Physics 1230: Light and Color
• The Eye: Vision variants and Correction
http://www.colorado.edu/physics/phys1230
What does 20/20 vision mean?
Snellen chart
Visual acuity is usually measured with a Snellen chart
Furthest distance
that the test subject
can see object
20/30
Furthest distance that a
person with normal
vision can see object
Examples:
20/20 vision - Normal
20/40 vision - Worse than normal.
- Can see at 20 feet what someone
with normal vision can see at 40 feet
- Can only see letters that are twice as
large as someone with normal vision
20/15 vision - Better than normal
http://www.bgsm.edu/eye/cornea/normal1.htm
Levels of Vision
* 20/20 - Normal vision. Fighter pilot minimum. Required to read the stock
quotes in the newspaper, or numbers in the telephone book.
* 20/40 - Able to pass Driver's License Test in all 50 States. Most printed
material is at this level.
* 20/80 - Able to read alarm clock at 10 feet. News Headlines are this size.
* 20/200 - Legal blindness. Able to see STOP sign letters.
* For normal vision, the far point (or farthest point that can be seen) is usually
infinity.
* For normal vision, the near point (or closest point that can be seen) is ≈ 25
cm.
How does the eye form an image? (revision)
T he eye uses 2 lenses to form a sharp image on the retina :
• Cornea – Strong lens of fixed focal length – does most of the focusing
• Eyelens – Weaker lens of variable focal length
- Enables us to focus on objects at different distances
cornea
eyelens
retina
Common Eye problems - Near and far-sightedness
Relaxed eyes viewing a distant object
retina
Normal
Myopic (Near-sighted)
Hyperopic (Far-sighted)
Primarily determined by:
• Shape of cornea (crude focusing)
• Length of eyeball
Normal Eye
THE NORMAL EYE
• For clear vision, objects focused exactly on retina
• Cornea’s curvature (or its focal length) exactly match to length of eyeball
http://www.lasersite.com/Eyeworks/index.htm
Near-sighted eye (Myopic)
THE NEAR-SIGHTED EYE
- Cornea is too curved (focal length too short) or eyeball too long
- Image of distant object forms in front of retina.
- Image on retina is blurred
What the world looks like with myopia
• Foreground clear
• Distant objects blurred
Who has myopia?
Approximately one in four Americans is near-sighted, totaling 70 million
people. The degree of myopia can vary from low (-1 to -3 diopters) to high
(greater than 6 diopters). Myopia tends to start in the early teens (earlier
for high myopes), and increases as the eye grows in length during puberty. It
tends to stabilize after age 18.
What causes myopia?
Myopia is not caused by reading at an early age, prolonged reading, reading in
the dark, watching TV too closely, wearing glasses too strong, wearing
glasses too weak, or other similar folklore. Some controversy exists over
whether myopia can be made worse by prolonged near work as a child, but
this has never been proven.
In studies, it has been correlated with higher I.Q.s., but this probably has to
do with the fact that myopes tend to read more since that's where they can
see the best without glasses (see below). Myopia tends to run in families, so
it is probably inherited.
Concept question on myopia
To correct for myopia or near-sightedness, your glasses
need to contain:
A. Positive (convex) lenses
B. Negative (concave) lenses
C. Bifocals
Concept question on myopia
To correct for myopia or near-sightedness, your glasses
need to contain:
A. Positive (convex) lenses
B. Negative (concave) lenses
C. Bifocals
Correction for myopia
Relaxed myopic eye
No glasses -
This is the furthest object
that can be seen clearly
With glasses with
negative lenses -
A very distant object can
be seen clearly
Far sighted eye (Hyperopia)
THE FAR-SIGHTED EYE
- Cornea is not curved enough (focal length too long) or eyeball too short
- Image of distant object forms behind retina.
- Image on retina is blurred
What the world looks like with hyperopia
- Distant objects blurred
- Foreground even more fuzzy
Concept question on hyperopia
To correct for hyperopia, do you need glasses with:
A: Convex lens
B: Concave lens
C: Bifocals
Concept question on hyperopia
To correct for hyperopia, do you need glasses with:
A: Convex lens
B: Concave lens
C: Bifocals
Correction for hyperopia
Relaxed hyperopic eye
a) Viewing nearby object -blurred
b) Viewing nearest clear object
c) Viewing nearby object with
convex glasses – clear image
Other facts about hyperopia
Hyperopia (i.e far-sightedness) is much less common than myopia or
emmetropia. It is typically in the +1.00 to +4.00 diopter range, rarely it can
be as high as +8.00 diopters.
