Experiment 2 Simple Lenses
Introduction
In this experiment you will measure the focal lengths of (1) a simple positive lens and (2) a simple negative lens. In each case, you will be given a specific method of measurement, and be told how to calculate the focal length from this measurement. Material on thin lenses can be found in J. &W. 4.1 - 4.9, 4.14, 4.15 and P. &P. 3-9, 3-10, and 3-11.
Focal Lengths of Simple Lenses
There are six sections in this lab. In each section you will measure the focal length of a simple lens.
1. Positive Lens
Procedure For the first section, you will make several measurements of image and object distances for a simple positive focal length lens (f = +20 cm).
Place an illuminated object at one end of the optical bench.
Then place the positive lens 60 cm from the object.
Place a large white screen on the other end of the bench and move it toward the lens until you find the image.
Record both the object distance and the image distance. Move the screen a few centimeters away and then find the image position again. Take total of five measurements of the image distance.
Repeat the above steps for an object distance of 30 centimeters.
Make only one careful measurement of the image distance for object distances of 55, 50, 40, 45, and 35 cm.
You will continue to move the lens toward the object but now the images will become virtual, since you will be moving inside the focal length of the lens. Since you can no longer use the screen to find the image, you must locate the image by an alternative method. Here, you will employ a device called a range finder. The operation of the range finder will be explained in lab. The range finder should be located 20 cm from the simple lens (see Figure 2 and 3).
Replace the illuminated object with the white screen. Note that the screen has a black line on the back. This line will be the new object.
Place the lens 16cm from the object.
Figure 1: Positive Lens, Real Image
Figure 2: Positive Lens, Virtual Image Measure the image distance. Remember the range finder will tell you the distance of the image from the range finder, you must subtract the distance of the range finder from the lens in order to find the image distance. Take a total of five measurements of the image distance.
Repeat the above steps for an object distance of 8 cm.
Make only one careful measurement of the image distance for object distances of 14, 12 and 10 cm.
Analysis In order to find the focal length of the lens from these data, the simple-minded approach would be to use the lens equation, compute several values for the focal length and average. This is not what you are going to do. Instead, you will plot the data and find the focal length from the intercepts. Plot the values of (1/u) vs. (1/v). The intercepts of this graph will be (1/f). Of course there are two intercepts that can be used. Compute f from both these intercepts. Be sure to estimate the error in the intercepts using a least squares fit. Then from the error in the intercepts calculate the errors in the focal length. If you need help with this, see your instructor. See the Report Outline for additional instructions.
2. Negative Lens
Procedure In the second section you will repeat Section 1, but you will use a negative lens (f = -20cm) instead of a positive lens. Make five measurements of the image distance for object distances of 55, 35, and 15 cm. Then make only one measurement with object distances of 50, 45, 40, 30, 25, 20 cm. You will note that a negative lens always produces a virtual image, so you will need to use the range finder to measure all of the image distances in this section.
Figure 3: Negative Lens
Analysis The method for computing the focal length is the same as Section 1. However, you will note that in this case you are computing the focal length by extrapolation, while in Section 1 you're using interpolation. Do you see any difference in accuracy?
3. Spherometer
Procedure In this section you will use the spherometer to measure the focal length of both lenses. Actually you will measure the radius of curvature, and using an assumed value for the refractive index of glass, calculate the focal length.
Figure 4: Spherometer
Measure the distance from the center of the spherometer to one of the legs. You can measure the distance r with a simple scale.
Place the spherometer on a plane mirror and record the reading. This reading on the micrometer corresponds to zero curvature.
Place the spherometer on each lens and record the reading. (This is a special case. You only need one careful measurement here. We have found that repeating the measurement many times would only give the same result many times. There are no averages to be taken in this section.) Also note that you only need to measure one side of each lens. You will assume that they are symmetric. (they are indeed close).
Analysis Now from your readings you can calculate the focal length using the lens makers formula. The radius of curvature can be calculated using,