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How Sharp Are Your Eyes?
	Visual Acuity and the Unaided Eye

What is the smallest thing you can see with your unaided eye?

EXPERIMENT #1:

1. (Here comes what might be the hardest part of this whole page!) Find some fine powder that is medium gray in color. No, not sand! A very fine powder!
2. Sprinkle some of this on smooth white paper, and some on a smooth black paper. Can you see individual granules of the dust on either paper? Do you see them better on white or on black?
3. Next, move away until you can no longer discern the individual granules on either paper. Measure that distance from paper to your eye.
4. Now shine a bright light onto the two papers. Are you able to see individual granules on either paper? How far can you move away from the paper and no longer see them?
5. What happens if you shine an even brighter light on the papers? Can you see them again?

In essence what you have been doing is comparing "bright-field" and "dark-field" observations.

EXPERIMENT #2:

Perhaps you have had the experience of sitting on a sunny day in a dark room with the shades drawn or pulled down. A beam of sunshine came into the room through a very small hole in the drape or windowshade. As you watched from the side you could see dust and small threads moving through the air. This is another instance of "dark-field" observation. Would you have seen the dust in the air had the room been well lit? How small were the particles wafting in the air? Do you think you could see your gray dust particles in that beam of sunlight? See if you can make a similar setup using a strong flashlight that is aimed across a dark room and out a window into the night blackness.

TIME OUT!

You are studying vision and how well you can see things. Of course, you know that you see light that comes into your eyes. Can you see pitch blackness? Technically, no, because there is no light coming from the blackness. You see what comes from around the black object. Thus, when the powder was on the white paper, you saw the white paper - and some holes in that whiteness. The question then became how small a hole you could see.

However with the black paper, the powder was relatively light colored. Now your eyes did not see the paper, but the powder. How could you see the powder even better? Yes, by shining more light on it so that more light would be reflected and reach your eyes.

For an ultimate example of darkfield observation, consider looking at the stars. Many that you see are millions and billions or miles away. Yet you see them against the blackness of the night sky - but not against the daytime sky.

Subtended Angle of Vision

Let's return to bright-field observation. When you look at an object such as shown here, there is an angle in your vision between the top of the object and its bottom. The angle in the picture is designated by the Greek letter phi (φ, pronounced "fee" - fraternities mispronounce it as fye). That is the angle subtended by your eye (see the figure to the left of the title, above). Obviously, as the object comes closer to you, the angle grows larger. And vice versa when the object moves away from you. Finally, it will be so far away that you can no longer see it and its angle will be very close to zero. Thus a person with very sharp eyes can see something that subtends a smaller angle than most other people can. That small angle below which you can no longer see the object, we shall call the "limit angle." (Click to get information on how to calculate the angles in your experiment.)

EXPERIMENT #3:

In a brightfield situation, you will determine your limit angle.

1. Cut out a black circle that is 5 mm in diameter. You will also need a very large piece of white posterboard.
2. Give the circle to a friend, and then you walk far away.
3. Your friend will stick the black circle onto the posterboard at some place (but not closer than a couple of cm from edge)
4. You should be so far away that you cannot see the black circle when you friend holds up the posterboard.
5. Slowly approach the posterboard until you can detect where the black circle is. Make the spot. Make three or four repeats of this, but each time your friend places the black circle at different places. (Or the friend can put several identical black circles on the posterboard and you have to detect the correct number of circles.)
6. Average your various "spots" of recognition and determine the distance from the posterboard.
7. Divide the 5 mm by the distance (make sure you are using metric measurements or the right conversion factors!). That result is the tangent of the angle subtended by your eye.

   tan φ = 5 mm/distance (VERY strong hint: don't overlook reading the GREEN section of the tangent page!).

8. Now switch places with your friend to determine your friend's limit.

TIME OUT!

Let's return to the darfield situation of the stars in the sky. What size angles must be subtended by them? Yup! VERY small angles - so small that we cannot see that they are any larger than 0.0000000000 degrees. As said: 'VERY small' indeed! They are so small that they still seem to have no size even with the largest telescopes (except for our sun and a couple of near stars).

But how is it possible that we can see them if they appear so small? You got it! It is because they are in a darkfield situation. What we were talking about with regard to things disappearing at a distance were in brightfield situations. But in darkfield situations it is the amount of light coming from the object that counts - use a brighter beam of light on the gray dust on the black paper, or a brighter beam on dust wafting in the air of a dark room, or a brighter star, and you can see them from further away. (Or for the dust on the paper or in the air: the brighter the light beam, the smaller the things can be in order to be seen.)

THE LINEAR ENIGMA

First, I suppose you will have to go to the dictionary to find out what 'enigma' means! After that you may be sufficiently enticed to push further into studying "sharp eyes."

So far you have been dealing with 1 cm black circles, and you have determined how far away you have to be before you can no longer see them. Now find a long street or a countryside that has some distant telephone or power lines crossing the sky (ah, ha! brightfield!). Go so far from them that you can no longer see them. Estimate your distance from them. Next get as close to them on the ground below and try to guess how wide (diameter) they are. They will probably be about 1 cm in diameter. Yet you stood much, much further away before you lost sight of them! What does the linear characteristic of the wire have to do with limit angle subtended by the wire? Obviously the linearity improves your vision! But how?

An Experiment!

If you imagine that any line consists of an infinite number of points, then it is easy for you to think of the distant telephone wire as being a series of 1 cm circles all lined up side-by-side. And you already know that any one of those circles would be invisible at that distance. Thus you can attack this problem by considering how many of those lined-up circles you can remove before you can no longer see the line. Or, as an alternative, how close you have to move to be able to see the "line" again.

You might start out by making a thin black line on your white posterboard. Determine the distance at which the line can no longer be seen. Move a little closer so that you can just see that there is a line.

Your friend will take a few minutes now to use some white secretarial correction fluid or white paint on a small artist's brush to start making the line into a dashed line. Perhaps the white "paint" will break the line into 5 cm lengths. Can you still see the line? Then your friend will use the white paint to divide the lengths in half. Can you still see the line? If not move closer (always measuring your distances and recording them according to the status of the line). As those bits of line are halved and then halved again, you will probably need to move closer and closer. This author doesn't really know, but is guessing. You need to do the experiment to find out. How happy your teacher will be with all the graphs you will use in your presentation!

You might then see if the line is a unique enigma, or do other geometric figures work also - triangles, squares and circles.

Final TIME OUT!

Really bright students will want to include something about the human eye in their reports. We see because light impacts the "rods" and "cones" in our retinas. You will want to determine how far apart those visual elements are because that may limit our eyes' discrimination between one object and two or more.

And brilliant students will extrapolate the physiology of the human eye to that of - say - the eyes of hawks.

Meanwhile super-genius students will extrapolate all this to how microscopes and telescopes work, and how their resolving power can be improved.

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