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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

http://www.bgsm.edu/eye/cornea/normal1.htm

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

20/30

Visual acuity is usually measured with a Snellen chart

Furthest distance that a person with normal vision can see object

Furthest distance that the test subjectcan see object

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

eyelenscornea

retina

Normal Myopic (Near-sighted) Hyperopic (Far-sighted)

Common Eye problems - Near and far-sightedness

Relaxed eyes viewing a distant object

retina

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.

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.

What causes myopia?

Concept question on myopia

To correct for myopia or near-sightedness, your glasses need to contain:A. Positive (convex) lensesB. Negative (concave) lensesC. 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 lensB: Concave lensC: 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

http://www.youtube.com/watch?v=aVTjyB0S7Rw&feature=related

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

Ftotal

F1

Lens #1 Lens #2

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?

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

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 to0.5 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

xo’ xi

After correction (viewing new far point)

1/xi + 1/ xo’ = 1/Ftotal= 1/Feye + 1/Fglasses

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 DB. +1 DC. -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 DB. +1 DC. -2 D

Concept Question


Answer:A. -3.0 DB. -0.3 DC. +0.3 D

Concept Question


Answer:A. -3.0 DB. -0.3 DC. +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


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 DB. +1.25 DC. +3 D


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. -3DB. +1.25 DC. +3 D


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 DB. +1 DC. +2.7 D

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