Download Chapter 8 The Telescope and more Exercises Optics in PDF only on Docsity!
Chapter 8
The Telescope
8.1 Purpose
In this lab, you will measure the focal lengths of two lenses and use them to construct a simple telescope which inverts the image like the one developed by Johannes Kepler. Because one lens has a large focal length and the other lens has a small focal length, you will use different methods of determining the focal lengths than was used in ’Optics of Thin Lenses’ lab.
8.2 Introduction
8.2.1 A Brief History of the Early Telescope
Although eyeglass-makers had been experimenting with lenses well before 1600, the first mention of a telescope appears in a letter written in 1608 by Hans Lippershey, a Dutch spectacle maker, seeking a patent for a telescope. The patent was denied because of easy telescope duplication and difficulty in patent enforcement.
The instrument spread rapidly. Galileo heard of it in the early 1600s and quickly made improvements in lens grinding that increased the magnification from a relatively low value of 2 to as much as 30. With these more powerful telescopes, he observed the Milky Way, the mountains on the Moon, the phases of Venus, and the moons of Jupiter.
These early telescopes were a type of ‘opera glass,’ producing erect or ‘right side up’ images but having limited magnification. When Johannes Kepler, a German mathematician and astronomer working in Prague under Tycho Brahe, heard of Galileo’s discoveries, he perfected a different form of telescope. Although Kepler’s design inverts the image, it is much more powerful than the Galilean type.
This lab we will use the lenses supplied with the telescope kit. The kit consists of two lenses
and other components to hold the lenses in the proper alignment. The short focal length lens is called the eyepiece and the large focal length lens is called the ’objective’ lens.
First, you will measure the focal length of the eyepiece (magnification) lenses using a simple imaging method. Next, you will measure the focal length of the larger objective lens using an auto-collimation technique.
After this is completed, you will construct a simple telescope. The length of the telescope, when in focus, will be compared with the value expected from your measurements of the focal lengths. As a final exercise, the magnification of the telescope will be determined experimentally and compared against the expected, calculated, values.
8.3 Procedure
8.3.1 Simple Measurement of Eyepieces Lens’s Focal Length
As discussed in the ’Optics of Thin Lenses’ lab, the focal length is the distance from the lens in which parallel light rays are bent and focused to a point (the focal point) after passing through the lens. The focal length is a characteristic of each lens and does not change. Refer to the following diagram.
Figure 8.1: Focusing parallel light rays from a distant object
The eyepiece lens is the smaller diameter lens found inside of the foam holder with a small cardboard tube to align the lens in the foam.
- Tape a sheet of white paper to the table directly under one of the fluorescent ceiling lights. The ceiling light serves as the light source and the paper serves as the imaging screen for focal length measurements.
- Using a ruler, measure the focal length of the eyepiece lens by holding the lens between your fingers and varying the lens height until the image of the light source on the paper is smallest and in focus. (You should be able to see the lines of the light panel; that’s how you know the image is in focus.). Record the value below
Eyepiece lens focal length
Figure 8.2: Auto-Collimation
If d = f , then the emerging rays are parallel to each other. These rays reflect from the mirror, pass back through the lens, and form an image at d. Since the rays incident upon the mirror are parallel, the reflected image is independent of the lens mirror distance, dmirror! If, however, d 6 = f , then the rays emerging from the lens are not parallel and the quality of the reflected image will depend on dmirror.
The method isn’t practical for the small eyepiece lens, so we’ll only do it with the objective lens.
Figure 8.3: Setup for the auto collimation procedure. The light source has an aperture to produce a narrow slit of light. The mirror is at the far end of the optic rail. The objective lens is attached to the holder 35-45 cm from the light source.
- Attach the cardboard aperture slit to the light source face with a small magnet to define a narrow vertical beam of light.
- Attache the object lens to a holder with rubber bands at the edge of the lens. Attach the mirror to another holder. Place the mirror at the far end of the optics rail from the light source. Place the lens 35 - 45 cm from the light source. See figure 8.
