All answers have been checked against the answer key, and should be presumed to be correct. You should ask for help in the recitations if you are unable to obtain these results.
2. f/2.3
8. 6.9 m to infinity
18. (a) 2.0 cm, (b) 1.9 cm
26. (a) 6.0 x, (b) 1.9 x
28. -28.6 x, L = 83 cm
32. -50 x
40. (a) 744 x, (b) eyepiece: 2.08 cm, objective: 0.284 cm, (c) 0.289 cm from the objective lens.
46. 2.64 x 10-7 radians = 1.51 x 10-5 degrees
2. If the lens opening is made so small that it is comparable to the wavelength of light, then the image would begin to get fuzzier again because diffraction would spread out the image of point sources into diffuse peaks.
3. The lens equation says that the sum of the inverse distances to the image and object must equal the inverse focal length. Therefore, if the object is moved closer to the lens, the film must be moved further from the lens to focus on it.
4. The lens in the eye becomes larger and stiffer with age. Therefore, it does not adjust as readily to focus on short focal lengths. Bifocals are needed to do the accomodation to different focal lengths.
5. The index of refraction of water is only a little greater than the index of refraction of the eye membranes, so the focal length of the cornea becomes much longer under water. This makes distant objects focus behind the retina. Goggles correct this because they are flat in front, so no refraction occurs there. They leave air space in front of the corneas, so that normal diffraction occurs in the eye.
6. A nearsighted person has a longer eyeball than normal, which may compensate, at least partially, for the longer focal length of the cornea underwater. Therefore, a severely nearsighted person may see more clearly underwater, depending on how nearsighted they are.
7. If the face appears to be shrunk, the person is near-sighted and wearing diverging lenses. Converging lenses, used to correct far-sightedness, would magnify the face.
8. They eye is more like a movie camera than a still camera. The image is updated approximately every 1/30 second, as the brain processes the signal from the retina.
9. Squinting reduces the light coming in from large angles, and is similar to limiting the aperture on a camera. This reduces the circle of confusion from out of focus light, making an unfocussed image appear clearer.
10. The image on the retina is inverted, just as in a camera. The fact that we perceive things to be upright depends on the brain's processing of the image, and its interpretation. This can be changed: people who wear inverting glasses for a long period have been found to be able to flip the image back again after a time.
11. Yes, reading glasses are magnifiers, although that is not their primary purpose. The fact that they are a magnifier means that if you put something closer than you could normally look at it, its image will occupy a larger angle. Objects at a fixed distance will not be bigger, however, they will just be less fuzzy.
12. The colored fringes produced by inexpensive microscopes are due to the chromatic aberration of the lens, in which dispersion causes different wavelengths to be refracted by different amounts. Better microscopes correct for this using specially designed compound lenses to minimize dispersion.
13. Imagine a ray of light coming from infinity, going through the lens, and striking a focal point. If the curved surface of the plano-convex lens faces the object, then the light bends more equally at each surface. If the lens is turned around with the flat side facing the object, then the same ray of light would make a much larger angle with respect to the curved surface than the flat one. As the question suggests, it helps to draw a picture, using the same incoming and outgoing rays in each case.
14. Read page 733 for a complete discussion of the aberrations in lenses and the eye.
15. Chromatic aberration occurs because of refraction, when different wavelengths refract different amounts. This does not occur for mirrors, which use u reflection. All wavelengths reflect in the same manner, with the angle of incidence equal to the angle of reflection.
16. It is easier to make a large mirror than a large lens. Large lenses are heavy and may tend to sag, while a mirror can be made very thick. Lenses are subject to chromatic aberration, which is absent for mirrors.
17. Shorter wavelengths give less diffraction, so blue light gives better resolution than red.
18. No. Atomic diameters are about 1/10 of a nanometer, while visible light is hundreds of nanometers. Therefore, the diffraction from an atom would be enormous, and it would be impossible to resolve any detail.
| Physics 222 | Department of Physics | University of Tennessee |