PHYSICS EXPERIMENTS — 132 7-1
Experiment 7
Simple Lenses
PHYSICS EXPERIMENTS — 132 7-3
In this experiment you investigate image formation by a 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 will verify thin lens theory and determine the lens focal lengths.
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.
Focal length for a diverging lens is negative and a simple diverging lens does not produce a real image. A virtual image forms where the backwards extensions of diverging rays cross and it cannot be viewed on a screen. However, combining a converging lens with a diverging lens may result in a real image that can be viewed on a screen.
Procedure.
Part A. Converging Lens.
· Object at Infinity: In this part you will make a single measurement of the image distance with the object distance . Hold the lens in one hand and the screen in the other hand. Focus the image of a distant bright object (such as a window across the room) on the screen. Have your partner measure the distance from the lens to the screen. This is the image distance . Use this measurement to calculate the focal length of the lens.
· In this part, you will determine the focal length by measuring several pairs of object and image distances and plotting 1/s versus 1/s’. Place the light source and the screen on the optics bench 115 cm apart with the light source’s crossed-arrow object toward the screen. Place the lens between them as shown in Figure 2.
Figure 2. Experimental set-up for converging lens
1. Starting with the lens close to the screen, slide the lens away from the screen to a position where a clear image of the crossed-arrow object is formed on the screen. Measure the image distance and the object distance. Measure the object size and the image size for this position of the lens.
2. Without moving the screen or the light source, move the lens to a second position where the image is in focus. Measure the image distance and the object distance. Measure the object size and image size for this position also. Note that you will not see the entire crossed-arrow pattern. Instead, measure the image and object sizes as the distance between two index marks on the pattern.
3. Cover half of the lens with an opaque object (you can use the lens-holder with white semicircular plastic in the lens mount). Observe the effect on the image.
4. Repeat steps 1 and 2 with light source-to-screen distances of 110-85 cm by 5 cm increments. For each light source-to-screen distance, find two lens positions where clear images are formed. (You don’t need to measure image and object sizes.)
5. Plot 1/s versus 1/s’ and find the best-fit line (linear fit). This will give a straight line with the x- and y-intercepts equal to 1/f. Find the slope and x and y intercepts of your graph. Is the slope consistent with equation 1? Average the two values of the focal length you obtained from the intercepts.
6. For the first two data points only (1.15 m source-to-screen distance, at each position of the lens), use the image and object distances to calculate the magnification, M. Check your results by calculating magnification from your measurements of the image size and object size.
Part B. Diverging Lens.
A virtual image cannot be viewed on a screen. You can see a virtual image by looking at it through a lens.
· Place the diverging lens (with focal length -150 mm) on the bench at the 30 cm mark. Place the light source at the 10 cm mark with the crossed-arrow object toward the lens. Record the object distance s (the distance between the light source and the lens). Look through the lens toward the light source (see Figure 3). Describe the image. Is it upright or inverted? Does it appear to be larger or smaller than the object?
Figure 3. Observing a virtual image
· Without removing the light source and the diverging lens, place the converging lens with focal length +200 mm on the bench anywhere between the 50 cm and 80 cm marks. Place the viewing screen behind the converging lens (see Figure 4). Slide the screen to a position where a clear image is formed on it. The real image you see on the screen is formed by the converging lens with the virtual image (formed by the diverging lens) acting as the object.
Figure 4. Experimental set-up for the converging lens
· Measure the image distance s’ for the converging lens (between the converging lens and the screen). Using this measurement and the known focal length of the converging lens, calculate the object distance for the converging lens.
· Make a sketch of the location of each optical component, similar to figure 4, and mark the location of the object for the converging lens (this is also the location of the virtual image formed by the diverging lens.) Now you know the object and the image distance for the diverging lens, use them (be careful with the signs of your object and image distances) to find the focal length of the diverging lens and compare with the given value.
Questions (Answer clearly and completely).
1. Is your converging lens data consistent with the thin lens formula given by equation 1? What value did you obtain for the slope?
2. (a) What value did you determine for the converging lens focal length using an object at infinity in Part A? What is the percentage difference between the given focal length and this value?
(b) What value did you determine for the converging lens focal length from the 1/s vs. 1/s’ graph in Part A? What is the percentage difference between the given focal length and this value?
3. What happens to the image if half of the converging lens is covered?
4. When you looked through the diverging lens toward the light source (as in Figure 3) was the image upright or inverted? Did it appear to be larger or smaller than the object?
5. What value did you determine for the diverging lens focal length in Part B? What is the percentage difference between the given focal length and this value?
6. Challenge question: For the converging lens case, with a source-to-screen distance of L, show that no image will form if L < 4f. Compute that minimum distance for the converging lens in this lab.
rev. 10/13