Cases – Chapter 14
1. The clear plastic safety reflector on a bicycle has a flat front surface, but its back interior surface is covered with the corners of
cubes. These cube corners or “corner cubes” stick up from the surface into the air like hundreds of small triangular pyramids.
What makes the reflector so useful is that light striking it is sent directly back toward its source.
a. When light hits the reflector at a right angle to its front surface, most of that light propagates to the back of the reflector
where it encounters one of the corner cubes. It hits the surface of the cube at a shallow angle and instead of leaving the plastic,
the light reflects perfectly. In fact, it reflects perfectly from all three faces of the corner cube and ends up returning directly
toward the source of the light. But the back surface of the reflector is clear plastic followed by air. Why does light reflect
perfectly off each surface of the corner cube?
b. While the reflector works best for light that hits it at a right angle to its surface, it also works for light that arrives at other
angles. But when that angle becomes too shallow, the reflector stops working and light passes through its back surface. Explain
why the light is able to get through in this case.
c. How does refraction at the front surface of the reflector help to widen the range of angles over which the reflector is able to
send light directly back toward its source?
d. Why won’t a flat mirror work well as a safety reflector?
2. 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.
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 eyeglasses containing converging lenses help a farsighted person see nearby objects.
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 glasses containing diverging lenses, lenses that bend light rays apart, help a nearsighted person see distant objects.
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?
3. The inexpensive disposable cameras that are sold in grocery stores produce remarkably good pictures considering the financial
constraints on their design. Despite their apparent simplicity, these cameras are sophisticated devices.
a. A disposable camera has no focus adjustment yet it produces reasonably sharp images. How does its small lens contribute to
this result?
b. The camera lens is normally made from a single piece of clear plastic with a refractive index of 1.55. If they accidentally
used a plastic with a refractive index of 1.45 and left the rest of the camera unchanged, the photographs would be blurry. Why?
c. The plastic used in the camera lens exhibits very little dispersion. How would dispersion affect the photographs?
d. The shutter in a disposable camera is a thin metal plate with a hole in it. When you take a picture, a spring pulls this plate
past the lens and the hole allows light to reach the film. How do the spring’s tension and the plate’s mass affect the exposure
time?
4. A video camera uses a converging lens to form a real image of a scene on an electronic imaging device. This device forms a
video signal out of the pattern of light on its surface.
a. Why must the lens of the video camera be a converging lens, rather than a diverging lens—a lens that bends light rays apart?
b. The camera focuses automatically by analyzing the contrast in the video image. As you shift the camera from a distant
object to one that’s closer, the lens moves. Does it move toward the imaging device or away from it? Explain.
c. The camera has an automatic iris—a diaphragm that controls the lens’s aperture. When you turn the camera toward a bright
scene, the iris reduces the lens’s aperture. What effect does this change have on the camera’s depth of focus?
d. The camera has a zoom lens that changes its focal length at the touch of a button. When you zoom in on a person for a closeup, does the focal length increase or decrease?
e. As the lens changes its focal length, it also moves toward or away from the electronic image device. As you zoom out to
view more of the scene, does the lens move toward or away from the imaging device?
5. 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.
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?
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?
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.
e. Why must the slide be upside down in the projector in order to produce an upright real image on the screen?
6. Doctors use endoscopes to look inside patients through narrow openings. An endoscope contains a 1- or 2-meter long bundle
of optical fibers that are carefully arranged and bonded together at their ends but that are independent and flexible in between.
Each optical fiber is a pipe for light—light entering one end emerges from the other. When one end of the endoscope’s fiber
bundle is illuminated with a particular pattern of light, that same pattern of light appears at the bundle’s other end.
a. The core of each optical fiber is made from a glass with a large refractive index. This core is wrapped in a glass with a lower
refractive index. Each time light tries to leave the core at a shallow angle, it is perfectly reflected. Why?
b. The endoscope uses an objective lens to form a real image of nearby tissue on one end of the fiber bundle. Why must the
objective lens have a very short focal length in order to form a real image of nearby tissue?
c. The doctor uses an eyepiece to view light emerging from the other end of the bundle. How does the focal length of that
eyepiece affect the magnification of the endoscope?
d. To obtain a large depth of focus, should the aperture of the endoscope’s objective lens be large or small?
*e. To illuminate the patient’s tissue, the endoscope has a second bundle of fibers that carries light from a bulb to the tissue. It
uses a converging lens to form a real image of the bulb’s filament on the entry surface of the fibers. If the bulb’s filament and
the fibers are 4 cm apart and the lens is halfway between them, what should the lens’s focal length be?
7. A fiber optic light guide consists of a narrow glass fiber core coated by a second layer of glass with a lower refractive index.
The core is made of an extremely pure and homogeneous glass so that it absorbs very little light.
a. Light in the fiber core hits the core’s surface at a very shallow angle and is reflected. Why can’t the light propagate into the
surrounding layer of glass?
b. The glass is free of bubbles. What would happen to the light if it had to pass through a series of air bubbles on its way
through the fiber?
*c. Light passing through an optical fiber must travel through an enormous amount of glass. If impurities in the glass halved
the light intensity each time it traveled 1 km, how much light would remain after 10 km of fiber?
d. Information is usually sent through a fiber as brief pulses of light. Those pulses are formed by effectively blocking and
unblocking the light from a laser. Since that technique is equivalent to amplitude modulating a carrier light wave, the light
pulses contain sideband waves at slightly different frequencies and wavelengths from the carrier wave. Because each pulse of
light is formed by the combination of many waves with different frequencies and wavelengths, the fiber must exhibit very little
dispersion. What would happen to a single pulse of light if it passed through a long fiber with strong dispersion?
e. Since even the best glass fibers absorb some light, light passing through a long fiber must be amplified by short segments of
laser amplifier fiber that are spliced into the main fiber. As light passes through a segment of laser amplifier fiber, each photon
is duplicated hundreds of times. Explain why this laser amplifier fiber needs power to operate.
