Materials Included In Kit

Additional Materials Required

Safety Precautions

This activity should be conducted in reduced light conditions and with burning candles. All safety precautions should be taken for this unique laboratory setting. All flammable items should be removed from the laboratory and laboratory benches. Caution students about paper items, loose clothing and fly-away hair.

Disposal

All items can be reused many times. Eventually candles will need to be replaced as they burn down.

Teacher Tips

• Enough materials are provided in this kit for one group of students. Groups of 2–4 students are recommended. The laboratory exercise can be reasonably completed in one 50-minute class period.
• As students work further with other lenses, they will discover that convex lenses invert their image and things appear upside down on the screen.
• The two lenses can be set up in series on the optical bench (use two lens holders) and the concept of a telescope can be illustrated. (Is the image upside down when using two lenses?) Use the short focal length lens as an “eyepiece” and place it closest to the eye as viewed down the length of the optical bench. Place the longer focal length lens between the eyepiece lens and a far away object. Move the lens until the object comes into focus. For more information on telescopes and materials to build a model telescope, see Flinn Catalog No. AP6266 “Build a Telescope.”
• If incandescent light sources (Flinn Catalog No. AP4705) and object pointers (Flinn Catalog No. AP4708) are available, the same experiments can be completed without lighted candles. The light source is placed behind the object pointer shining toward the screen.

Sample Data

Answers to Questions

1. Draw a ray diagram of the lens with the shortest focal length. Draw it actual size. Label the rays and the focal point.
   {11937_Figure_7}
2. How does the calculated focal length from the optics bench measurements compare with the focal length determined by the direct measurement? Explain any differences.
   Very similar. Exact location of “clear” image is subject to human eyesight variation.
3. Why is the distance i not equal to the focal length in the calculated measurement?
   On the optics bench the entering rays are bent and not totally parallel like they would be from a very distant object.

Discussion

Lens Equation Derivation

The equation used in this activity

can be derived using simple algebra and geometry. The derivation is provided here as a background and could be used with advanced students if necessary. The ray diagram is used for the derivation symbols that follow. Since triangle CDP is similar to triangle CD′P′ Since triangle AD′P′ is similar to triangle ACR Combining Equation 2 and 3 which reduces to Dividing by foi results in the lens equation

Introduction

An optics bench can be used to quantify and verify optics principles. This optics bench uses a meter stick as a support bench—the markings on the meter stick provide a simple and convenient way to make key measurements.

Concepts

• Optics bench
• Converging lens
• Focal length
• Parallel rays
• Diverging lens
• Ray diagrams

Background

Lenses

Lenses are made of glass or similar transparent materials, that refract light at their surfaces. Lenses are shaped so that they either diverge or converge a bundle of parallel rays. After leaving the lens, the parallel rays cross at a point known as the focal point.

The focal length (f) is the distance between the center of the lens and the focal point. The focal length is a characteristic property of a given lens and depends upon the material and the shape of the lens. A lens that converges light is called a convex lens and the value of f is positive. If a lens diverges light, it is called concave and the value of f is negative.
Ray Diagrams

Diagrams, like those in Figure 1, help to visualize the path of rays and to understand how lenses work and how images are formed. A few simple ray diagram rules help to keep the diagrams consistent. Figure 2 illustrates each of the simple rules. Read each rule and observe it as drawn in Figure 2.

1. Draw the focal points of the lens on both sides of the lens (F₁ and F₂).
2. If two rays from a source point (SP) one point where light rays start, intersect at another point (SP′),then all rays from that source point (SP) will intersect at the second point (SP′)
3. It is convenient to use three kinds of rays from a source point (SP in Figure 2). Ray a, enters the lens parallel to the lens axis and bends (refracts) through the focal point behind the lens (F₂). Ray b, passes through the focal point in front of the lens (F₁) and leaves the lens parallel to the axis of the lens. Ray c, goes through the center of the lens in a straight line and does not bend. Note: All three of the rays (a, b, c) meet at SP′ on the opposite side of the lens.

Lens Positions and Equation

Figure 5 shows ray diagrams for different positions of an object relative to a converging lens. Notice that six different arrangements are possible. Suppose a converging lens is placed between an object and a screen and is positioned so that a sharp image of the object appears on the screen. The distance between the object and the lens (o), the image and the lens (i) and the focal length (f) of the lens are related by the equation: where f is the focal length of the lens, o is the distance between the object and the lens (object distance) and i is the distance between the image and the lens (image distance). See Figure 4.

Materials

Safety Precautions

This activity uses a burning candle; watch for hot wax drippings on hands and other objects. Use appropriate caution when working with a burning candle. Remove all flammable materials from the vicinity of the burning candle and keep the laboratory work area cleared of all non-essential items. Do not leave burning candle unattended. Follow all laboratory safety guidelines.

Procedure

1. Place the screen in the screen holder, a convex lens in the lens holder and the candle in the candle holder. Attach the meter stick to the bench supports and arrange the objects on the bench as shown in Figure 6.
   {11937_Procedure_Figure_6_Optics bench arrangement}
2. Slide the screen and screen holder to one end of the optics bench at the 2- to 3-cm mark.
3. Light the candle. Be sure the flame is about the same height as the height of the center of the lens. If it is too high, extinguish the candle, remove it from the holder, and cut off the appropriate amount from the bottom of the candle, if necessary. Replace the candle and light it.
4. Close window blinds or shades and dim the lights in the work area so that there is a reduced amount of light shining on the screen. It need not be completely dark.
5. Experiment with the distances o and i by slowly sliding the lens and the candle along the meter stick optics bench. Watch for an image of the candle flame to appear on the screen. When the image becomes visible, adjust the position of the lens and the candle until the image is as clear as possible.
6. Extinguish the candle and carefully record the distances o and i on the Lens Test Worksheet. Record the distances to the nearest 0.1 cm. Use the pointed tips on the candle holder, lens holder, and screen holder to read the positions on the meter stick.
7. In the space provided on the Lens Test Worksheet, calculate the focal length of the lens. Show your calculations in the space provided.
8. Repeat steps 1–7 using the second convex lens. Record the results for lens 2 on the Lens Test Worksheet and calculate the focal length of lens 2.
9. Extinguish the candle and let it cool. Remove the screen from its holder and the meter stick from the optic bench supports.
10. Use a direct measurement technique to measure the focal length of lens 1. Do this by using the screen and the lens to focus on an object that is far away. It can be a ceiling light grid or an object out a window. Pick a bright, clear object. Focus the lens on the screen until the distant object is in sharp focus on the screen. With the object in sharp focus, measure the distance between the screen and the lens with a ruler. Record this focal length on the Lens Test Worksheet in the Direct Focal Length Measurement space.
11. Repeat the direct measurement test for lens 2. Record the focal length on the Lens Test Worksheet.
12. Answer the questions on the Lens Test Worksheet.
13. Return all materials to the instructor.

Student Worksheet PDF

11937_Student1.pdf