Visual Acuity

Visual acuity often is referred to as “Snellen” acuity.  The chart and the letters are named for a 19th-century Dutch ophthalmologist Hermann Snellen (1834–1908) who created them as a test of visual acuity.

One’s visual acuity is an indication of the clarity or clearness of one’s vision.  It is a measurement of how well a person sees.  The word “acuity” comes from the Latin acuitas, which means sharpness.

20/20 or 6/6 visual acuity

The reason that the number “20” is used in visual acuity measurements is because, in the United States, the standard length of an eye exam room (that is, the distance from the patient to the acuity chart) is about 20 feet.

Someone with 20/20 or 6/6 vision (visual acuity) is just able to decipher a letter that subtends a visual angle of 5 minutes of arc (written 5') at the eye.  (5' of arc is 5/60 of a degree, since there are 60' of arc in 1 degree.)  What this means is that if you draw a line from the top of a 20/20 letter to the eye and another line from the bottom of the letter to the eye, the size of the angle at the intersection of these two lines at the eye is 5' of arc.

Also, the individual parts of the letter subtend a visual angle of 1' of arc at the eye.  It does not matter how far away something is from the eye; if it subtends an angle of 5' of arc at the eye, then a person with 20/20 visual acuity will just be able to distinguish what it is.

A person with 20/20 vision could stand 30 feet away from a test chart and just decipher a 20/30 letter on the chart, since at that distance a 20/30 letter would subtend an angle of 5' of arc at the person’s eye.  That same person could stand 80 feet away from the chart and be able to decipher a 20/80 letter, or 200 feet away to be able to decipher a 20/200 letter.

20/20 compared with other acuities

Someone with 20/20 visual acuity does not have “perfect” vision, since it is quite possible to see better than 20/20.  The less the bottom number in the visual acuity ratio, the better the acuity; and the greater the bottom number, the worse the acuity.  Therefore, 20/15 acuity is better than 20/20 acuity, while 20/30 acuity is not as good as 20/20 acuity.  Also, 20/15 acuity is equivalent to 6/4.5 acuity, while 20/30 acuity is the same as 6/9 acuity.

As noted before, although 20/20 is "normal" visual acuity for most people, it is possible (and, in fact, very common) to be able to see better than that.  For instance, many people have 20/15 visual acuity.  A person with 20/15 acuity can stand 20 feet away from an object and see it as well as a person with 20/20 acuity moving up to 15 feet away from the object to view it.

If that is true, let’s take a person with 20/15 vision looking at an object from 100 feet away.  Where would a person with 20/20 vision need to stand to see the object just as well?  The answer is 75 feet away from the object.  (That is, 15/20 × 100 feet = 75 feet.)

It even is possible, although not too common, for someone to have 20/10 visual acuity.  Let’s say a person with 20/20 vision can just detect a ship which is 25 miles away out on the ocean.  A person with 20/10 acuity could be 50 miles away from the ship and still be able to just detect it.  That is, if a person with 20/10 acuity can just tell what an object is, a person with 20/20 vision would need to stand half that distance away to be able to see what it is.

You can use the same rationale when considering someone with less than 20/20 acuity.  Consider a person with 20/40 visual acuity (which is what someone needs in most states to acquire a driver’s license).  If a person with 20/20 acuity can just read a sign which is 60 feet down the road, the person with 20/40 acuity would have to be 30 feet away to read the same sign.  Also, a person with 20/15 acuity could be 80 feet away, and a person with 20/10 acuity 120 feet away, to read the same sign.

Compared to a person with 20/20 vision reading a sign 30 feet away, how far do people with various visual acuities need to stand away from the sign to be able to read it as well as the person with 20/20 acuity?  See the following chart:

near visual acuity

Besides a person’s visual acuity being tested at a far distance, one’s near acuity also can be tested.  Testing typically is done by holding a nearpoint Snellen acuity card at 40 centimeters (about 16 inches).  Some near acuity charts are calibrated for 35 centimeters (about 14 inches).  Just as on a far acuity chart, a 20/20 letter on a near chart subtends a visual angle at the eye of 5' of arc (5 minutes of arc, or 1/12 of a degree).

Without a lens correction, a myopic (nearsighted) person generally will have better visual acuity at near than at far, while a hyperopic (farsighted) person generally will have better acuity at far than at near.  Until the early to mid-forties, a person with 20/20 distance acuity usually also has 20/20 acuity at near.  However, once presbyopia sets in, one’s uncorrected near visual acuity decreases, creating the need for reading glasses or bifocals.

size of a 20/20 letter

When an eye doctor sets up an examination room, care should be taken in calibrating the size of the letters on the visual acuity chart (which usually is projected onto a highly reflective screen). 

The correct size of a 20/20 letter can be calculated using the diagram below, where

• the letter’s visual angle subtended at the eye is 5' of arc (5 minutes of arc), one-half of which is 2.5' of arc,
• d is the distance (or virtual distance, if using a mirror), along the line of sight, from the eye to the chart in feet, and
• h is the height of the 20/20 letter in millimeters.

