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All Textbook Solutions for College Physics
Make a drawing similar to Figure 23.14, but with the pendulum moving in the opposite direction. Then use Faraday’s law, Lenz’s law, and RHR—l to show that magnetic force opposes motion.Figure 23.59 A coil is moved into and out of a region of uniform magnetic field. A coil is moved through a magnetic field as shown in Figure 23.59. The field is uniform inside the rectangle and zero outside. What is the direction of the induced current and what is the direction of the magnetic force on the coil at each position shown?Calculate the peak voltage of a generator that rotates its 200-turn, 0.100 m diameter coil at 3600 rpm in a 0.800 T field.At what angular velocity in rpm will the peak voltage of a generator be 480 V. if its 500-turn, 8.00 cm diameter coil rotates in a 0.250 T field?What is the peak emf generated by rotating a 1000-turn, 20.0 cm diameter coil in the Earth’s 5.00105T magnetic field, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in 10.0 ms?What is the peak emf generated by a 0.250 m radius, 500turn coil is rotated one-fourth of a revolution in 4.17 ms, originally having its plane perpendicular to a uniform magnetic field. (This is 60 rev/s.)(a) A bicycle generator rotates at 1875 rad/s, producing an 18.0 V peak emf. It has a 1.00 by 3.00 cm rectangular coil in a 0.640 T field. How many turns are in the coil? (b) Is this number of turns of wire practical for a 1.00 by 3.00 cm coil?Integrated Concepts This problem refers to the bicycle generator considered in the previous problem. It is driven by a 1.60 cm diameter wheel that rolls on the outside rim of the bicycle tire. (a) What is the velocity 0f the bicycle if the generator’s angular velocity is 1875 rad/s? (b) What is the maximum emf of the generator when the bicycle moves at 10.0 m/s, noting that it was 18.0 V under the original conditions? (c) If the sophisticated generator can vary its own magnetic field, what field strength will it need at 5.00 m/s to produce a 9.00 V maximum emf?(a) A car generator turns at 400 rpm when 1he engine is idling. Its 300-turn, 5.00 by 8.00 cm rectangular coil rotates in an adjustable magnetic field 50 that it can produce suf?cient voltage even at low rpms. What is the field strength needed to produce a 24.0 V peak emf? (b) Discuss how this required field strength compares to those available in permanent and electromagnets.Show that if a coil rotates at an angular velocity (, the period of its AC output is 2(/(.A 75-turn, 10.0 cm diameter coil rotates at an angular velocity of 8.00 radius in a 1.25 T field, starting with the plane of the coil parallel to the field. (a) What is the peak emf? (b) At what time is the peak emf first reached? (c) At what time is the emf first at its meet negative? (d) What is the period of the AC voltage output?(a) If the emf of a coil rotating in a magnetic field is zero at t = 0, and increases to its first peak at t = 0.100 ms, what is the angular velocity of the coil? (b) At what time will its next maximum occur? (c) What is the period of the output? (d) When is the output first one-fourth at its maximum? (e) When is it next one-fourth at its maximum?Unreasonable Results A 500-turn coil with a 0.250 m2 area is spun in the Earth’s 5.00105T field, producing a 12.0 kV maximum emf. (a) At what angular velocity must me coil be spun? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?Suppose a motor connected to a 120 V source draws 10.0 A when it first starts. (a) What is its resistance? (b) What current does it draw at its normal operating speed when it develops a 100 V back emf?A motor operating on 240 V electricity has a 180 V back emf at operating speed and draws a 12.0 A current. (a) What is its resistance? (b) What current does it draw when it is first started?What is the back emf of a 120 V motor that draws 3.00 A at its normal speed and 20.0 A when first starling?The motor in a toy car operates on 6.00 V. developing a 4.50 V back emf at normal speed. If it draws 3.00 A at normal speed, what current does it draw when starting?Integrated Concepts The motor in a toy car is powered by four batteries in series, which produce a total emf of 6.00 V. The motor draws 3.00 A and develops a 4.50 V back emf at normal speed. Each battery has a 0.100 (internal resistance. What is the resistance