Physics Experiments 13215-1
PHYSICS EXPERIMENTS — 13215-1
Experiment 15
Simple Lenses
PHYSICS EXPERIMENTS — 13215-1
In this experiment you investigate image formation by simple optical lens systems. A lens is a piece of transparent material shaped so that all light rays hitting the lens from the same (object) point end up going through the same (image) point after being bent by passage through the lens. The location of the image point depends on that of the object point and on a property of the lens called the focal length. You verify thin lens theory and determine lens focal length.
Preliminaries.
Part A. Converging Lens.
Figure 1 is a schematic representation of the formation of a real image by a converging lens. Real images may be projected onto a screen. In this experiment, only real images may be observed.
Figure 1. Image Formation by a Thin Converging Lens
The theory for thin lenses gives the following:
(eq. 1)
(eq. 2)
where f is the focal length of the lens, M is the magnification, s and s’ are the object and image distances, respectively, and y and y’ are the object and image heights. The trick in using eq.1 and eq. 2 is the correct assignment of signs. A focal length for a converging lens is positive. All other symbols in these equations are positive as shown in Figure 1, with the exception of y’, which is negative.
Part B. Diverging Lens.
A simple diverging lens does not produce a real image. However, combining a known converging lens with the unknown diverging lens may result in a real image that can be projected on a screen. If the two lenses are in contact, the lenses acting together have an effective focal length feffgiven by:
(eq. 3)
where f1 and f2are the focal lengths of the individual lenses in contact.
Procedure.
Part A. Converging Lens.
•Align the system components on the optical bench.A backlit screen with an arrow is the object. The image falls on white cardboard. Set the lens between object and image screen and move the image screen until a sharply focused image appears. Record the object and image distances relative to the lens.
•Cover the top half of the lens with an opaque object. Your hand will do! Observe the effect on the image.
•Reposition the lens and screen to obtain another sharp image configuration. Repeat. Get enough data (at least 15 data points) so that the screen is moved over the entire length of the optical bench. When you graph and analyze your data you can decide if more data is needed. If you think you need more then go back and get it.
•Measure and record the height of the object and that of the image at one data point. Be sure to note if the image is upright or inverted.
•Graph the data with the image distance on the vertical axis and object distance on the horizontal axis. Determine the focal length of the lens from the asymptotes of the graph using eq. 1.
•Graph the data with the reciprocal image distance on the vertical axis and the reciprocal object distance on the horizontal axis. Measure the slope and intercepts of this graph. Determine whether your graph verifies eq. 1 and find the focal length of the lens.
•Use the measured image and object heights to compute the magnification. Check eq. 2 using the appropriate image and object distances.
Part B. Diverging Lens.
•Carefullyconstruct a compound lens combination with your converging and diverging lens as shown in Figure 2. Check to be sure there is a rubber o-ring between the two lenses. Tighten the retaining screw just enough to hold the lenses in the holder. Tightening too much may break the diverging lens.
Figure 2. Two lens combination
•Mount the lens combination on the optical bench and find one single sharp object-lens-image configuration. Measure and record image and object distances.
• Use eq. 1 to determine the effective focal length feff. Use eq. 3 and the converging lens focal length you determined in Part A to determine the focal length of the unknown diverging lens.
Questions (Answer clearly and completely).
1. Is your converging lens data consistent with the thin lens eq. 1?
2.What happens to the image if the top half of the converging lens is covered?
3.What value do you determine for the converging lens focal length from the asymptotes of the image vs. object graph in Part A?What value do you determine for the converging lens focal length from the reciprocal image vs. reciprocal object graph in Part A? Which value do you think is better?
4.Does the orientation of the lens combination in Part B (which lens is in front) matter?
Refer to eq. 3 and try it!
5.What value do you determine for the diverging lens focal length in Part B? How do you know from the focal length that the lens is diverging?
6.Can you combine any converging lens in contact with any diverging lens to make a system which forms real images?