to P5.1.2.3.
Measuring example
Table. 1: Comparison of the measured and given focal length
-1
of convergent lens f = + 100 mm (1/f = 0.01 mm ).
b / mm
163
220
125
200
g / mm
250
195
500
200
1
/ mm-1
g
0.004
0.005
0.002
0.005
1
/ mm-1
b
0,006
0.005
0.002
0.005
0.0010
0.010
0.010
0.010
B / mm
3.5
4.5
21
5
G / mm
5
5
5
5
b
g
0.7
0.9
4.0
1.0
B
G
0.7
0.9
4.2
1.0
1 1 1
-1
+ = / mm
g b f
Evaluation and results
1. Experimental verification of the lens equation
From Table 1 follows that the image distance decreases with
an increasing object distance.
The image distance b is equal to the object distance g when g
equals 2 f.
The sum of the reciprocals of the object and image distance
does not change when the distance between the object and
the image is changed. The sum of the reciprocal image and
object distance is equal to the reciprocal of the focal length:
1 1 1
= +
f g b
LD Didactic GmbH . Leyboldstrasse 1 . D-50354 Huerth / Germany . Phone: (02233) 604-0 . Fax: (02233) 604-222 . e-mail: info@ld-didactic.de
©by LD Didactic GmbH
Printed in the Federal Republic of Germany
Technical alterations reserved
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