of the motor?A plug—in transformer, like that in Figure 23.29, supplies 9.00 V to a video game system. (a) How many turns are in its secondary coil, if its input voltage is 120 V and the primary coil has 400 turns? (b) What is its input current when its output is 1.30 A?An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so that she can use some small appliances on her trip. (a) What is the ratio of turns in the primary and secondary coils of her transformer? (b) What is the ratio of input to output current? (c) How could a New Zealander traveling in the United States use this same transformer to power her 240 V appliances from 120 V?A cassette recorder uses a plug-in transformer to convert 120 V to 12.0 V, with a maximum current output of 200 mA. (a) What is the current input? (b) What is the power input? (c) Is this amount of power reasonable for a small appliance?(a) What is the voltage output of a transformer used for rechargeable flashlight batteries, if its primary has 500 turns, its secondary 4 turns, and the input voltage is 120 V? (b) What input current is required to produce a 4.00 A output? (c) What is the power input?(a) The plug-in transformer for a laptop computer puts out 7.50 V and can supply a maximum current of 2.00 A. What is the maximum input current if the input voltage is 240 V? Assume 100% ef?ciency. (b) If the actual efficiency is less man 100%, would the input current need to be greater or smaller? Explain.A multipurpose transformer has a secondary coil with several points at which a 1inziltage can be extracted, giving outputs of 5.60, 12.0, and 480 V. (a) The input voltage is 240 V to a primary coil of 280 turns. What are the numbers of turns in the parts of the secondary used to produce the output voltages? (b) If the maximum input current is 5.00 A, what are the maximum output currents (each used alone)?A large power plant generates electricity at 12.0 kV. Its old transformer once converted the voltage to 335 kV. The secondary at this transformer is being replaced so that its output can be 750 kV for more efficient cross-country transmission on upgraded transmission lines. (a) What is the ratio of turns in the new secondary compared with the old secondary? (b) What is the ratio of new current output to old output (at 335 IN) for the same power? (c) If the upgraded transmission lines have the same resistance, what is the ratio of new line power loss to old?If the power output in the previous problem is 1000 MW and line resistance is 2.00 (, what were the old and new line losses?Unreasonable Results The 335 kV AC electricity from a power transmission line is fed into the primary coil of a transformer. The ratio of the number of turns in the secondary to the number in the primary is Ns/Np = 1000. (a) What voltage is induced in the secondary? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?Construct Your Own Problem Consider a double transformer to be used to create very large voltages. The device consists of two stages. The first is a transformer that produces a much larger output voltage than its input. The Output of the first transformer is used as input to a second transformer that further increases the voltage. Construct a problem in which you calculate the output voltage of the final stage based on the input voltage of the first Stage and the number of turns or loops in bath parts of both transformers (four coils in all). Also calculate the maximum output current of the final stage based on the input current. Discuss the possibility of power losses in the devices and the effect on the output current and power.Integrated Concepts A short circuit to the grounded metal case of an appliance occurs as shown in Figure 23.60. The person touching the case is wet and only has a 3.00 k(resistance to earth/ground. (a) What is the voltage on the case if 5.00 mA flows through the person? (b) What is the current in the short circuit if the resistance of the earth/ground wire is 0.200 ? (c) Will this trigger the 20.0 A circuit breaker supplying the appliance? Figure 23.60 A person can be shocked even when the case of an appliance is grounded. The large short circuit current produces a voltage on the case of the appliance, since the resistance of the earth/ground wire is not zero.Two coils are placed close together in a physics lab to demonstrate Faraday’s law of induction. A