Job #4:The World's First Camera, or, How the Human Eye Works

  The human eyeball is roughly a sphere about 4cm. in diameter. In the front of the eye, just inside the opening called the pupil, is the lens. It is a soft lens, surrounded by muscles which can cause it to change shape slightly. In this way the focussing reflexes of your eye can bring objects at various distances into focus, by changing the focal length of the eye lens.

  Objects that you "see" are imaged at the rear surface of the eyeball, on a region called the retina. On the retina are the rods and cones which contain the light-sensitive chemicals that translate light into nerve signals, which are then passed on to your brain.

  In the calculations that you do in this part, assume that the distance from the eye-lens to the retina is fixed at 4.0cm. (This is d(i), the image distance, and not the focal length.) While a camera focusses by changing the image distance (the distance from the camera lens to the film), the eye focusses by adjusting the focal length of the eye-lens.



(a) We should, at this point, introduce you to "Ferdinand." (The drawing above is not to scale.)
your teacher will fill in the blank for Ferdinand's height here
Ferdinand is actually         cm tall (from his feet to the top of his hat)
  Draw the rays which cross at the center of the lens, and thus show where on the retina Ferdinand's hat and his shoes are imaged. Calculate the height of the Image of Ferdinand.

Equation that you used:



h(i)
the image height

_______cm
  Calculate the focal length of the eye-lens when the eye is looking at Ferdinand at a distance of 10 meters. Assume that the eye lens is able to fucus his image on the retina.
Equation that you used:



f
the focal length

_______cm

(b)  The closest distance at which most people can "focus" an object is about 10cm. Can you do this well? or better? Measure the closest distance at which your eye can focus on an object. Close or cover one of your eyes, and hold this page in front of your open eye. Bring the page toward you gradually (or move your head gradually toward the computer screen) until you can no longer read the small print.

The measured object distance of closest approach for your eye, do, is _______ cm

    In order to read the small print at your closest object distance, do, as you have just done, your eye muscles had to change the focal length of your eye-lens from its value in (a) to a new value. Calculate what focal length your eye-lens has when it is focuses at your closest distance.

Equation that you used:


f
at closest approach for your eye


_____cm
Solved for focal length, f


Is this a ______ rounder    or a ______ flatter    lens than in (a)?

(c) Resolving Power of your Retina

   In Part (b) above, you determined how close you could place an object to your eye and still be able to focus your eye-lens and obtain a clear image of the object on your retina.

   There is one other limitation on the ability of your eye to "see" an object clearly. This has to do with size, rather than focusing.
   The rods and cones in your retina are the "antennae" that translate the image that is focused on the retina into nerve impulses.
   If an object, or the details in an object, are so small that their image size is not much larger than the distance between the rods and cones, then you will not be able to see the object clearly. The name given to the ability of the eye to distinguish the smallest object is "resolving power."

   To determine the resolving power of your retina, have someone hold the ½cm tall letters above (or look at them on the computer screen), and see how far away you can be and still read them. (Since this is a matter of resolving power, rather than focussing, wear your corrective glasses for this experiment if you normally wear glasses.)

The measured farthest distance at which you can read RZAFLPDQ is _______cm

   Now find from this information what the smallest image is that your retina can distinguish. Calculate the height of the image of the ½cm letters on your retina; assume that the distance from your eye to RZAFLPDQ is the distance you have just measured. Assume that the distance from the eye-lens to the retina is 4cm.

Equation that you used:




height of smallest
image your retina
can distinguish:

_______cm

  Say "RZAFLPDQ" seven times, out loud, as fast as you can.

(d) The moon is 380,000 km away. The ruins of an ancient civilization of moon-beings lies buried in the Rzaflp Crater.
your teacher will give you the crater's diameter (check "answers" for possible values)

You are given that the diameter of the Rzaflp Crater is _____ km

   Can your eye resolve ("see") the Rzaflp Crater? To determine the answer, calculate the diameter ("height") of the image of this crater on the retina of your eye. (Use eye-lens to retina distance of 4cm)

Equation that you used:



the size of the
image of the crater
on your retina is

_______cm

Compare the retinal image size of the crater with the "size of the smallest image you can distinguish," [above].

Thus, can you distinguish the Rzaflp Crater?
Your conclusion: Can your eye distinguish the Rzaflp Crater? _________

Do you think a telescope might help?

[Well, of course. That's what telescopes are for! Read on...]

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