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.

    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.

(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.)

   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.

(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)

   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)

Do you think a telescope might help?