Physlet Illustration: Correcting Far-Sightedness

 

 

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Focal Length = mm

The human eye accommodates for near and far objects by changing its focal length.   However, in the case of a far-sighted person, even when the ciliary muscles are completely relaxed, the image that is formed is behind the retina.  Therefore, this person must wear corrective lenses in order to be able to focus on nearby objects.  In this simulation the object is an arrow located 200 mm to the left of the retina.  What focal length must these lenses be if they are worn 20 mm in front of the eyes? Once again, the effect of the cornea has been included in the eye's lens (outlined in red) and positions are given in millimeters and angles in degrees.  You may vary the focal length of the corrective lens from -2000 mm to 2000 mm.  The uncorrected eye can be observed by setting the focal length to 2000 mm.

Hints:

  1. Where is the image from the eye's lens formed when the corrective lens has a negative focal length?
  2. Where is the image from the eye's lens formed when the corrective lens has a positive focal length?
  3. Adjust the focal length of the corrective lens until the image forms on the retina.  What power does this correspond to?
  4. Can you calculate the effective focal length of the eye's lens in this case?

Reference

See Walker, Sections 27-2

Illustration written by Chuck Niederriter