Activity 7
Resolving Power of the Eye
Materials needed. Index cards; felt tip markers (sharp point) of different colors; sheet of black
construction paper; White-Out or a sharp-pointed white crayon; meter stick, yardstick, or steel
tape rule; transparent tape.
Discussion. Humans are very creative and ingenious in building gadgets to extend human
capabilities, witness the innovations in transportation and technology in the nineteenth and
twentieth centuries.
But what can the human body itself do? In this exercise, you will examine the resolving power of
the human eye. By "resolving power," we mean the ability of the eye (or a telescope or a radar
set) to perceive two distant objects as separate and distinguishable.
We will express the resolving power of the human eye in terms of an angle. As shown in the
figure below, for two point-like objects a distance d apart, we need to determine the largest
distance D from the two objects so that they are still distinguishable as two separate objects.
Once d and D are known, the angle in the figure can be determined. We will refer to the angle
as the resolving power of the human eye.
When the triangle is long and thin (as in the figure below), the angle is given to a good
approximation by = d/D. The angle is expressed in radians. In a circle of 360o, there are 2
radians; to convert an angle in radians to one in degrees, you need to multiply by 360/2 57.29. (NOTE: The symbol means, "is approximately equal to.") The question "What is the resolving power of the human eye?" is not well phrased - it is too
vague. Does the angle depend upon the experimental arrangement? If so, then a unique answer
cannot be provided to the question of the eye's resolving power. In this exercise you will examine
the parameters influencing the resolving power and attempt, despite these parameters, to answer
the central question.
Procedure. Unlike other exercises you will do this semester, you will not be given step-by-step
instructions. Only some general guidelines and ideas will be offered. Draw your points on an
index card and tape it to the wall at eye level. Be sure that there are no obstacles between you
and the wall. 31 Questions
1. Your point-like objects should be separated by about 3-5 mm. The point-like objects
themselves should be no larger than about ½ mm in diameter (i.e., they must be small when
compared to their separation).
2. Does it matter that the point-like objects are black dots on white paper or white dots on black
paper?
3. Does the resolving power depend on whether the dots are luminous, point-like sources? Does
the brightness of the dots matter?
4. Does the color of the dots affect the resolving power?
5. Does it matter whether you start far away and approach the point-like objects or stand nearby
and then move away?
6. Do you want to make a single measurement to answer a question, or do you want to make
multiple measurements and average the results? Resolving Power of the Eye
Answer the following questions on the basis of your results. Do not give
simple "Yes" and "No" answers to questions 1 to 5; explain why you
answered as you did.
1. Does it matter that the point-like objects are black dots on white paper or white
dots on black paper? 2. Does the resolving power depend on whether the dots are luminous, point-like
sources? Does the brightness of the dots matter? 3. Does the color of the dots affect the resolving power?
32 4. Does it matter whether you start far away and approach the point-like objects or
stand nearby and then move away? 5. Do you want to make a single measurement to answer a question, or do you
want to make multiple measurements and average the results? 6. Write a short account of what factors influence the resolving power of the
human eye and how they influence it. 7. How would you answer the question, "What is the resolving power of the
human eye?" Let = d/D be the resolving power (see the Activity 7 directions). 8. It is claimed that an eagle can spot a mouse at 3000 feet (~ 910 meters),
although it is not certain just what the eagle is detecting. Estimate the resolving
power of the eagle's eye and compare it to your own. 33 9. Most people cannot focus their eyes on objects closer than about 10 centimeters
(~ 4 inches) from the eye. Using the results of your investigation, what is the
smallest object that you can see? 34

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