current of 5.00 A in one is switched off in 1.00 ms, inducing a 9.00 V emf in the other. What is their mutual inductance?If two coils placed next to one another have a mutual inductance at 5.00 mH, what voltage is induced in one when the 2.00 A current in the other is switched off in 30.0 ms?The 4.00 A current through a 7.50 mH inductor is switched off in 8.33 ms. What is the emf induced opposing this?A device is turned on and 3.00 A flows through it 0.100 ms later. What is the self-inductance of the device if an induced 150 V emf opposes this?Starting with emf2=MI1t, show that the units of inductance are (Vs)/A=s.Camera flashes charge a capacitor to high voltage by switching the current through an inductor on and off rapidly. In what time must the 0.100 A current through a 2.00 mH inductor be switched on or off to induce a 500 V emf?A large research solenoid has a self-inductance of 25.0 H. (a) What induced emf opposes shutting it off when 100 A of current through it is switched off in 80.0 ms? (b) How much energy is stored in the inductor at full current? (c) At what rate in waits must energy be dissipated to switch the current off in 80.0 ms? (d) In View of the answer to the last part, is it surprising that shutting it down this quickly is difficult?(a) Calculate the self-inductance of a 50.0 cm long, 10.0 cm diameter solenoid having 1000 loops. (b) How much energy is stored in this inductor when 20.0 A of current flows through it? (c) How fast can it be turned off if the induced emf cannot exceed 3.00 V?A precision laboratory resistor is made of a coil of wire 1.50 cm in diameter and 4.00 cm long, and it has 500 turns. (a) What is its self-inductance? (b) What average emf is induced it the 12.0 A current through it is turned on in 5.00 ms (one-fourth of a cycle for 50 Hz AC)? (c) What is its inductance if it is shortened to half its length and counter-wound (two layers of 250 turns in opposite directions)?The healing coils in a hair dryer are 0.800 cm in diameter, have a combined length of 1.00 m, and a total of 400 turns. (a) What is their total self-inductance assuming they act like a single solenoid? (b) How much energy is stored in them when 6.00 A flows? (c) What average emf opposes shutting them off if this is done in 5.00 ms (one-fourth at a cycle for 50 Hz AC)?When the 20.0 A current through an inductor is turned off in 1.50 ms, an 800 V emf is induced, opposing the change. What is the value of the self-inductance?How fast can the 150 A current through a 0.250 H inductor be shut off if the induced emf cannot exceed 75.0 V?Integrated Concepts A very large, superconducting solenoid such as one used in MRI scene, stores 1.00 MJ of energy in its magnetic field when 100 A flows. (a) Find its serf-inductance. (b) If the coils “go normal,” they gain resistance and start to dissipate thermal energy. What temperature increase is produced it all the stored energy goes into heating the 1000 kg magnet, given its average speci?c heat is 200 J/kg(°C?Unreasonable Results A 25.0 H inductor has 100 A of current turned off in 1.00 ms. (a) What voltage is induced to oppose this? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?It you want a characteristic RL time constant of 1.00 s, and you have a 500 (resistor, what value of self-inductance is needed?Your RL circuit has a characteristic time constant of 20.0 ns, and a resistance of 5.00 M (a) What is the inductance of the circuit? (b) What resistance would give you a 1.00 ns time constant, perhaps needed for quick response in an oscilloscope?A large superconducting magnet, used for magnetic resonance imaging, has a 50.0 H inductance. It you want current through it to be adjustable with a 1.00 s characteristic time constant, what is the minimum resistance of system?Verify that alter a time of 10.0 ms, the current for the situation considered in Example 23.9 will be 0.183 A as stated.Suppose you have a supply of inductors ranging from 1.00 nH to 10.0 H, and registers ranging from 0.100 (to 1.00 M What is the range of characteristic RL time constants you can produce by connecting a single resistor to a single inductor?