In contrast to myopia, hyperopia occurs when the eye is too short for the
power of its optical components (i.e. lens is too weak). In hyperopia, the
cornea is not steep enough and light rays hit the retina before they come
into focus. Distant objects appear blurred, and nearby objects are even more
fuzzy. Most farsighted individuals need corrective eyewear to see clearly at
all distances.
Correction of hyperopia requires a lens which is convex (i.e. thicker in the
middle than the edges). This acts as a magnifier, and causes objects to
appear bigger by 2% per diopter. For this reason hyperopes while wearing
their spectacle correction, appear to have "big" eyes. Optical aberrations and
decreased peripheral vision occur are likely to occur with large amounts of
hyperopia.
Treatments for myopia
• Glasses
• Contact lenses
• Eye surgery → flatten the cornea
– Radial keratotomy
– Photorefractive keratotomy (PRK)
– LASIK
Radial Keratotomy
• Cut several spoke-like slits in the cornea with a diamond knife
• Causes central area to flatten and focal length increase.
• 85% of people achieve 20/40 vision or better
Photorefractive keratotomy (PRK)
• Uses a computer controlled eximer laser
• Laser emits pulses lasting only billionths of a second
• Laser vaporises microscopic slivers from the cornea – theoretically making very
accurate and specific modifications to its shape.
• Procedure takes 1-2 minutes
• Procedure is pain free but 10-20% of people feel pain for weeks afterwards
• 95% achieve 20/40 vision or better
LASIK
•
•
•
•
Like PRK but performed deeper inside the cornea
A surface flap is removed and then replaced to give access inside cornea.
Generally results in quicker and less painful recovery than PRK
Early studies suggest better final vision than RK or PRK
Side effects of corrective eye surgery
* May still need glasses — With RK, approximately 10 percent to 30 percent of
people who have the procedure require some use of corrective lenses; with PRK,
between 5 percent and 15 percent. Also, everyone's eyes degenerate with age, so by
about age 40, you may find yourself needing bifocals for sharp near vision.
* Night vision may be poor: Some may see "halos" around lights, which can make
night driving difficult. For some, this side effect passes. For others, it is permanent.
* May see variation in visual acuity — For some, eyesight may be better in the
morning and less sharp at day's end. Some may experience light sensitivity and glare.
•In very rare cases, there may be corneal scarring or rupturing — Because the
cornea is weakened in RK, there is a threat of corneal rupture at the incision site if
the eye is hit.
• Unknown or unexpected complications – e.g. blindness at altitude in 1996 Everest
disaster
DIOPTERS AND
YOUR PRESCRIPTION
Diopters are used to measure the refractive error of the eye and the
power of the lens needed to correct this error
-Negative number (myopia, nearsightedness)
-Positive number (hyperopia, farsightedness).
-A -1.00 diopter myope is able to see objects at 1m clearly
-A -2.00 diopter myope is able to see objects at 1/2m clearly
Your prescription contains 4 numbers:
1. Amount (in diopters) of myopia (- numbers) or hyperopia (+ numbers).
2. Amount of astigmatism.
3. Axis of the astigmatism.
4. Amount of magnification needed for clear vision at near (bifiocals)
Concept question - Adding lenses
Lens #1
Lens #2
F1
F2
What is the combined focal length of two convex lenses
A: Shorter than either F1 or F2?
B: Between F1 and F2?
C: Longer than either F1 or F2?
Concept question - Adding lenses
Lens #1
Lens #2
F1
F2
Ftotal
What is the combined focal length of two convex lenses
A: Shorter than either F1 or F2?
B: Between F1 and F2?
C: Longer than either F1 or F2?
Formula for adding lenses
F
To add lenses, add their POWERS (not their focal lengths)
Power (in diopters) = 1/F, and F is the focal length (in m)
So Ptotal = P1 + P2
or 1/Ftotal = 1/F1 + 1/F2
Example of adding lenses
F
Question: If F1 is 25 cm, and F2 is 1 m, what is Ftotal?
Answer:
P1 = 4 D and P2 = 1 D
=> Ptotal = P1 + P2 = 5 D
=> Ftotal = 1/5 m = 20 cm
Another example of adding lenses
Question: If F1 is 0.5 m, and F2 is -1 m, what is Ftotal?
