Materials Included In Kit

Additional Materials Required

Safety Precautions

Please follow normal laboratory safety guidelines. Do not look directly at sunlight or other strong light source with the telescope.

Teacher Tips

• This classroom set contains enough material to build eight telescopes—four astronomical telescopes and four terrestrial telescopes. This laboratory activity can reasonably be completed in one 50-minute class period.
• One method to complete this laboratory is to have each student group build one telescope (astronomical or terrestrial). Then after the data are collected with one telescope design, the students should switch telescopes in order to collect data for the other telescope design.
• White glue can be used to permanently secure the lens units inside the tubes.
• The Telescope Construction can be performed by the students or by the teacher to save time.
• The amount of tape necessary to keep the lens units secure inside the tubes will depend on the thickness of the tape. To limit the amount of tearing that can occur with paper tubes when the lens units are taken apart, masking tape is recommended. Also, use as little tape as possible to secure the rings if they are going to be taken apart frequently.
• Make sure students view objects at least 30 feet away when collecting data. Very close objects (less than 5 feet away) may be difficult to view with these telescopes.
• The length of the telescope tube will depend on the distance the viewed object is away from the telescope. For very distant objects (>50 feet), the telescope length will be similar to the sample data. If the viewed object is relatively close to the telescope, the length of the telescope tube will be longer because the image produced by the objective lens will be focused beyond the back focal point of the objective lens. Ideally, when an object is very far away from an astronomical telescope, the back focal point of the objective lens and the front focal point of the eyepiece lens will be at the same point in the telescope tube. And when an object is very far away from a terrestrial telescope, the back focal point of the objective and the back focal point of the eyepiece will be at the same point.
• When viewing a far away object, the telescope may measure slightly smaller than the “expected” size. This may be due to the precision of the lens. The precision of the 250-mm focal length lens is ±20 mm. The precision of both the 50-mm focal length concave and convex lenses is ±5 mm. Also, the largest image produced by an astronomical telescope occurs when the image formed by the objective lens is positioned slightly between the front focal point of the eyepiece lens and the eyepiece lens, instead of directly at the front focal point of the eyepiece lens. This makes a slightly shorter than expected telescope, but also puts more strain on the eyes. This occurs with the terrestrial telescope as well, but the image formed by the objective lens is positioned just behind the back focal point of the eyepiece lens.
• To better estimate the true focal length of the convex objective lens, hold the lens in sunlight to form a very sharp point of light on the ground. Make sure that the light does not converge onto any combustible material. Measure, to the nearest mm, the distance between the lens and this sharp point of light with a ruler. This is the approximate focal length of the lens. This measured focal length can than be used to determine the magnification of the telescope and the “expected” lens separation.
• Students may not understand why a concave eyepiece lens can act as a simple magnifier since it does not produce a magnified image under normal viewing conditions. However, a concave lens can act as a simple magnifier when it magnifies a virtual object. A virtual object is an “object” located on the transmission side of the focusing lens. This object does not actually exist. In the focused terrestrial telescope, the objective lens will focus the incident light to its back focal point. However, the eyepiece lens is positioned in front of this point, between the objective lens and its back focal point. Therefore, the focused light from the objective lens will be bent by the eyepiece lens before it can actually form a real image. The final image produced by the eyepiece lens will be located and oriented as if the viewed object has a negative distance (according to the thin-lens equation), meaning it is located on the transmission side of the eyepiece lens. The object is virtual, and the optics allow the concave lens to act as a simple magnifier in this situation.
• Over time, the paper tubes may shrink as moisture evaporates from the paper. Once the paper is completely dry, the tubes’ sizes will no longer change. However, the final “dry” size may effect how well the pieces fit inside one another. If a piece is too loose inside a tube, use masking tape to tape around the outside of the tube to add to the diameter of a tube. If a ring’s diameter is too large to fit inside a tube, a small section of the ring can be clipped with scissors. The ends of the cut sections can then be squeezed together so that the ring fits inside the tube. The rigidity of the ring will cause it to expand inside the tube and therefore create a snug fit. Clip the ring starting with about a ¼" section. If the ring is still too large, clip additional segments from a clipped end until the ring fits inside the tube.
  {12054_Tips_Figure_4}

Sample Data

Answers to Questions

1. What is the lens separation between the objective lens and the eyepiece lens for the sharply focused astronomical telescope? (Assume that the center of each lens is positioned 15 mm inside the tube at each end.)

