Preparation
Prepare for this experiment by reading about virtual images formed by simple magnifiers, converging lenses and converging mirrors.
Principles
Virtual images are not formed by converging rays. Rather they are created by rays that diverge or spread from the lens or mirror. These rays can, however, serve as a virtual object for the eye or some other converging system.
Virtual images do have an apparent location in space and the thin lens equation can still be used to predict this location. The thin lens equation can also be used to predict the size and orientation of virtual images. The image distance for virtual images is always negative indicating that the image will be on the same side as the object for the lenses and on the opposite side as the image for the mirror.
The focal length of a simple magnifier is positive since it is just a converging lens. In order to get a virtual image you must make the object distance less than the focal length of the lens. We can see this by rearranging the thin lens equation,
1 1 1
= + f p q
, to solve for the image distance, q , fp q = . p - f
Since f and p are positive, q can only be negative if p is less than f . So one can only form a virtual image with a simple magnifier if p is less than f . This also means that q must be greater f than p since p - f
must be greater than 1.
If we compare this result to the magnification equation, h' q
M = = h p
, we see that when we form a virtual image using a simple magnifier, M must always be greater than +1.
The focal lengths of the diverging lens and diverging mirror are negative. When you take this into consideration and rearrange the thin lens equation in the form

1 1 1
= q f p
, you see that q is always negative since 1/f is negative for a diverging lens and -1/p is also always negative for a real object. Rearranging this equation into the form q = p
⎛
⎝ f p - f
⎞
⎠ shows us that the image distance, q , is always negative and of smaller magnitude than the object distance since f p-f
must be less than 1 when f is negative. If we again compare this to the magnification equation, we see that the image must always be upright since q is always negative.
For the diverging lens and mirror, M will always be between 0 and +1.
Equipment
1 two meter stick
1
1
30 cm converging lens
15 or 20 cm converging lens
1 -20 cm diverging lens
Procedure
Virtual images can be directly observed, but they cannot be projected onto a screen. Therefore, some method must be used to locate the image in order to find the image distance for thin lens calculations. One such method is called the reference point method. With this method, the virtual image serves as the virtual object for a converging lens. The image produced by the converging lens can then be projected onto a screen. In effect, a converging lens and screen act as a virtual image "detector".
1. Place the 15 or 20 cm converging lens in a holder and place it near the middle of the two meter stick. Make a screen out of a piece of white paper and place it on the table near the end of the stick.
2. Place an object light on the two meter stick and adjust its position so that a clear, slightly reduced image is formed on the screen. Measure the size of some feature of this image.
Record the position of the object light. This is the reference point. An image will always form on the screen when an object is at this point. Do not move the converging lens or the screen during each part of an experiment.

3. Use a 30 cm lens as the simple magnifier. Place the magnifier and the light on the two meter stick. Remember that the distance from the light to the lens must be less than the nominal focal length of the lens for the lens to act as a simple magnifier. The light and lens should be between the reference point and the "detector" lens. When the image produced by the magnifier is located at the reference point an image will appear on the screen, just as it did when you had the lamp at the reference position. The image size on the screen will be different; this difference is attributable to the magnifier.
4. Move the light and magnifier until an image appears on the screen. The image produced by the magnifier has become the object for the "detector" lens. Therefore that image is located at the reference point.
5. Record the position of the light and the magnifying lens. Repeat the procedure until you have at least ten to fifteen measurements. Cover as wide a range of values for the object distance as possible. For two or three cases measure the height of the image on the screen.
Note the orientation of the images.
6. For the next part of the experiment use the 30 cm lens as the image detector. Find a new reference point. This reference point should be somewhere around the middle of the meter stick. Make sure that there is some distance between the reference point and the detector lens. This time the reference image should be somewhat enlarged. Measure the height of the image.
7. Replace the magnifier with a -20 cm diverging lens and repeat the measurements. The diverging lens will always be between the reference point and the "detector" lens. The light will always be on the other side of the reference point. Again, measure the height of several images.
8. Replace the diverging lens with the diverging mirror and make another set of measurements. Don't forget to measure the height of several of the images.
9. Note that the mirror will always be between the reference point and the "detector" lens and that the light will be between the mirror and the detector lens aimed "backwards" towards the mirror. This may cause some alignment problems. Take care that the reflected rays from the mirror actually pass through the "detector" lens. You may want to rearrange the reference set up for convenience. If you do rearrange the detector system be sure to measure the size of the reference image and note the position of the new reference point.
10. Put all your equipment away and be sure your instructor signs your notebook.
Data
Data will consist of the reference point positions and the initial image sizes, as well as the positions of the lens or mirror, the light positions, and the size and orientation of some of the images.

Analysis
1. Find q for each measurement. Use the thin lens equation to calculate f for each measurement? Are the results as consistent as the real image results?
2. Use the two methods for calculating magnification. Compare the results. Are they in good agreement?
3. For each set of data plot image distance vs. object distances. Use the results of your calculations to draw in the asymptotes.
Questions
1. Draw careful, neat ray diagrams for a simple magnifier, a diverging lens, and a diverging mirror.
2. Draw a careful diagram of the set up of the reference point method of finding an image.
Use the simple magnifier as an example and explain how you found the object and image distances. Explain in detail.
3. How do the graphs compare to those of the real images experiment? Do they have the same shape? Are they in the same quadrant? Are the graphs similar or different for the three elements?
4. For the simple magnifier, where the focal length is positive, one can produce a virtual image only if the object distance is less than the focal length according to the equation fp q= . p-f
In the case of a diverging lens or mirror where f is negative are there any limits on the object distance? Why or why not?
If it applies to you, write " I have not cheated on this lab report " and sign your name.
Grading
4 pts Data and Analysis.
4 pts For each for question.