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Test prep for ap courses

A tree that is 3 m tall is viewed from a distance of 25 m. If the cornea-to-retina distance of an ideal eye is 2 cm, how tall is the image of the tree on the observer’s retina?

  1. 0.24 cm
  2. 0.5 cm
  3. 0.5 m
  4. 0.08 cm

(a)

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Often people with lens-to-retina distances smaller than 2 cm purchase glasses to place in front of their eyes.

  1. Explain why people with lens-to-retina distances smaller than 2 cm need glasses.
  2. Explain whether the glasses should be composed of converging or diverging lenses.
  3. Draw a ray diagram demonstrating the ability to see with and without the glasses.
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Section summary

  • Image formation by the eye is adequately described by the thin lens equations:
    P = 1 d o + 1 d i and h i h o = d i d o = m . size 12{ { {h rSub { size 8{i} } } over {h rSub { size 8{o} } } } = - { {d rSub { size 8{i} } } over {d rSub { size 8{o} } } } =m} {}
  • The eye produces a real image on the retina by adjusting its focal length and power in a process called accommodation.
  • For close vision, the eye is fully accommodated and has its greatest power, whereas for distant vision, it is totally relaxed and has its smallest power.
  • The loss of the ability to accommodate with age is called presbyopia, which is corrected by the use of a converging lens to add power for close vision.

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 a spectacle lens of about 16 D to be prescribed?

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A cataract is cloudiness in the lens of the eye. Is light dispersed or diffused by it?

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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?

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How does the power of a dry contact lens compare with its power when resting on the tear layer of the eye? Explain.

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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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Problem exercises

Unless otherwise stated, the lens-to-retina distance is 2.00 cm.

What is the power of the eye when viewing an object 50.0 cm away?

52.0 D

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Calculate the power of the eye when viewing an object 3.00 m away.

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(a) The print in many books averages 3.50 mm in height. How high is the image of the print on the retina when the book is held 30.0 cm from the eye?

(b) Compare the size of the print to the sizes of rods and cones in the fovea and discuss the possible details observable in the letters. (The eye-brain system can perform better because of interconnections and higher order image processing.)

(a) 0 . 233 mm size 12{ - 0 "." "233"" mm"} {}

(b) The size of the rods and the cones is smaller than the image height, so we can distinguish letters on a page.

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Suppose a certain person’s visual acuity is such that he can see objects clearly that form an image 4.00 μm high on his retina. What is the maximum distance at which he can read the 75.0 cm high letters on the side of an airplane?

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People who do very detailed work close up, such as jewellers, often can see objects clearly at much closer distance than the normal 25 cm.

(a) What is the power of the eyes of a woman who can see an object clearly at a distance of only 8.00 cm?

(b) What is the size of an image of a 1.00 mm object, such as lettering inside a ring, held at this distance?

(c) What would the size of the image be if the object were held at the normal 25.0 cm distance?

(a) +62.5 D

(b) –0.250 mm

(c) –0.0800 mm

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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