1.The Color of the Sky Depends on the Weather and the Air

Cases – Chapter 13

1.The color of the sky depends on the weather and the air.

a.On a very humid day, when the air contains many water droplets that are about 1 micron (0.000001 m) in diameter, the air appears hazy and white. Why?

b.On a very clear, dry day when there is no dust or water in the air, the sky is very dark blue. Why?

c.Why is the sky black on the airless moon?

d.When you look at the surface of a calm lake, you see a reflection of the sky. The water is not a metal, yet you see a reflection. What change occurs as light passes from air to water that causes some of the light to be reflected?

e.Mirages appear on sunny days in the desert when very hot air from the earth’s surface bends light from the horizon upward so that you see it as though it were coming from the ground in the distance. Hot air has fewer air molecules in it than colder air at the same pressure. Why does light bend slightly as it moves from colder air to hotter air?

2.The electronic flash in a typical camera is based on a xenon flashlamp, a tube filled with xenon gas at high pressure with an electrode at each end. This flashlamp is electrically connected to a small but powerful capacitor to form a circuit so that if the flashlamp were to conduct current, it would allow current to flow from one plate of the capacitor to the other.

a.Before you take a picture, the camera places separated electric charge on the two plates of the capacitor until a voltage drop of about 300 V appears across the xenon flashlamp. The flashlamp, however, conducts no current. Why not?

b.When you take a picture, the shutter opens and the camera causes a small high-voltage transformer to inject a few electrons into the gas in the flashlamp. The lamp suddenly allows current to flow from one plate of the capacitor to the other and the lamp “flashes.” Why does this introduction of electrons into the flashlamp cause it to “flash”?

c.The flashlamp will only last for a certain number of flashes because each flash damages the electrodes. Why does the flash damage the electrodes?

d.The flashlamp uses high-pressure xenon rather than low-pressure xenon. Why does high-pressure xenon give a more uniform spectrum of light than low-pressure xenon?

e.The flashlamp uses xenon gas rather than sodium gas, in part because xenon emits light over a very broad range of wavelengths and does a good job of simulating sunlight. But why wouldn’t a high-pressure sodium vapor flashlamp be practical, even if you didn’t care that it was orange in color?

3.A paint is a plastic that contains dye molecules and small clear particles. While the dye molecules absorb certain wavelengths of light and give the paint its color, the particles are often completely clear. Nonetheless, these randomly shaped and oriented particles are very important to the paint’s appearance.

a.The speed of light is different in the particles than it is in the plastic surrounding them. When light strikes the surface of one of these particles, why does some of it reflect?

b.A dyeless paint appears white because light bounces around among its particles and emerges heading in all directions. Sketch a few of the paths light could take in the paint and show how it could reach the surface beneath the paint.

c.Lead carbonate is a clear, toxic chemical that was put in paints before 1930 to make them white. The speed of light in a particle of lead carbonate isn’t that much slower than in plastic. How does this fact help explain why “lead paints” weren’t very good at covering dark surfaces, requiring lots of layers of paint before the surfaces really looked white?

d.Modern paints contain particles of clear, nontoxic titanium dioxide. Light travels very slowly in this material. Explain why titanium dioxide based paints look so white, even after only a single layer of paint.

e.Red paint usually contains a mixture of titanium dioxide particles and red dye molecules. The red dye molecules absorb any light that isn’t red but they don’t affect red light at all. How would the appearance of this paint change if it didn’t contain any titanium dioxide particles?

4.Interior house paints contain dye molecules that absorb certain wavelengths of light and give the paints their colors.

a.Dye molecules only absorb light of certain wavelengths for the same reason as atoms. Explain that reason briefly.

b.The dyes in most house paints eventually convert the light energy they absorb into thermal energy. However, fluorescent or neon paints emit light of a new color. Why is the light emitted by fluorescent paints always longer in wavelength than the light they absorb?

c.A paint’s appearance depends strongly on the light that illuminates it. Why are a white wall and a red wall indistinguishable when they’re both illuminated by 650-nm light?

d.Two paints that contain different dyes can look indistinguishable when illuminated by sunlight, even though they absorb slightly different portions of the visible light range. In what way can their absorptions differ without your being able to see any difference between the paints?

e.Two paints that look indistinguishable in sunlight may look very different when illuminated by a fluorescent lamp. Why does the difference between the paints only appear for certain illuminations?

f.If you’re trying to match new paint to old paint and want the match to work regardless of illumination, you’ll have to find a new paint that uses exactly the same dye molecules as the old paint. Why?

