WSU ASTRONOMY Lab: Resolving Power of the Human Eye Purpose: In this experiment, you will determine the resolving power of the human eye and investigate on what factors it depends. Introduction: Humans are a very clever lot. In our never-ending attempt to adapt to the world, we sometimes encounter physical obstacles that might hinder the adaptive scheme. We need to fell a tree to build a shelter, but our bare hands are inadequate for the purpose. No matter, we extend the capabilities of our hands and make an axe. The tree is down. We perceive a need to hurl an object a great distance and we invent catapults and ICBM’s. We make extensions for our eyes (telescopes) and we see into the great dark between the stars. Our struggle to adapt to the world has usually involved extending the human body and its senses, and in doing so we have given ourselves greater control over our environment and its influences. But just what can our bodies do? How fast can humans run, how faint a sound can we hear? In this lab experiment, you will examine the resolving power of the human eye; that is, for two point-like objects separated by a particular distance, how far away can you be and still see the two 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 separate. Once d and D are known the angle θ in the figure can be determined. We will refer to θ as the resolving power of the human eye. When the triangle is long and thin as in the figure below, the angle θ is given to a good approximation by θ = d/D. The angle θ in this relation is in radians. Recall that there are 2π radians in a circle of 360˚, so if you want to convert an angle in radians to one in degrees, you need to multiply by 360/2π ≈ 57.29. In science, and often in everyday affairs, a well-phrased question is frequently half the answer. Unfortunately the question “What is the resolving power of the human eye?” is not well-phrased. Does the angle θ depend on the experimental arrangement? If it does, then a unique answer cannot be provided. In this experiment you will investigate the parameters influencing the resolving power and attempt, nonetheless, to answer the central question. The Experiment: Unlike other experiments you will be doing this semester, you will not be given step-by- step instructions; only some general guidelines and ideas will be offered. 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; that is, 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 it matter whether you start far away and approach the point-like objects or stand nearby and then move away? 4. Do you want to make a single measurement to answer a question, or do you want to make multiple measurements and average? 5. How do your results compare with your partner’s and with others? Available for your use are various supplies to help you. You may also want to discuss with your instructor other ideas for factors influencing the resolving power of the eye. Problems: 1. Write a short account of what factors influence the resolving power of the human eye and how they influence it. 2. How would you answer the question: “What is the resolving power of the human eye?” 3. It is claimed that an eagle can spot a mouse at 3,000 ft (≈ 1,000 m), although it’s not certain just what the eagle is detecting. Estimate the resolving power of the eagle’s eye and compare it to your own. 4. Most people cannot focus their eyes on objects closer than about 10 cm (≈ 4 inches) from the eye. Using the results of your investigation, what is the smallest object that you can see?