   Lens separation for the astronomical telescope: 298 mm

2. Compare the lens separation of the astronomical telescope to the sum of the focal lengths of the two respective lenses. What does this tell you about where the focal point of the objective lens falls in comparison to the focal point of the eyepiece lens for the astronomical telescope?

   The separation between the lenses is very close to the sum of the focal lengths of the two lenses. This means that the back focal point of the objective lens and front focal point of the eyepiece lens are at the same point in the telescope tube.

3. Describe the image produced by the astronomical telescope. Is the image inverted? Is there distortion? Using Equation 3, determine the magnification of the astronomical telescope.

   The image is inverted (upside-down). The field of view for the image is very large and there is little distortion (aberration) in the image except near the edges. Image is sharply focused. The angular magnification of the astronomical telescope (from Equation 3) is –5, meaning that the image is 5 times larger than when viewed with the unaided eye and the image is inverted.

4. What is the lens separation between the objective lens and the eyepiece lens for the sharply focused terrestrial telescope? (Assume that the center of each lens is positioned 15 mm inside the tube at each end.)

   Lens separation for the terrestrial telescope: 195 mm

5. Compare the lens separation of the terrestrial telescope to the sum of the focal lengths of the two respective lenses. What does this tell you about where the focal point of the objective lens falls in comparison to the focal point of the eyepiece lens for the terrestrial telescope?

   The separation between the lenses is very close to the difference between the eyepiece focal length from the objective focal length. This means that the back focal point of the objective lens is at the same point as the back focal point of the eyepiece lens.

6. Describe the image produced by the terrestrial telescope. Is the image inverted? Is there distortion? Using Equation 3, determine the magnification of the terrestrial telescope.

   The image is upright (looks normal). The field of view for the image is smaller than for the astronomical telescope and there is more distortion (aberration) at the edges of the image. The magnification of the terrestrial telescope (from Equation 3) is 5, meaning the image is 5 times larger than when viewed with the unaided eye and the image is upright. This is the same magnification as the astronomical telescope but the telescope length is shorter and the image is upright.

7. What are the advantages and disadvantages of the two different telescope designs?

   The astronomical telescope creates an image that’s sharper and appears larger than the terrestrial telescope even though the angular magnification is the same. There is less aberration in the astronomical telescope lens system. The astronomical telescope creates an inverted image and would not be a good telescope to view nearby objects on Earth. It would be more useful when viewing planets and moons in space where up and down do not really matter. The terrestrial telescope produces an upright image which makes it more suitable for viewing objects on Earth.

8. (Optional) Draw ray diagrams for the astronomical and terrestrial telescopes that are sharply focused on a distant object.
   {12054_Answers_Figure_5}

References

Tipler, Paul A.; Physics for Scientists and Engineers, 3rd Ed., Vol. 2; Worth Publishers: New York, 1990, pp 1041–1058.

Introduction

Telescopes have been used for centuries to observe the far reaches of our galaxy. The complexity of modern telescopes (such as the Hubble telescope) has increased dramatically since the first telescope, but they still follow the same lens and optics principles. In this laboratory, two simple types of telescopes will be constructed—an astronomical (or Keplerian) telescope and a terrestrial (or Galilean) telescope. By measuring the length of the focused telescope you will determine how each telescope’s lens combination works to magnify an object. You will also observe the advantages and disadvantages of each telescope design.

Concepts

• Telescopes
• Refraction
• Real versus virtual images
• Lenses
• Ray diagrams

Background

Nearly 400 years ago, while experimenting with the optical properties of lenses and optical lens systems, Galileo Galilei discovered a way to bring distant objects into better view by making them appear as if they were only a few meters away instead of a few hundred meters—he did this with a telescope. The first telescope used a simple two-lens system with an objective lens and an eyepiece lens.