(a) What is the characteristic time constant of a 25.0 mH inductor that has a resistance of 4.00 ? (b) If it is connected to a 12.0 V battery, what is the current after 12.5 ms?What percentage of the final current I0 flows through an inductor L in series with a resistor R, three time constants after the circuit is completed?The 5.00 A current through a 1.50 H inductor is dissipated by a 2.00 ( resistor in a circuit like that in Figure 23.44 with the switch in position 2. (a) What is the initial energy in the inductor? (b) How long will it take the current to decline to 5.00% of its initial value? (c) Calculate the average power dissipated, and compare it with the initial power dissipated bythe resistor.(a) Use the exact exponential treatment to find how much time is required to bring the current through an 80.0 mH inductor in series with a 15.0 (resistor to 99.0% of its final value, starting from zero. (b) Compare your answer to the approximate treatment using integral numbers of (c) Discuss how significant the difference is.(a) Using the exact exponential treatment, find the time required for the current through a 2.00 H inductor in series with a 0.500 (resistor to be reduced to 0.100% of its original value. (b) Compare your answer to the approximate treatment using integral numbers of . (c) Discuss how signi?cant the difference is.At what frequency will a 30.0 mH inductor have a reactance of 100 ?What value of inductance should be used if a 20.0 k(reactance is needed at a frequency of 500 Hz?What capacitance should be used to produce a 2.00 M(reactance at 60.0 Hz?At what frequency will an 80.0 mF capacitor have a reactance of 0.250 ?(a) Find me current through a 0.500 H inductor connected to a 60.0 Hz, 430 V AC source. (b) What would the current be at 100 kHz?(a) What current flows when a 60.0 Hz, 480 V AC source is connected to a 0.250 (F capacitor? (b) What would the current be at 25.0 kHz?A 20.0 kHz, 16.0 V source connected to an inductor produces a 2.00 A current. What is the inductance?A 20.0 HZ, 16.0 V source produces a 2.00 mA current when connected to a capacitor. What is the capacitance?(a) An inductor designed to filter high-frequency noise from power supplied to a personal computer is placed in series with the computer. What minimum inductance should it have to produce a 2.00 k(reactance for 15.0 kHz noise? (b) What is its reactance at 60.0 Hz?The capacitor in Figure 23.55(a) is designed to filter low—frequency signals, impeding their transmission between circuits. (a) What capacitance is needed to produce a 100 k reactance at a frequency of 120 Hz? (b) What would its reactance be at 1.00 MHz? (c) Discuss the implications of your answers to (a) and (b).The capacitor in Figure 23.55(b) will filler high—frequency signals by shorting them to earth/ground. (a) What capacitance is needed to produce a reactance of 10-0 m for a 5.00 kHz signal? (b) What would its reactance be at 3.00 Hz? (c) Discuss the implications of your answers to (a) and (b).Unreasonable Results In a recording of voltages due to brain activity (an EEG), a 10.0 mV signal with a 0.500 Hz frequency is applied to a capacitor, producing a current of 100 mA. Resistance is negligible. (a) What is the capacitance? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?Construct Your Own Problem Consider the use of an inductor in series with a computer operating on 60 Hz electricity. Construct a problem in which you calculate the relative reduction in voltage of incoming high frequency noise compared to 60 Hz voltage. Among the things to consider are the acceptable series reactance of the inductor for 60 Hz power and the likely frequencies of noise coming through the power lines.An RL circuit consists of a 40.0 (resistor and a 3.00 mH inductor. (a) Find its impedance Z at l60.0 Hz and 10.0 kHz. (b) Compare these values of Z with mouse found in Example 23.12 in which there was also a capacitor.An RC circuit consists of a 40.0 (resistor and a 5.00 (F capacitor. (a) Find its impedance an 60.0 Hz and 10.0 kHz. (b) Compare these values of Z with those found in Example 23.12, in which there was also an inductor.An LC circuit consists of a 3.00 mH inductor and a 5.00 (F capacitor. (a) Find its impedance at 60.00 Hz and 10.0 kHz. (b) Compare these values of Z with those found in Example 23.12 in which there was also a resistor.What is the resonant frequency of a 0.500 mH inductor connected to a 40.0 (F capacitor?To receive AM radio, you want an RLC circuit that can be made to resonate at any frequency between 500 and 1650 kHz. This is accomplished with a fixed 1.00 (H inductor connected to a