Physics 102 Homework set 8 Solutions L. Weinstein Exercises: ---------- 26.4: Radio waves have the lowest frequency and hence the longest wavelength (see figure 26.3 and use v = f*lambda). 26.12: Both are electromagnetic waves and therefore both travel at the speed of light. 26.22: v = f * lambda. Shorter wavelength corresponds to higher frequency. Therefore, the 515 nm light has a higher frequency. 26.26: Glass is opaque to light at its natural frequencies. At those frequencies (corresponding to ultraviolet and infrared light), the glass absorbs the radiation. 26.30: The reading glasses are transparent and do not absorb the sunlight. The dark (ie: not mirrored) sunglasses absorb a lot of the sunlight and therefore they get warmer. 26.36: When an observer on the Earth sees a lunar eclipse, the Earth blocks the Sun as seen by the Moon and the shadow of the Earth falls on the Moon. This will be seen as a solar eclipse from the Moon because the Earth blocks the Sun. Similarly, when an observer on Earth experiences a solar eclipse, the lunar observer will see the shadow of the Moon fall on the Earth, causing a "Terran Eclipse". 26.38: Objects illuminated by moonlight lack color because there is not enough light for our cone cells to function. Therefore we see with our rod cells which cannot perceive colors. 27.18: Color ink-jet printers use cyan, magenta and yellow inks. They use color subtraction (since pigments absorb colors). 27.22: A cyan filter will absorb red light and a magenta filter will absorb green light. Therefore only blue light will be transmitted through overlapping cyan and magenta filters. 27.24: Deep underwater the remaining sunlight is predominantly blue with a bit of green. The red blood absorbs blue and green light and appears black (just like the red rose illuminated in green light). The flashbulb provides white light so that the red blood appears red. 27.28: The yellow banana reflects red and green light and absorbs blue light. Therefore, it will only appear black under blue light. 27.32: The sky appears blue because the atmosphere scatters the blue light from the sun. At higher altitudes, there is less air above you and therefore there is less blue light scattered. Problems: ------------------ 26.4: The distance to the Moon is 4*10^8 m, so the round trip distance is 8*10^8 m. The speed of light is 3*10^8 m/s so that the time required is t = d/v = 8*10^8 m / 3*10^8 m/s = 8/3 s = 2.7 s. 26.6: v = f*lambda so that f = v/lambda = 3*10^8 m/s / (589 nm) = 3*10^8 m/s / (589*10^(-9) m) = 5.1*10^14 1/s = 5.1*10^14 Hz Estimation: ------------------- If you looked at the Sun (warning: do NOT try this at home), then your pupils would get as small as possible. This is a radius of about 1-2 mm so that the area of the pupil is A = pi r^2 = 6 mm^2 = (6 mm^2) * (1 m / 1000 mm) * (1 m / 1000 mm) = 6*10^(-6) m^2 The light that enters the eye from the Sun would then be P = 1000 W/m^2 * 6*10^(-6) m^2 = 6*10^(-3) W = 6*10^(-3) J/s In 0.1 s, this would be an energy E = 6*10^(-3) J/s * 0.1 s = 6*10^(-4) J b) Now we compare 6*10^(-4) J to 2.5*10^(-18) J. The ratio of the two number is 6*10^(-4) J / 2.5*10^(-18) J = 2.5*10^(14) The eye can see light levels that range over 14 powers of ten! This is a tremendous range! By contrast, you can feel about 0.1 g, but 1000 kg = 10^6 g would kill you. This is a range of only about 10^7.