20. (II) The closely packed cones in the fovea of the eye have a diameter of about 2 um. For the eye to perceive two point-like objects as distinct, the images on the fovea must be separated by at least one cone that is not excited. Assume the eye's focal length is 2.0 cm. How far apart are two objects at the top of a 34-m-tall tree if their images on the retina are separated by 2.0 um?
21. (I) A nearsighted person has near and distant points of 16 cm and 20.0 cm, respectively. If she puts on contact lenses so that her far point is now at infinity, what are her new near and far points?
22. (I) What is the focal length of a magnifying glass of 3.2x magnification for a relaxed normal eye?
23. (I) What is the magnification of a lens used as a magnifier if its focal length is 16 cm? (a) What is the magnification for an image at the near point; (b) what is its magnification if the 3.5X refers to the relaxed eye?
24. (I) A magnifier is rated at 3.5X for a normal eye focusing at infinity. What is its focal length?
25. (II) Sherlock Holmes is using an 8.20-cm-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume normal eye) and what will be the magnification?
26. (II) A small insect is placed 4.85 cm from a +5.00-cm-focal-length lens. Calculate (a) the position of the image and (b) the angular magnification.
27. (II) A 3.80-mm-wide bolt is viewed with a 9.60-cm-focal-length lens. A normal eye views the image at its near point. Calculate (a) the angular magnification, (b) the angular width of the image, and (c) the object distance from the lens.
28. (II) A magnifying glass with a focal length of 9.2 cm is used to read print placed at a distance of 8.0 cm. Calculate (a) the position of the image; (b) the angular magnification.
29. (III) A writer uses a converging lens of focal length f = 12 cm as a magnifying glass to read fine print on his book. Initially, the writer holds the lens above the fine print so that its image is at infinity. To get a better look, he then moves the lens so that the image is at his 25-cm near point. How far, and in what direction (toward or away from the lens) did the writer move the print? Assume his eye is always very near the lens.
30. (III) A magnifying glass is rated at 3.0X for a normal eye that is relaxed. What would be the magnification for a person with a near point of (a) 15 cm and (b) 75 cm?