- Vary d until a sharp reflected image is produced at the source position. Refer to Figure
- Confirm that the reflected image in independent of dmirror Change the position of the mirror and make sure that the quality of the image is not affected. Use your hand to
Figure 8.4: Auto-Collimation Set-up
block the light between the lens and the mirror. The image should disappear. If it does not then it’s just a reflection from the front surface of the lens, and not what we want.
- Then f = d. Record the focal length of the objective lens below.
Object lens focal length
- Block part of the light from the slit with your finger or an object like a pencil. Does the top or bottom of the image disappear? Is it right-side-up or inverted? Image right-side-up or inverted?
8.3.3 A Two-Lens System: The Telescope
A telescope is designed to perform two functions simultaneously. The first is light collection, and the second is magnification.
Light Collection by the Objective Lens
The size of the objective lens is the most important feature of modern astronomical tele- scopes. The light-gathering property of a telescope is proportional to the surface area of the objective lens (πr^2 ). A large objective lens allows the observation of extremely faint astro- nomical objects and is the telescope’s most costly component. Objective lenses are more expensive because they are large and still must accurately focus the incidence light.
- Pick up the large lens, being careful not to smudge it with your fingers. Fit the curved side of the lens snugly against the front of the outer tube, making sure it is positioned perpendicular to the tube. Also make sure that it is centered on the tube. Slip the plastic cap over this end of the tube so that the lens is firmly held in place.
- Being careful not to smudge it, push the small lens into the foam lens holder.
- Slide the spacer into the foam holder so that it pushes against the flat part of the lens. Push the spacer into the holder just far enough so that the end of the spacer is flat with the end of the foam holder.
- With the curved side of the lens facing toward the large lens, slide the foam holder into the end of the smaller of the sliding tubes. The foam holder should be flat with the end of the tube.
Determining the Properties that Affect the Telescope’s Length
As previously mentioned, the telescope will be in focus when the eyepiece lens is placed approximately one (eyepiece) focal length away from the objective’s inverted image. If the object that you’re looking at is very far away, the objective lens’s image is one (objective) focal length from the objective lens. The eyepiece-to-objective lens separation (L) is thus the sum of these two focal lengths^2 :
L = feyepiece + fobjective
- Go out into the hall and focus your telescope on an object that’s far away. After doing this, measure the length of the telescope.
Measured length of telescope
Do your results agree with the theory? If not, why? (Identify specific sources of error that would result in this inconsistency.) Explain below:
(^2) This is true only when viewing an object that’s far away. For nearby objects, you must determine di
from the thin lens equation, and then add feyepiece to find the telescope’s length.
Investigating the Magnification of a Telescope
In this two-lens system, the magnification of the telescope is equal to the ratio of the objective lens’s focal length to that of the eyepiece lens. You have already measured both of these.
M =
fobjective feyepiece
Directly measuring a telescope’s magnification can be a tricky task. Fortunately, we have a clever way to do it.
Figure 8.7: Count the number of divisions that lie within one of the magnified spaces.
- Aim the telescope towards the ruled scale mounted on the lab wall. Use one eye to look through the telescope, and the other eye to simultaneously look at the wall scale. This method will take some time to perfect. You’ll have to steady the telescope by leaning against a lab table or something.
The magnified image of the scale as scene through the telescope will be visually super- imposed on the unmagnified scale, as depicted in Figure 8.7.
- Count the number of divisions on the unmagnified scale that overlap one division on the magnified scale. This number is the telescope’s magnification. Record the magnification below.
Measured telescope magnification
- Calculate the theoretical magnification predicted by Equation 8.2.
- Calculate the percentage difference between the theoretical magnification and the mea- sured value.
Percentage difference
8.4 Conclusion
Write a conclusion about what you have learned. Include all relevant numbers you have measure with errors. Sources of error should also be included.