5.While fluorescent lamps can be dimmed, it’s not as easy as dimming an incandescent light bulb. Fluorescent lamps tend to turn off when they don’t run at full power, so a dimmed fluorescent fixture must make sure that the discharge continues to operate, even at low power.

a.Why can a fluorescent fixture be dimmed only if it continuously heats the filaments of its fluorescent tubes?

b.While an incandescent light bulb can be dimmed by reducing the voltage drop across its filament, reducing the voltage drop across a fluorescent tube will spoil its discharge. With the voltage drop across the tube reduced, the average energy of its electrons would be substantially lower than normal and its mercury atoms would emit almost no ultraviolet light at all. Why is there a minimum energy that an electron must have in order to cause a mercury atom to emit ultraviolet light?

c.Reducing the voltage drop across the fluorescent tube would virtually stop the production of positive mercury ions in the vapor. That would make the tube’s filaments last longer, but the discharge wouldn’t operate. With no positively charged particles inside the tube, what would happen to the electrons as they flowed from one electrode to the other?

d.Rather than reducing the voltage drop across its fluorescent tubes, a dimmed fluorescent fixture turns the discharge on and off about 120 times a second. Fortunately, this rapid pulsed operation doesn’t shorten the tube life. Why don’t we see this flickering light output?

e.Current passing through the electronic switching system of the dimmed fluorescent fixture experiences a small voltage drop. Why does the switching system get warm?

6.In 1965, American physicists Arno Penzias and Robert W. Wilson discovered that space is filled with thermal radiation, left over from the Big Bang that formed the universe. While this thermal radiation was once extremely hot, the universe’s expansion has cooled it to only 3 K. It now consists mostly of microwaves that are extremely difficult to detect.

a.Satellite dish antennas are designed to detect coherent microwave radiation—a low-frequency equivalent of coherent light. Why are microwaves emitted by a normal microwave transmitter and antenna (e.g., a magnetron) coherent?

b.The microwaves reaching us from space are thermal radiation and effectively come from individual charged particles that moved back and forth to produce them. Why is this microwave radiation incoherent?

c.A normal satellite dish antenna will have trouble detecting microwaves from the Big Bang because they are incoherent. Why won’t the charges on the antenna of a satellite dish respond strongly to these incoherent microwaves?

d.To detect the incoherent microwaves, Penzias and Wilson used a maser amplifier—a device that amplifies microwave photons via stimulated emission. How did introducing this amplifier make it possible to detect the microwave photons with a microwave antenna and receiver?

7.The bright red, green, and yellow lights that you find on many electronic devices are light emitting diodes or LEDs. Like any other diode, an LED carries current in only one direction. But unlike a normal diode, an LED emits a photon of light whenever an electron shifts from a conduction level in its n-type cathode to a valence level in its p-type anode.

a.Explain why an LED’s brightness is proportional to the electric current flowing through it.

b.Light carries energy. Use conservation of energy to show that the current passing through an LED must experience a voltage drop.

c.A photon of green light has more energy than a photon of red light. Why must an LED that produces green photons have a larger voltage drop than an LED that produces red photons?

d.The power supply in a typical electronic device delivers current at too high a voltage for an LED. If that current were sent directly through the LED and then returned to the power supply, the LED would receive too much power, overheat, and burn out. To prevent such a disaster, the electronic device first sends the current through a resistor and then through the LED. How does the resistor protect the LED?

e.An LED’s color is determined by the energy needed to shift an electron across the band gap in the semiconductor from which the LED is made. Because blue photons have more energy than green photons, development of blue LEDs took a long time. The materials needed to produce blue LEDs are almost true insulators rather than semiconductors. What distinguishes a semiconductor from an insulator?

8.Your local market has an electric eye that rings a bell as you walk in the door and block a light beam. The light beam is emitted at one side of the door and normally strikes a small photoconductor on the other side of the door.

a.When the light beam is turned off or blocked, no light strikes the photoconductor. A battery pumps negative charges onto one side of the photoconductor and positive charges onto the other. These opposite charges exert attractive forces on one another so why don’t they move together?

b.Because the photoconductor is in the dark, the battery soon stops sending charges to it. What makes it stop?

c.When the light beam reaches the photoconductor, charges can move through it. What has happened inside the photoconductor that allows it to conduct electricity?

d.When the photoconductor is exposed to light, the battery can continue to send charges to it. How has light made it possible for the battery to keep sending charges?

e.You bend down to play with the electric eye. You block the light beam with your back and shine your own flashlight onto the photoconductor. The bell turns off, as though you were out of the way. But when you shine red light from your bicycle taillight onto the photoconductor, it doesn’t respond. Why doesn’t red light (which has relatively low-energy photons) affect the photoconductor?