Solutions to homework problem set #2
Text pages 68 and 69 problems P4, P7, P8, PH2
P4. He used a candle as an approximation for a point source because a point source produces a clear, well-defined shadow. Although an extended source might have been brighter, each point on its surface would make its own contribution to the shadow. The total shadow would be the sum of all of them. Since the various sources are not at exactly the same location, the resulting shadow would be blurry and not as well defined. The degradation would depend on how large a source he used.
P7. The size of each image can be found by drawing straight lines passing through the pinhole from the tip of each arrow to the screen. This method shows that the smaller arrow labeled b actually has the larger image on the screen. Although arrow b is smaller than arrow a it is much closer to the pinhole, and that more than compensates for its smaller size. The geometrical construction also shows that the image is inverted relative to the object, so that the image of arrow b will be pointing up. Thus arrow b is the answer to both parts of the question.
P8. Only a small fraction of the light coming from the Sun can get through the pinhole, only a fraction of that fraction is reflected from the white screen and only a fraction of that fraction reaches your eyes. The light that actually reaches your eyes in this configuration is therefore far less than what your eye would receive if it looked directly at the Sun.
PH2. (a ) A Lunar eclipse is shown below. The Moon is much smaller than the Earth, so that it is completely hidden in the shadow of the Earth as shown below:
The two straight lines that are tangent to the Sun and the Earth show the region of the Umbra behind the Earth the area behind the Earth that is totally dark because no rays from the Sun can reach there.
(b) The moon disappears when viewed from the Earth, since no light from the Sun reaches the moon (in the approximation that the moon is completely in the geometrical shadow of the Earth. Even in a complete eclipse, a small amount of light reaches the Moon because light from the Sun is scattered in the Earths atmosphere.
(c) Since the Earth emits essentially no light of its own, standing on the Moon looking up at the Earth would show just a faint ring of light caused by the scattering of the light from the Sun in the upper atmosphere of the Earth. The result might look something like the central image of the Sun in figure 2.4 (page 31). The center of the field is dark because the Earth is blocking the direct rays from the Sun.