The aim of this experiment is to measure the focal length and power of a diverging lens. Since negative or diverging lenses do not form real images of real objects, an experimental virtual object will need to be set up for the diverging lens by using a converging lens. To do this, place a converging lens in front of the diverging lens. If the converging lens has a shorter focal length than the diverging lens, the two-lens combination will form a real image of a distant object.

Figure 1

When the lenses of individual focal lengths f c and f D, are placed in contact, the effective focal length f of the combination is given by:

Equation 1

The power of a lens is given by the equation:

Equation 2

The total power of these two lenses is given by the equation:

P tot = P c + P D Equation 3

where P c is the power of the converging lens, P D is the power of the diverging lens, and P tot is the power of the two lenses, converging and diverging, combined.

Apparatus

Lamp

Meter ruler

Screen

Object

Converging lens

Diverging lens

3 Lens holders (one for lens, one for screen and one for object)

Set up apparatus as follows:

Figure 2

Variables that effect Experiment:

Plan

Step 1: Measure the focal length and power of a converging lens:

1. Measure the focal length of the converging lens roughly by using light from a distant source and moving the lens and the viewing screen until a clearly focused image is obtained. The distance from the image to the lens is the same as the focal length, f.

2. Set up the apparatus as shown in figure 2. With the object to lens distance, u, at 6f , move the viewing screen until a clearly focused image can be seen.

3. Measure the image to lens distance and include uncertainty measurements (where the distance can be changed more but the image is still in focus).

4. Repeat procedures 2 and 3 for object to lens distance at 5f, 4f, 3f, 2f, and just over 1f.

5. Solve the lens equation:

(Where u is the object to lens distance and v is the image to lens distance) using the values found in the above procedures to give a more accurate focal length.

6. Use Equation 2 to find the power of the lens.

Step 2: Measure the focal length and power of the combination of the converging and diverging lens:

1. Measure the combined focal length of the diverging and the converging lens roughly by using light from a distant source and moving the attached lenses and the viewing screen until a clearly focused image is obtained. The distance from the image to the lenses is the same as the combined focal length, f.

2. Set up the apparatus as shown in figure 2 but with both the converging and diverging lenses in the lens holder. With the object to lens distance, u, at 6f , move the viewing screen until a clearly focused image can be seen.

3. Measure the image to lens distance and include uncertainty measurements (where the distance can be changed more but the image is still in focus).

4. Repeat procedures 2 and 3 for object to lens distance at 5f, 4f, 3f, 2f, and just over 1f.

5. Solve the lens equation (Equation 1) using the values found in the above procedures to give a more accurate combined focal length.

6. Use Equation 2 to find the power of the combined lens.

Step 3: Finding the focal length and power of the diverging lens:

1. To find the focal length of the diverging lens manipulate Equation 1 to give the equation:

And insert the value of the focal length found for the converging lens and for the combination of lenses.

2. To find the power of the diverging lens use Equation 2

and insert the value found in the step above for the focal length of the diverging lens.

Results

Converging lens:

u, object to lens (cm)

v, image to lens (cm)

1/u

1/v

1/f

f (cm)

11

110

0.090909

0.009091

0.1

10

20

21

0.05

0.047619

0.097619

10.2439

30

13.8

0.033333

0.072464

0.105797

9.452055

40

13.1

0.025

0.076336

0.101336

9.868173

50

11

0.02

0.090909

0.110909

9.016393

60

12.4

0.016667

0.080645

0.097312

10.27624

Diverging lens:

u, object to lens (cm)

v, image to lens (cm)

1/u

1/v

1/f

f (cm)

15

170

0.066667

0.005882

0.072549

13.78378

30

31

0.033333

0.032258

0.065591

15.2459

45

22

0.022222

0.045455

0.067677

14.77612

60

17

0.016667

0.058824

0.07549

13.24675

75

16

0.013333

0.0625

0.075833

13.18681

90

15

0.011111

0.066667

0.077778

12.85714