Physics 106N - How Things Work - Spring, 1997 

Problem Set 3 - Answers



Problem 1:  Chapter 15, Case 2a-e (Pg. 553) 

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? 
Answer: The gas within the flashlamp contains no mobile electric charges (the xenon atoms are electrically neutral) so there is nothing to carry electric current through the flashlamp. 
Why: A material can only carry electric current when it contains mobile electric charges that can respond to electric fields. Since the xenon atoms in the flashlamp are electrically neutral, they don't respond to electric fields and cannot carry electric current through the flashlamp. 

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"? 
Answer: The injected electrons are mobile electric charges that can carry current through the flashlamp. 
Why: With some free electrons in the flashlamp's gas, that gas can begin to carry electric current. In fact, the electrons accelerate quickly toward the positively charged wire of the flashlamp and they begin to collide with the xenon atoms. These collisions occasionally ionize xenon atoms, releasing more electrons as well as positively charged xenon ions. These new charged particles enhance and perpetuate the current flow through the flashlamp. 

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? 
Answer: Sputtering. 
Why: During startup, the xenon positive ions that are produced accelerate to high speeds before crashing into the flashlamp's negatively charged electrode. These high speed collisions knock atoms off that electrode and damage it, reducing the flashlamp's life. 

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? 
Answer: Any one of the following answers will do: (1) Radiation trapping of xenon's principal emission wavelengths allows the rarer wavelengths to become more important in the spectrum of light leaving the lamp. (2) Radiation trapping keeps energy trapped in the gas so that the xenon atoms become more highly excited than normal and often emit wavelengths that aren't emitted by less highly excited atoms. (3) Collisions allow the xenon atoms to radiate what are normally forbidden wavelengths of light by allowing those atoms to shift between orbitals in a step that normally isn't allowed. (4) Light emitted during a collision can emerge at a wavelength that's somewhat different from its normal wavelength because the collision interrupts the emission and disturbs the wavelength of the outgoing light. 
Why: All of these phenomena extend and enrich the spectrum of light emitted by the xenon. With a more varied spectrum, the xenon appears whiter than it would at lower pressure. 

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? 
Answer: Sodium is a solid at room temperature. 
Why: Without something to preheat the sodium and transform some of it to vapor, the sodium vapor flashlamp would contain no gas atoms at all. Virtually all of the sodium atoms would be in the solid form. 

Problem 2: Chapter 15, Case 4a-f (Pg. 554) 

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. 
Answer: The electrons in dye molecules can only move in certain allowed paths or orbitals and a dye molecule can only absorb a photon of light if that photon has just the right energy to shift the electrons in the molecule from one arrangement of orbitals to another. 
Why: As in atoms, the electrons in a dye molecule travel in specific molecular orbitals. When the dye molecule absorbs a particle of light, the electrons rearrange and travel in different orbitals. Since each arrangement of electrons in orbitals has a certain energy, the amount of light energy needed for each rearrangement is fixed. Only light that causes an allowed rearrangement can be absorbed. 

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? 
Answer: The energy of a photon of light increases as its wavelength decreases, so that a dye that has absorbed a low energy long-wavelength photon doesn't have enough energy to emit a high energy short-wavelength photon. 
Why: When a molecule fluorescences after being exposed to light, the photon of light it emits can have either the same energy as the photon of light it absorbed or less energy. To do otherwise would not conserve energy. 

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? 
Answer: A red wall reflects red light, including 650 nm light and so does a white wall. In both cases, you see the reflection of the red light so the walls like identical. 
Why: A wall can only reflect the light to which it is exposed. If you expose a white wall to red light, it will reflect red light. If you expose a red wall to red light, it will reflect red light. The appearances of the two walls in this illumination will be indistinguishable. 

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? 
Answer: They absorptions of specific red light wavelengths can differ as long as their overall absoptions of red light wavelengths are equal. The same for green light and blue light. (For example, yellow pigment can either absorb everything but 590 nm light--at the edge of both the red and green wavelengths or it can absorb everything but 630 nm light and 530 nm lights, the middles of the red and green wavelengths respectively. In both cases, the amount of red light and the amount of green light reflected toward your eyes when the pigment is illuminate by sunlight will be the same.) 
Why: Your eyes can only detect the amount of red, green, and blue lights present in the light you see. There are many combinations of wavelengths that cause you to see the same color. As long as a pigment achieves the same balance of red, green, and blue reflected light, you'll see the same color reflected from that pigment. 

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? 
Answer: A paint can only reflect the light to which it is exposed. If the illumination contains special wavelengths that are particularly bright, then the paint's ability to absorb of reflect those wavelengths will be put to the test. Two paints that handle sunlight equivalently may handle those specific wavelengths very differently and will reflect lights with very different appearances. 
Why: Paints are usually formulated to have a particular color when illuminated by sunlight. They expect to receive a broad range of red light wavelengths, blue light wavelengths, and green light wavelengths. But in other illuminations, those ranges of wavelengths are shifted and skewed. The illuminations may appear white but they may not contain even balances wavelengths within the red, green, or blue ranges. Since a particular paint is not necessarily meant to handle every last red wavelength (or green wavelengths or blue wavelengths) properly, it may look strange if the illumination makes strong use of one of the mishandled wavelengths. 

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? 
Answer: How a paint handles each wavelength of light is uniquely determined by its dye molecules. If you want the responses to all wavelengths to be identical for two paints, you need them to contain the same molecules. 
Why: Two paints that contain different dye molecules are going to handle some wavelengths of light differently. As a result, there will always be some illuminations in which those two paints will look different. 

