<< Chapter < Page 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

the meaning of phrase in physics
Chovwe Reply
is the meaning of phrase in physics
Chovwe
write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
Gabriel Reply
how does a model differ from a theory
Friday Reply
what is vector quantity
Ridwan Reply
Vector quality have both direction and magnitude, such as Force, displacement, acceleration and etc.
Besmellah
Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
Jack Reply
what's electromagnetic induction
Chinaza Reply
electromagnetic induction is a process in which conductor is put in a particular position and magnetic field keeps varying.
Lukman
wow great
Salaudeen
what is mutual induction?
je
mutual induction can be define as the current flowing in one coil that induces a voltage in an adjacent coil.
Johnson
how to undergo polarization
Ajayi Reply
show that a particle moving under the influence of an attractive force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v²k² and distance uk²/√u-vk as origin
Gabriel Reply
show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
Gabriel Reply
No idea.... Are you even sure this question exist?
Mavis
I can't even understand the question
Ademiye
yes it was an assignment question "^"represent raise to power pls
Gabriel
mu/y³ u>v²k² uk²/√u-vk please help me out
Gabriel
An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg . Pendulum 2 has a bob with a mass of 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º .
Imtiaz Reply
no ideas
Augstine
if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
Ademiye
Modern cars are made of materials that make them collapsible upon collision. Explain using physics concept (Force and impulse), how these car designs help with the safety of passengers.
Isaac Reply
calculate the force due to surface tension required to support a column liquid in a capillary tube 5mm. If the capillary tube is dipped into a beaker of water
Mildred Reply
find the time required for a train Half a Kilometre long to cross a bridge almost kilometre long racing at 100km/h
Ademiye
method of polarization
Ajayi
What is atomic number?
Makperr Reply
The number of protons in the nucleus of an atom
Deborah
type of thermodynamics
Yinka Reply
oxygen gas contained in a ccylinder of volume has a temp of 300k and pressure 2.5×10Nm
Taheer Reply
Practice Key Terms 2

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