variable capacitor. What range of capacitance is needed?Suppose you have a supply of inductors ranging from 1.00 nH to 10.0 H, and capacitors ranging from 1.00 pF to 0.100 F. What is the range of resonant frequencies than can be achieved from combinations of a single inductor and a single capacitor?What capacitance do you need to produce a resonant frequency of 1.00 GHz, when using an 8.00 nH inductor?What inductance do you need to produce a resonant frequency of 60.0 Hz, when using a 2.00 F capacitor?The lowest frequency in the FM radio band is 88.0 MHz. (a) What inductance is needed to produce this resonant frequency if it is connected to a 2.50 pF capacitor? (b) The capacitor is variable, to allow the resonant frequency to be adjusted to as high as 108 MHz. What must the capacitance be at this frequency?An RLC series circuit has a 2.50 (resistor, a 100 (H inductor, and an 80.0 (F capacitor. (a) Find the circuit's impedance at 120 Hz. (b) Find the circuit’s impedance at 5.00 kHz. (c) If the voltage source has Vrms = 5.60 V, what is Irms at each frequency? (d) What is the resonant frequency of the circuit? (e) What is Irms at resonance?An RLC series circuit hag a 1.00 k(register, a 150 (H inductor, and a 25.0 nF capacitor. (a) Find the circuit’s impedance at 500 Hz. (b) Find the circuit’s impedance at 7.50 kHz. (c) It the voltage source has Vrms = 408 V, what is Irms at each frequency? (d) What is the resonant frequency of the circuit? (e) What is Irms at resonance?An RLC series circuit has a 2.50 (resistor, a 100 (H inductor, and an 80.0 (F capacitor. (a) Find the power factor at f = 120 Hz. (b) What is the phase angle at 120 Hz? (c) What is the average power at 120 Hz? (d) Find the average power at the circuit's resonant frequency.An RLC series circuit has a 1.00 k(resistor, a 1.50 (H inductor, and a 25.0 nF capacitor. (a) Find the power factor at f = 7.50 Hz. (b) What is the phase angle at this frequency? (c) What is the average power at this frequency? (d) Find the average power at the circuit’s resonant frequency.An RLC series circuit has a 200 (resistor and a 25.0 mH inductor. At 8000 Hz, the phase angle is 45.0°. (a) What is the impedance? (b) Find the circuit’s capacitance. (c) If Vrms = 408 V is applied, what is the average power supplied?Referring to Example 23.14, find the average power at 10.0 kHz.The direction of the electric field shown in each part of Figure 24.5 is that produced by the charge distribution in the wire. Justify the direction shown in each part, using the Coulomb force law and the definition of E = F/q, where q is a positive test charge.Is the direction of the magnetic field shown in Figure 24.6 (a) consistent with the right—hand rule for current (RHR-2) in the direction shown in the figure?Why is the direction of the current shown in each part of Figure 24.6 opposite to the electric field produced by the wire’s charge separation?In which situation shown in Figure 24.24 will the electromagnetic wave be more successful in inducing a current in the wire? Explain. Figure 24.24 Electromagnetic waves approaching long straight wiles.In which situation shown in Figure 24.25 will the electromagnetic wave be more successful in inducing a current in the loop? Explain. Figure 24.25 Electromagnetic waves approaching a wire loop.Should the straight wire antenna of a radio he vertical or horizontal to best receive radio waves broadcast by a vertical transmitter antenna? How should a loop antenna be aligned to best receive the signals? (Note that the direction at the loop that produces the best reception can he used to determine the location at the source. It is used for that purpose in hacking tagged animals in nature studies, for example.)Under what conditions might wires in a DC circuit emit electromagnetic waves?Give an example of interference of electromagnetic waves.Figure 24.26 shows the interference pattern of two radio antennas broadcasting the same signal. Explain how this is analogous to the interference pattern for sound produced by two speakers. Could this he used to make a directional antenna system that broadcasts preferentially in certain directions? Explain. Figure 24.26 An overhead view of two radio broadcast antennas sending the same signal, and the interference pattern they produce.Can an antenna be any length? Explain your answer.If you live in a region that has a particular