The objective lens is a convex, or converging, lens and it focuses incoming light from a distant object through the back focal point of the lens to form a real image on the transmission side (exiting-light side) of the lens. The focal point of any lens is the point at which a beam of light parallel to the principle axis of the lens converges. A real image is an image that can be formed on a screen and therefore can be seen by the naked eye (see Figure 1).

The eyepiece lens of the telescope then acts as a simple magnifier to magnify the very small real image produced by the objective lens. The eyepiece lens can be either a convex lens for an astronomical telescope or a concave, or diverging, lens for a terrestrial telescope. A simple magnifier is used as the eyepiece lens so that the final image is an enlarged virtual image. A virtual image is an image that forms on the incident side (incoming-light side) of the lens. Unlike a real image, a virtual image can only be seen when looking directly through the lens. It will not form an image on a screen. Therefore, when looking through a telescope, your eye sees this final virtual image as an apparent enlarged, closer object and the convex lens of the eye focuses the incoming light from this “object” to form a large real image on the retina. The result—the original object appears closer and larger than it did with the unaided eye.

The actual position of the image formed by any (thin) lens in relation to the object’s position from the lens can be determined using the thin-lens equation shown in Equation 1, or by drawing ray diagrams as in Figure 1. This equation can also be used in a stepwise fashion for multiple lens systems, such as that for a telescope, to determine where the final image is formed.

f is the focal length of lens
i is the image distance from lens
o is the object distance from lens

The thin-lens equation uses the convention that convex lenses have positive focal lengths and concave lenses have negative focal lengths. The focal length is the distance between the center of the lens and the focal point of the lens. Another convention is that light travels from left to right. So, objects to the left (on the incident side) of the focusing lens and images formed to the right (on the transmission side) of the focusing lens have positive distances and are real. Objects to the right (transmission side) and images formed to the left (incident side) of the focusing lens have negative distances and are virtual. Please refer to your physics or physical science textbook for more information and examples using the thin-lens equation.

How does a simple magnifier work? A simple magnifier allows an object to be placed much closer to the eye than the near point of the eye and allows the eye to focus on an enlarged image without strain. The near point of the eye is the closest distance an object can be placed in front of the eye in which the eye’s lens can still clearly focus the image on the retina. Any object positioned closer than the near point will be blurry. For a “normal” eye, the near point is 25 centimeters. However, when an object is positioned at the front focal point of a simple magnifier with the focal length much shorter than the near point distance, and the magnifier is held very close to the eye, the eye is able to focus on the enlarged virtual image produced by the magnifying lens. The virtual image formed by the simple magnifier is located an infinite distance away from your eye on the incident side of the lens. This allows your eye to stay relaxed when viewing the clear, enlarged image. The enlarged image will not be infinitely large, however. The apparent enlargement of the object will depend on the angular magnification of the lens. Angular magnification is measured as the ratio of the angle subtended by the magnified virtual image (Θ_i) (the “object” the eye’s lens actually focuses on when using a simple magnifier) compared to the angle subtended by the real object (Θ_o) when viewing the object at the near point of the eye (see Figure 2). The effective angular magnification of a simple magnifier when the lens is close to the eye and the viewed object is at the front focal point of the magnifier is given by Equation 2.

M_sm is the Angular magnification of a simple magnifier
25 is the near point for a normal eye (25 cm)
f is the focal length of the magnifying lens (the distance the object is from the lens)

When an objective lens and an eyepiece lens are used together to magnify an object, as with the simple two-lens telescope, the effective angular magnification of this lens system is given by Equation 3.

M_st is the Angular magnification of a simple telescope
f_o is the focal length of the objective lens*
f_e is the focal length of the eyepiece lens*
*Concave lenses have negative focal lengths. Convex lenses have positive focal lengths.

You will notice that the images formed by the telescopes will be slightly distorted. This distortion is known as aberration. For thin, theoretical lenses, aberration is neglected. For thick, real-life lenses, aberration is natural, and correcting it or minimizing it is important for producing the best images. Modern telescopes use complicated optics to eliminate distortion and create sharp, finely tuned images. Aberration is not caused by defects in the lenses, but is due to the laws of refraction and reflection on spherical surfaces. That is, since lenses are not uniformly thick (thicker in the middle than at the edges for a convex lens, and thicker at the edge than in the middle for a concave lens) the lens will not bend light uniformly from the center of the lens to the edge of the lens. Therefore, the focused rays do not all meet at the focus of the lens resulting in a distorted or blurry image.

Materials

Safety Precautions

Please follow normal laboratory safety guidelines. Do not look directly at sunlight or other strong light sources with the telescope.

Procedure

Telescope Construction

1. To build the objective lens unit, sandwich the 50-mm diameter convex lens (O) between the two 1¾" i.d. x ½" wide rings (A). Apply a small amount of tape around the seam to secure the rings.
2. Slide the objective lens unit inside the 2" i.d. x 7" long tube until the ends of the tube and the objective lens unit’s rings are flush. If the lens unit fits loosely, wrap additional tape around the rings until the objective lens unit will slide inside the tube and remain tight and secure at the end. Alternately, “double-backing” a long piece of tape to form a ring of tape with the sticky-side out can also be used to secure the objective lens unit inside the tube.
3. To build the eyepiece lens unit, sandwich the 38-mm diameter convex lens (E), or the 38-mm diameter concave lens (E), between two 1⅜" i.d. x ½" wide rings (B), inside a 1½" i.d. x 1⅛" long short tube (C). The lens should be centered inside the tube and secure. A small amount of tape may be necessary to hold the rings inside the 1⅛" long tube. For the concave lens, the 1⅜" i.d. × ½" wide rings (B) will stick out slightly at each end of the 1⅛" tube (C) since the concave lens is thicker at the edges than the convex lens. Note: If the B ring is too loose inside the C ring, apply a small amount of tape to increase the diameter of the B ring. If the B ring is too large for the C ring, a small section of the B ring can be removed with scissors. Clip just enough so when the ends of the cut sections are squeezed together, the B ring fits inside the C ring.
4. The convex lens unit for the astronomical telescope goes inside the 1¾" i.d. x 7½" long tube. The concave lens unit for the terrestrial telescope goes inside the 1¾" i.d. x 6½" long tube. Slide the eyepiece lens unit inside the appropriate tube until the end of the 1⅛" long tube is flush with the end of the 1¾" i.d. tube. The end of 1⅜" ring holding the concave lens in place should stick out slightly so the concave lens will be in the middle of the eyepiece lens unit. If the eyepiece lens unit fits loosely, wrap tape around the unit until it fits tightly inside the end of the tube.
5. To complete the telescope: Insert the 1¾" i.d. x 7½" (or 6½") long telescope tube into the 2" i.d. x 7" long telescope tube so that the lenses are on opposite ends.
   {12054_PreLab_Figure_3_Telescope construction}

Activity

1. Obtain an astronomical or terrestrial telescope.
2. Look through the smaller diameter opening and point the telescope at a large object across the room, or outside the classroom (through a window). The object should be at least 30 feet away. Sharpen the focus of the image by sliding the smaller diameter tube in and out of the larger diameter tube. Adjust the telescope length until the largest and clearest image is seen through the telescope. How does the object appear? Does the object appear larger than before? Is the object upside-down (inverted) or upright (erect)? Record your observations in the appropriate space in the data table.
3. With a meter stick, measure, to the nearest millimeter, the total length of the focused telescope. Record the measurement in the appropriate space in the Data Table.
4. Obtain the other telescope design and repeat Procedure steps 2 and 3 and enter your observations and data into the appropriate spaces in the data table.
5. Consult your instructor for appropriate storage procedures.

Student Worksheet PDF

12054_Student1.pdf