Problem 3: Chapter 15, Case 6a-d (Pg. 554) 

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? 
Answer: A normal microwave transmitter and antenna form a single electromagnet wave (with a single electric and magnetic field) and that single wave is coherent. 
Why: All of the microwave photons in the wave are identical; they have to be in order to be part of the same giant electromagnetic wave. 

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? 
Answer: Thermal microwaves are all emitted independently and consist of innumerable independent waves. These independent waves are incoherent. 
Why: Each electromagnetic wave emitted by a charge due to its thermal motion is emitted independently and without relationship to other electromagnetic waves around it. These unrelated waves are 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? 
Answer: The incoherent microwaves push the electric charges in the antenna in all directions randomly and don't cause any overall response in the antenna's charges. 
Why: For all of the charges in the antenna to respond together, they must be pushed on by many coherent photons at once. They respond feably and randomly to the incoherent photons from a thermal source. 

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? 
Answer: The amplifier duplicates one microwave photon over and over again to produce a strong coherent microwave that can be detected. 
Why: While each incoherent microwave is difficult to detect on its own, a copied incoherent microwave is a much stronger wave and can be detected. The copies are coherent and they can cause significant motions of charge in the antenna. 


Problem 4: Chapter 16, Case 3a-d (Pg. 592) 

The lens of your eye resembles that of a camera--light from the scene in front of you focuses to a real image on your retina. But unlike a camera lens, the lens of your eye can actually change its focal length by changing its curvature. The more curved the lens's surfaces are, the more strongly it bends light together and the shorter its focal length. The lens's variable focal length allows you to focus the real image of a particular object onto your retina without having to change the distance between the lens and the retina. 

a. Explain why focusing on a distant object requires less lens curvature than focusing on a nearby object. 
Answer: The light rays from a distant object are diverging less than those from a nearby object and are easier to bring together to a focus. 
Why: The nearer an object is to the lens, the more the rays reaching the lens diverge from one another. Bending these diverging rays together is harder and takes a more curved lens. 

b. The lens of a farsighted person has trouble becoming curved enough to form a real image of a nearby object on the retina. Explain why wearing glasses containing converging lenses helps a farsighted person see nearby objects. 
Answer: The converging eyeglass lens helps the eye's lens to converge the highly diverging rays from a nearby object. 
Why: Two converging lenses can work together to make the equivalent of a single more highly curved lens. 

c. The lens of a nearsighted person has trouble becoming flat enough to form a real image of a distant object on the retina. Explain why wearing glasses containing diverging lenses helps a nearsighted person see distant objects. 
Answer: The diverging eyeglass lens increases the divergence of the rays from a distant object so the the eye's lens has more trouble bringing them back together. 
Why: The diverging lens works with the eye's lense to make the equivalent of a single less highly curved lens. 

d. The iris of your eye changes diameter to control how much light reaches your retina. The brighter the light, the smaller the iris's opening. Why is your eye's depth of focus greater in bright light than in dim light? 
Answer: The smaller iris opening selects only light rays that are near the center of your eye's lens. Because these rays are already very close together, they form an acceptible image well in front of or behind the actual real image. 
Why: A narrow aperture allows a lens to handle light rays that are very close together already. While the light rays from a particular point in the scene do merge together perfectly at only a single distance behind the lens, they are pretty near one another over a substantial range of distances from the lens. As a result, the exact curvature of the lens or the distance between the lens and the retina just isn't that important and the scene appears in focus in any case. 

Problem 5: Chapter 16, Case 6a-e (Pg. 592) 

A slide projector is essentially the reverse of a camera. Light from an illuminated slide passes through a converging lens and forms a real image on the screen. 

a. Since the slide is the object, the object distance is the separation between the slide and the lens. Compare this object distance to the lens's focal length when the projector casts a real image on a screen far at the other side of a room. 
Answer: The object distance is slightly more than the lens's focal length. 
Why: When you use a converging lens to form a real image of a very distant object, that real image will form at an image distance that's equal to the lens's focal length. If the object isn't quite so far away, then the image distance will be a little more than the focal length. Now if you reverse the roles of object and image, so that the new object is just a little farther from the lens than the lens's focal length, the new image will form a little closer than very far away. That's how the projector works--it puts the slide at just a little more than the focal length of the lens away from the lens and the real image of the slide forms at the other side of the room. 

b. You focus the projector by moving the lens toward or away from the slide. If you want to focus the real image on a closer screen, which way should you move the lens? 
Answer: Move the lens away from the slide. 
Why: The farther the lens is from the slide, the less diverging are the light rays the lens must handle. The lens is thus able to bend them together more easily and they focus closer to the lens on the other side. 

c. The projector has a zoom lens that changes its focal length when you turn a dial. This lens makes it possible to change the size of the image on the screen. Zooming the lens also moves it toward or away from the slide. As the lens's focal length increases, should it move toward or away from the slide to keep the real image focused on the screen? 
Answer: It should move away from the slide. 
Why: The slide should always be slightly more than the focal length away from the lens. As the focal length increases, the lens must move away from the slide to maintain this relationship. 

d. As you change the focal length of the zoom lens and move it toward the slide, the real image on the screen grows larger. Draw pictures of the light rays to show why moving the lens toward the slide causes the real image to grow. 
Answer: Many possibilities, including:  
Why: The closer the lens is to the slide, the greater the angles separating various points on the slide, as viewed by the lens. The lens uses these same angles when it projects the real image on the screen, so that the highly curved, wide angle lens casts a huge image on the screen while the weak curved, telephoto lens casts a much smaller image on the screen.

e. Why must the slide be upside down in the projector in order to produce an upright real image on the screen?
Answer: Real images are always upside-down with respect to their objects.
Why: The lens flips the real image upside-down, so that if you want the image to be upright, you must insert the slide upside-down.