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  4. Geometric optics and image
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2.5 The eye  (Page 4/11)

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Correcting farsightedness consists simply of using the opposite type of lens as for nearsightedness (i.e., a converging lens), as shown in [link] .

Such a lens will produce an image of physical objects that are closer than the near point at a distance that is between the near point and the far point, so that the person can see the image clearly. To determine the optical power needed for correction, you must therefore know the person’s near point, as explained in [link] .

Figure shows two eyes with a bi-convex lens in front of each. The first one shows rays from a close object striking the lens and deviating towards each other before striking the cornea. They then converge on the retina. The second one shows an object close to the lens and an upright, larger image farther away from the lens.
Correction of farsightedness uses a converging lens that compensates for the underconvergence by the eye. The converging lens produces an image farther from the eye than the object, so that the farsighted person can see it clearly.

Correcting farsightedness

What optical power of eyeglass lens is needed to allow a farsighted person, whose near point is 1.00 m, to see an object clearly that is 25.0 cm from the eye? Assume the corrective lens is fixed 1.5 cm from the eye.

Strategy

When an object is 25.0 cm from the person’s eyes, the eyeglass lens must produce an image 1.00 m away (the near point), so that the person can see it clearly. An image 1.00 m from the eye will be 100 cm − 1.5 cm = 98.5 cm from the eyeglass lens because the eyeglass lens is 1.5 cm from the eye. Therefore, d i = −98.5 cm , where the minus sign indicates that the image is on the same side of the lens as the object. The object is 25.0 cm − 1.5 cm = 23.5 cm from the eyeglass lens, so d o = 23.5 cm .

Solution

Since d i and d o are known, we can find the optical power of the eyeglass lens by using [link] :

P = 1 d o + 1 d i = 1 0.235 m + 1 −0.985 m = + 3.24 D .

Significance

The positive optical power indicates a converging (convex) lens, as expected. If you examine eyeglasses of farsighted people, you will find the lenses to be thickest in the center. In addition, prescription eyeglasses for farsighted people have a prescribed optical power that is positive.

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Summary

  • Image formation by the eye is adequately described by the thin-lens equation.
  • The eye produces a real image on the retina by adjusting its focal length in a process called accommodation.
  • Nearsightedness, or myopia, is the inability to see far objects and is corrected with a diverging lens to reduce the optical power of the eye.
  • Farsightedness, or hyperopia, is the inability to see near objects and is corrected with a converging lens to increase the optical power of the eye.
  • In myopia and hyperopia, the corrective lenses produce images at distances that fall between the person’s near and far points so that images can be seen clearly.

Conceptual questions

If the lens of a person’s eye is removed because of cataracts (as has been done since ancient times), why would you expect an eyeglass lens of about 16 D to be prescribed?

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When laser light is shone into a relaxed normal-vision eye to repair a tear by spot-welding the retina to the back of the eye, the rays entering the eye must be parallel. Why?

A relaxed, normal-vision eye will focus parallel rays of light onto the retina.

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Why is your vision so blurry when you open your eyes while swimming under water? How does a face mask enable clear vision?

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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