8. The power supply in your stereo amplifier uses alternating current from the electric company to provide direct current to the
amplifier. This supply converts electric power from one form to another through the use of transformers, diodes, capacitors, and
transistors.
a. The power supply provides a relatively small voltage rise to the large current that it sends through the amplifier. The
voltages provided by the electric company are too high for the amplifier and the currents are too small. How does a transformer
make it possible for the power supply to provide a relatively small voltage rise to a relatively large current that flows between it
and the amplifier?
b. The power supply’s transformer provides AC electric power through two wires, but the amplifier needs DC electric power
through two wires. To fix this mismatch, the stereo connects these two pairs of wires with four diodes so that even though the
currents through the two wires of the transformer reverse, the currents through the two wires of the amplifier don’t reverse.
How are those four diodes connected between the transformer and amplifier? (Draw a picture and indicate which way current
can flow through each diode.)
c. While the diodes (see part b) ensure that current always flows in one direction through the amplifier, the transformer can’t
provide current when the current from the power company is reversing. To maintain a steady current through the amplifier, the
power supply uses a large capacitor. When the transformer’s current is large, some of that current is used to transfer charge
between the capacitor’s plates so that it stores separated charge. When the transformer’s current is small, this separated charge
is allowed to flow through the amplifier as current. Draw a graph of the voltage difference between the two plates of the
capacitor versus time. Mark the times when the amount of separated charge is increasing and when it’s decreasing.
d. The transformer, diodes, and capacitor do a pretty good job of sending direct current through the amplifier, but there still
tend to be periodic fluctuations in that current. To keep the current stable, the amplifier uses a regulating device. Just before the
current enters the amplifier, it passes through an n-channel MOSFET. An electronic sensor measures the current through the
amplifier and determines if that current is too high or too low. It then adjusts the charge on the gate of the MOSFET to increase
or decrease the MOSFET’s electrical resistance and lower or raise the current through the amplifier. If the sensor detects that
the current is too high, should it increase or decrease the positive charge on the MOSFET’s gate? Explain.
9. You enjoy listening to your little portable radio while jogging, but it hasn’t been working properly since it got wet in the rain
last week. The problem is that it keeps turning itself off. Because the radio makes no “click” sound when you press the “on” or
“off” buttons and because it turns itself off automatically after an hour, you know that the switch that controls the radio’s power
is electronic. It’s probably an n-channel MOSFET that’s connected in series with the radio’s electronics so that current from the
battery must pass through both the electronics and the MOSFET before returning to the battery.
a. Why won’t any power reach the electronics when the MOSFET isn’t conducting current?
b. What must the “on” button do to make the n-channel MOSFET conduct current so that the radio will operate?
c. What must the “off” button or the automatic shutdown do to stop the n-channel MOSFET from conducting current, so that
the radio will turn off?
d. Water is a poor conductor of electricity, but with patience you can send charge through it. If water is slowly turning off the
radio, what is it probably doing?
e. You discover a small drop of water inside the “off” button, allowing positive charge to flow slowly from the gate of the nchannel MOSFET to the negative terminal of the battery. You remove the water and the radio works perfectly. Why did the
drop cause trouble and why did removing the drop fix the radio?
10. Your new electric guitar and amplifier sound great, although all the neighbors seem to have gone on vacation since you
bought it last week. After 6 straight hours of jamming you decide to take a break and figure out how it works.
a. You begin by examining the strings and pickups—the devices that sense the strings’ motions and represent them as electric
currents. The pickup near each string is a coil of wire wrapped around a small permanent magnet. The permanent magnet
magnetizes the steel string so that it induces an alternating current in the pickup coil as it vibrates back and forth. What
provides the power for this alternating current?
*b. The electric power provided by the pickup is much too small to drive a speaker, so it must be amplified. The first step is to
send it through a preamplifier. Current from the pickup flows through the preamplifier’s input circuit and an amplified version
of that current flows through the preamplifier’s output circuit. The voltage rise at the preamplifier’s output is 10 times as large
as the voltage drop at its input, and the current passing through its output circuit is 10 times as large as the current passing
through its input circuit. The power the preamplifier is providing is how many times as large as the power it’s receiving from
the pickup?
c. The output of the preamplifier is connected to the main power amplifier. You open a side panel of the amplifier and notice
several large MOSFETs bolted to a heat sink. Since the amplifier was running recently (you wisely turned it off and unplugged
it before opening it up), the heat sink is quite warm. These MOSFETs have been controlling the flow of current from the
amplifier’s power supply to your speaker, so their electrical resistances have been fluctuating up and down. What has the
amplifier been doing to the MOSFETs to make their electrical resistances change?
d. Why have the MOSFETs been producing thermal energy?
e. You reinstall the amplifier’s side panel and take a look at the speaker cabinet. This cabinet contains several speakers, each of
which has a coil of wire that becomes magnetic when current flows through it. A nearby permanent magnet pushes on the
magnetic coil, and this force moves a paper cone to create sound. The currents needed for high volume are large, and they flow
to and from the speaker through the speaker wires. You notice that the speaker wires are warm—they have been wasting some
of the power from your amplifier! You knew it was a mistake to buy cheap thin speaker wire, but it’s too late now. You have
extra wire, which you can use to reduce the wasted power. Should you add a second wire in parallel to each of the present wires
or should you add a second wire in series with each of the present wires? Explain your answer.