1. Home
  2. College physics
  3. Vision and optical instruments
  4. Physics of the eye

26.1 Physics of the eye  (Page 3/5)

<< Chapter < Page
  College physics     Page 3 / 5
Chapter >> Page >

The eye can detect an impressive amount of detail, considering how small the image is on the retina. To get some idea of how small the image can be, consider the following example.

Size of image on retina

What is the size of the image on the retina of a 1 . 20 × 10 − 2 size 12{1 "." "20" times "10" rSup { size 8{ - 2} } } {} cm diameter human hair, held at arm’s length (60.0 cm) away? Take the lens-to-retina distance to be 2.00 cm.

Strategy

We want to find the height of the image h i , given the height of the object is h o = 1 . 20 × 10 − 2 size 12{h rSub { size 8{0} } =1 "." "20" times "10" rSup { size 8{ - 2} } } {} cm. We also know that the object is 60.0 cm away, so that d o = 60.0 cm size 12{d rSub { size 8{0} } } {} . For clear vision, the image distance must equal the lens-to-retina distance, and so d i = 2.00 cm size 12{d rSub { size 8{i} } } {} . The equation 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} {} can be used to find h i with the known information.

Solution

The only unknown variable in the equation 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} {} is h i size 12{h rSub { size 8{i} } } {} :

h i h o = − d i d o .

Rearranging to isolate h i size 12{h rSub { size 8{i} } } {} yields

h i = − h o ⋅ d i d o .

Substituting the known values gives

h i = − ( 1.20 × 10 − 2 cm ) 2.00 cm 60.0 cm = − 4.00 × 10 − 4 cm .

Discussion

This truly small image is not the smallest discernible—that is, the limit to visual acuity is even smaller than this. Limitations on visual acuity have to do with the wave properties of light and will be discussed in the next chapter. Some limitation is also due to the inherent anatomy of the eye and processing that occurs in our brain.

Got questions? Get instant answers now!

Power range of the eye

Calculate the power of the eye when viewing objects at the greatest and smallest distances possible with normal vision, assuming a lens-to-retina distance of 2.00 cm (a typical value).

Strategy

For clear vision, the image must be on the retina, and so d i = 2.00 cm here. For distant vision, d o ≈ ∞ , and for close vision, d o = 25.0 cm , as discussed earlier. The equation P = 1 d o + 1 d i as written just above, can be used directly to solve for P in both cases, since we know d i and d o size 12{d rSub { size 8{0} } } {} . Power has units of diopters, where 1 D = 1/m size 12{"1D"="1/m"} {} , and so we should express all distances in meters.

Solution

For distant vision,

P = 1 d o + 1 d i = 1 ∞ + 1 0.0200 m .

Since 1 / ∞ = 0 size 12{1/ infinity =0} {} , this gives

P = 0 + 50 . 0 / m = 50.0 D (distant vision).

Now, for close vision,

P = 1 d o + 1 d i = 1 0.250 m + 1 0.0200 m = 4.00 m + 50.0 m = 4.00 D + 50.0 D = 54.0 D (close vision). alignl { stack { size 12{P= { {1} over {d rSub { size 8{o} } } } + { {1} over {d rSub { size 8{i} } } } = { {1} over {0 "." "250 m"} } + { {1} over {0 "." "0200 m"} } } {} #= { {4 "." "00"} over {m} } + { {"50" "." 0} over {m} } =4 "." "00"D+"50" "." 0D {} # ="54" "." 0D {}} } {}

Discussion

For an eye with this typical 2.00 cm lens-to-retina distance, the power of the eye ranges from 50.0 D (for distant totally relaxed vision) to 54.0 D (for close fully accommodated vision), which is an 8% increase. This increase in power for close vision is consistent with the preceding discussion and the ray tracing in [link] . An 8% ability to accommodate is considered normal but is typical for people who are about 40 years old. Younger people have greater accommodation ability, whereas older people gradually lose the ability to accommodate. When an optometrist identifies accommodation as a problem in elder people, it is most likely due to stiffening of the lens. The lens of the eye changes with age in ways that tend to preserve the ability to see distant objects clearly but do not allow the eye to accommodate for close vision, a condition called presbyopia    (literally, elder eye). To correct this vision defect, we place a converging, positive power lens in front of the eye, such as found in reading glasses. Commonly available reading glasses are rated by their power in diopters, typically ranging from 1.0 to 3.5 D.

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

(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.

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Questions & Answers

material that allows electric current to pass through
Deng Reply
material which don't allow electric current is called
Deng
insulators
Covenant
how to study physic and understand
Ewa Reply
what is conservative force with examples
Moses
what is work
Fredrick Reply
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
AI-Robot
why is it from light to gravity
Esther Reply
difference between model and theory
Esther
Is the ship moving at a constant velocity?
Kamogelo Reply
The full note of modern physics
aluet Reply
introduction to applications of nuclear physics
aluet Reply
the explanation is not in full details
Moses Reply
I need more explanation or all about kinematics
Moses
yes
zephaniah
I need more explanation or all about nuclear physics
aluet
Show that the equal masses particles emarge from collision at right angle by making explicit used of fact that momentum is a vector quantity
Muhammad Reply
yh
Isaac
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
Majok Reply
what is frontier of physics
Somto Reply
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Gufraan Reply
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
Ezekiel Reply
please explain
Samuel
what's the definition of physics
Mobolaji Reply
what is physics
Nangun Reply
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
AI-Robot
<< Chapter < Page Page > Chapter >>
Practice Key Terms 2

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask