Job #5:The Telescope, or,
How the Dutch Lens Grinders Made Galileo Famous

You found out that your eye would not be able to resolve the Rzaflp Crater. Of course you know that telescopes are made for just that situation: to help your eye be able to an object that is too small to see with the naked eye. What we expect the telescope to do for us is to enlarge the image of the crater on your retina, so that the image spans the space occupied by many rods and cones.

Let us then have a look at the Rzaflp Crater through the telescope sketched below. Note that the drawing is not to scale.

My crater diameter is _______ km
To remind yourself of the diameter of your Rzaflp Crater (from Job #4) for the calculations that follow, write it again here:



Notice that the telescope consists of two lenses. It is easiest to break up the analysis of the telescope into two parts:

(1) The light comes in from the right, from very far off. The distance from the crater on the moon to the objective lens is the object distance for the objective lens; this distance is called do(objective lens). The objective lens forms the "first image", inside the telescope, a distance di(objective lens) to the left of the objective lens. This distance is essentially the length of the telescope, and, as you will see, telescopes are long because the longer this distance is, the greater is the magnification of the telescope.

(2) Next, this "first image" actually becomes the object for the second lens, in which the "first image" is viewed very close up by your eye. This second lens is a combination of the lens in your eye (your eye-lens) with the eye-piece lens of the telescope. This combination eye-and-eyepiece-lens "looks at" and focuses the "first image" of the crater on the retina of your eye. The "first image" is the object that the eye-and-eyepiece-lens focuses on the retina.

Now, here is your work assignment:

(a) The objective lens of our telescope has a focal length of 76cm. Compared with 76cm, the distance to the object (the crater) is practically infinite.
image distance, di(objective lens)
is _______ cm
Therefore you can immediately determine the image distance, di(objective lens) even without any calculations. This distance is how far back from the objective lens the crater will be imaged ("first image").

(b) Now Calculate the diameter ("height"), h(eyepiece object), of the "first image" of the Rzaflp Crater.

Equation that you used:



h(eyepiece object)
the diameter of "first image"

_______cm

(c) Now, forget the objective lens and all the distances associated with it, and consider only the "first image" and how your eye observes it, using the eye-piece optics. (Note: The "first image" is now the object. We could call it the "eye-piece object.")
  The eye-piece lens allows us to bring the eye closer to the "first image," which increases the size of the retinal image formed by the eye-lens. The eye-piece lens (of the telescope) works together with the eye-lens, as a combination lens, to focus the "first image" on the retina.

  The focal length of our telescope eyepiece is 3.8cm.
  The focal length of the eye-lens for comfortable viewing is 4.0cm.

  From this information, calculate the focal length of the combination lens made up of the eyepiece lens and the eye-lens.

Equation that you used:

1/(fcomb) =            

(fcomb)
the combination focal length

_______cm

(d) In a telescope, the eye-piece lens slides in and out so that you can place it at the appropriate "object" distance, do(eye-piece), of the eyepiece optics to make the eye-lens-eyepiece-lens combination focus the "first image" on the retina.
  You know that the image distance of the eyepiece, di(eye-piece), is 4cm, and you have just calculated the focal length of the eye-eyepiece combination.

  With this information, calculate the distance, do(eye-piece) from the "first image" to the eye-eyepiece combination.

Equation that you used:



do(eye-piece)
the eyepiece object distance

_______cm

(e) Now you can calculate the diameter ("height") of the retinal image of the crater as seen through the telescope. (You do not need to go back to the objective-lens optics.) Use the diameter of the "first image" and what you have calculated for the eyepiece optics.

Equation that you used:



Diameter of the retinal image of the Rzaflp crater

_______cm

_____Yes    _____No
(f) Compare this image size with "Size of the smallest image your retina can distinguish"
                  (part 4 [c]).Can your retina distinguish the crater with the help of the telescope?

(g) The Magnification of the telescope is the ratio of the magnified retinal image size [e] to the size of the crater image on the retina obtained with the unaided eye (part 4 [d]). Calculate this ratio.

The Magnification of this telescope:



(h) Now get ready for a very exciting surprise Are you ready?
  Write the ratio of the focal length of the objective lens to the focal length of the eyepiece lens (just the eyepiece lens of the telescope, not the combination of it with the eye-lens).

fobjective lens                  =
feye-piece lens

Compare [g] and [h]. What general rule does this suggest?

General rule that is suggested by this example:




(Of course this rule has not been proved by this one example alone. However, this rule can be proved to be generally true.)

(i) Would you like someone to give you a telescope for graduation?

Back to Job #1: Sally and Kenny go Wading
Back to Job #2: The famous fishing pole paradox
Back to Job #3: How a prism separates blue light from red light
Back to Job #4: The World's First Camera, or, How the Human Eye Works
On to the Telescope Lab: Take two lenses and make a telescope right there in the lab
Answers to "Job" problems
Back to Optics Main menu

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