Since a right angle is formed by the line of sight and the plane of the acuity chart, then simple trigonometry can be used:

1. 2.5' of arc ÷ 60 = 0.04167°
2. tangent 0.04167° = ½h ÷ d = ½h ÷ 20 feet
3. 0.0007272 = ½h ÷ 6,096 millimeters
4. ½h = 0.0007272 × 6,096 millimeters
5. ½h = 4.433 millimeters
6. h = total height of a 20/20 letter at 20 feet 8.87 millimeters

In general, to find the size of a 20/20 letter (in millimeters), multiply .4433 by d (where d is the viewing distance in feet).  That is:

h = height of 20/20 letter in millimeters = .4433 millimeters/foot × d feet

optical infinity

When an eye is looking at a far away distance (such as at the horizon or at the moon or at a star), the rays of light entering the eye are essentially parallel.  The crystalline lens of the eye is thin and relaxed because there is effectively zero accommodation.

When an optometrist, an optometric physician or an ophthalmologist examines and performs a refraction on someone’s eyes, it is optimal for the object being viewed (presumably a visual acuity chart) to be as far away as possible from the patient.  This is so that the incoming rays of light are as close to parallel as possible, and the amount of accommodation (increased curvature) of the crystalline lens in each of the patient’s eyes will be negligible.

Due to space limitations an examination room, though, this viewing distance (= “d” in the diagram above) can be only several feet or a few meters away from a patient.  Therefore, the goal of an eye doctor should be to position the eye chart at “optical infinity,” or the least distance at which there is no significant accommodation by the crystalline lenses of a patient’s eyes.

Traditionally, “optical infinity” has been accepted to be 20 feet or 6 meters.  However, at this distance, there is an accommodative demand on the eye of about 1/6 D (one-sixth of a diopter).  Although this amount of accommodative demand is not significant for most people, it can make a difference for some.  For very discriminating observers (such as myself), an accommodative fluctuation during an eye examination of more than 1/8 D can result in a variable endpoint in measuring a person’s refractive error (resulting in an imprecise lens prescription), and 1/6 D is greater than 1/8 D.

As a result, it is recommended that the viewing distance (d) in an examination room should be great enough to create no more than a 1/8 D accommodative demand on any patient’s eyes.  I maintain, then, that optical infinity, for purposes of examining the refractive error of the human eye, is at least 26¼ feet or 8 meters, rather than merely 20 feet or 6 meters.

If lack of space is a problem, front-surface reflective mirrors usually can be utilized to increase the virtual viewing distance in an exam room.  With this setup, a patient looks straight ahead into the mirror on the wall at the end of the room.  In the mirror, the patient can see the acuity chart located on the wall behind the patient’s exam chair.

The virtual optical distance of the chart is at least double the distance that it would be if, instead, the chart were at the end of the room where the mirror is located.  Thus, this alternate positioning of a mirror and an acuity chart is a viable means of simulating optical infinity in a relatively short eye examination room. The slight decrease in the illumination of the visual acuity chart usually is negligible, especially if the room is dark.

When I was in practice, the length of my exam room was too short, about 18 feet or 5¼ meters.  After placing a quality front-surface reflective mirror on the wall at the end of the room and the acuity chart on the wall behind the patient, the virtual viewing distance for my patients was about 37 feet or 11¼ meters.  When patients carefully followed my instructions during eye refractions, I consistently attained very accurate glasses and contact lens prescriptions.  So, for all practical purposes, during an eye examination, I consider “optical infinity” to be at least 26¼ feet or 8 meters in length.

Now, recall from the previous section that the following equation can be used to calculate the height of a 20/20 letter at any viewing distance, d:

.4433 millimeters/foot × d feet = height of 20/20 letter in millimeters

Therefore, it can be seen that the height of a 20/20 letter on a far acuity chart, located at a viewing distance from a patient’s eyes of d = 26¼ feet, is calculated as follows:

.4433 millimeters/foot × 26¼ feet 11.64 millimeters

Here is the calculation for the height of a 20/20 letter on a far acuity chart, located at a viewing distance from a patient’s eyes of d = 20 feet:

.4433 millimeters/foot × 20 feet 8.87 millimeters

For a near acuity chart, it is easier to measure the height of a 20/200 letter, which is 10 times the height of a 20/20 letter.  Here is the calculation for the height of a 20/200 letter on a near acuity chart, located at a viewing distance from a patient’s eyes of d = 16 inches 1.33 foot:

.4433 millimeters/foot × 1.33 foot × 10 5.89 millimeters

Here is the calculation for the height of a 20/200 letter on a near acuity chart, located at a viewing distance from a patient’s eyes of d = 14 inches 1.17 foot:

.4433 millimeters/foot × 1.17 foot × 10 5.18 millimeters

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