Answer:
P1 = 2 D and P2 = -1 D
=> Ptotal = P1 + P2 = 1 D
=> Ftotal = 1 m
Concept Question on Adding Lenses
F
Question: If F1 is 50cm, and F2 is 1m, what is Ftotal?
A. -1m
B. 33cm
C. 1.5m
Concept Question on Adding Lenses
F
Question: If F1 is 50cm, and F2 is 1m, what is Ftotal?
A. -1m
B. 33cm
C. 1.5m
Calculating your prescription
To calculate your prescription, calculate the
difference in diopters between what you want to
see and what you can see
Calculating your prescription -Example
Question: A near-sighted person wants to see to infinity
but does not see clearly beyond 2 meters. What kind and
strength of eyeglasses do they need?
Answer: -0.5 D
How did I get this answer?
Convert the infinity to zero diopters, and the 2 m to
0.5 D. The difference is -0.5 D.
Why is the number negative?
You need a negative lens to correct for near-sightedness
Calculating your prescription – application of thin lens equation
Before correction (viewing far point)
1/xi + 1/ xo = 1/Feye
xo
xi
After correction (viewing new far point)
1/xi + 1/ xo’ = 1/Ftotal
= 1/Feye + 1/Fglasses
xo’
xi
Subtract before from after:
1/xo’ – 1/xo = 1/Fglasses
Change in 1/(object distance) = Power of lens required (or your prescription)
Concept Question
Question: A near-sighted person wants to see to infinity
but does not see clearly beyond 1 meter. What kind
and strength of eyeglasses do they need?
Answer:
A. -1 D
B. +1 D
C. -2 D
.
Concept Question
Question: A near-sighted person wants to see to infinity
but does not see clearly beyond 1 meter. What kind
and strength of eyeglasses do they need?
Answer:
A. -1 D
B. +1 D
C. -2 D
Concept Question
Question: A near-sighted person wants to see to infinity
but does not see clearly beyond 3 meters. What kind
and strength of eyeglasses do they need?
Answer:
A. -3.0 D
B. -0.3 D
C. +0.3 D
Concept Question
Question: A near-sighted person wants to see to infinity
but does not see clearly beyond 3 meters. What kind
and strength of eyeglasses do they need?
Answer:
A. -3.0 D
B. -0.3 D
C. +0.3 D
.
Example on Hyperopia
Question: A far-sighted person sees no closer than 0.5
meters. They want to read at the normal 25 cm distance.
What kind and strength of eyeglasses do they need?
Answer: +2D
How did I get this answer?
Convert the 0.5 m to 2 D, and the 25 cm to 4 D. The
difference is +2 D.
Why is the sign +?
To correct for far-sightedness, you need a positive lens
Example on Hyperopia
Question:A far-sighted person sees no closer than 0.5 meters. They want to
read at the normal 25 cm distance. What kind and strength of eyeglasses do
they need?
Answer: +2 D
How did I get this answer?
Convert the 0.5 m to 2 D, and the 25 cm to 4 D. The difference is +2 D.
OR
Before correction 1/xi + 1/ xo = 1/Feye
So 2 + 1/L = 1/Feye
After correction So 4 + 1/L = 1/Feye + 1/Fglasses = 2 + 1/L + 1/Fglasses
=> 2 = 1/Fglasses
Concept question on hyperopia
Question: A far-sighted person sees no closer than 1
meter. They want to read at the normal 25 cm
distance. What kind and strength of eyeglasses do
they need?
Answer:
A. -3 D
B. +1.25 D
C. +3 D
Concept question on hyperopia
Question: A far-sighted person sees no closer than 1
meter. They want to read at the normal 25 cm
distance. What kind and strength of eyeglasses do
they need?
Answer:
A. -3D
B. +1.25 D
C. +3 D
Concept question on hyperopia
Question: A far-sighted person sees no closer than 0.75
meter. They want to read at the normal 25 cm
distance. What kind and strength of eyeglasses do
they need?
Answer:
A. -2.7 D
B. +1 D
C. +2.7 D
Concept question on hyperopia
Question: A far-sighted person sees no closer than 0.75
meter. They want to read at the normal 25 cm
distance. What kind and strength of eyeglasses do
they need?
Answer:
A. -2.7 D
B. +1 D
C. +2.7 D