TV station, you can sometimes pick up some at its audio portion on your FM radio receiver. Explain how this is possible. Does it imply that TV audio is broadcast as FM?Explain why people who have the lens of their eye removed because of cataracts are able to see low-frequency ultraviolet.How do ?uorescent soap residues make clothing look “brighter and whiter” in Outdoor light? Would this be effective in candlelight?Give an example of resonance in the reception of electromagnetic waves.Illustrate that the size of details of an object that can be detected with electromagnetic waves is related to their wavelength, by comparing details observable with two different types (for example, radar and visible light or infrared and X-rays).Why don't buildings block radio waves as completely as they do visible light?Make a list of some everyday objects and decide whether they are transparent or opaque to each of the types of electromagnetic waves.Your friend says mat more patterns and colors can be seen on the wings of birds if viewed in ultraviolet light. Would you agree with your friend? Explain your answer.The rate at which information can be transmitted on an electromagnetic wave is proportional to the frequency of the wave. Is this consistent with the fact that laser telephone transmission at visible frequencies carries far more conversations per optical fiber than conventional electronic transmission in a wire? What is the implication tor ELF radio communication with submarines?Give an example of energy carried by an electromagnetic wave.In an MRI scan, a higher magnetic field requires higher frequency radio waves to resonate with the nuclear type whose density and location is being imaged. What effect does going to a larger magnetic field have on the most efficient antenna to broadcast those radio waves? Does it favor a smaller or larger antenna?Laser vision correction often uses an excimer laser that produces 193-nm electromagnetic radiation. This wavelength is extremer strongly absorbed by the cornea and athletes it in a manner that reshapes the cornea to correct vision detects. Explain how the strong absorption helps concentrate the energy in a thin layer and thus give greater accuracy in shaping the cornea. Also explain how this strong absorption limits damage to the lens and retina of the eye.Verify that the correct value for the speed of light c is obtained when numerical values for the permeability and permittivity of free space (0 and 0) are entered into the equation c=100.Show that, when SI units for 0 and 0 are entered, the units given by the right-hand side of the equation in the problem above are m/s.What is the maximum electric field strength in an electromagnetic wave that has a maximum magnetic field strength of 5.00104T (about 10 times the Earth’s)?The maximum magnetic field strength of an electromagnetic field is 5106T. Calculate the maximum electric field strength if the wave is traveling in a medium in which the speed of the wave is 0.75c.Verify the units obtained for magnetic field strength B in Example 24.1 (using the equation B=Ec ) are in fact teslas (T).(a) Two microwave frequencies are authorized for use in microwave ovens: 900 and 2560 MHZ. Calculate the wavelength at each. (b) Which frequency would produce smaller hot spots in foods due to interference effects?(a) Calculate the range of wavelength for AM radio given its frequency range is 540 to 1600 kHz. (b) Do the same for the FM frequency range of 88.0 to 108 MHz.A radio station utilizes frequencies between commercial AM and FM. What is the frequency of a 11.12-m-wavelength channel?Find the frequency range of visible light, given that it encompasses wavelengths from 330 to 760 nm.Combing your hair leads to excess electrons on the comb. How fast would you have to move the comb up and down to produce red light?Electromagnetic radiation having a 15.0m wavelength is classified as infrared radiation. What is its frequency?Approximately what is the smallest detail observable with a microscope that uses ultraviolet light of frequency 1.201015Hz ?A radar used to detect the presence of aircraft receives a pulse that has reflected off an object 6105s after it was transmitted. What is the distance from the radar station to the reflecting object?Some radar systems detect the size and shape of objects such as aircraft and geological terrain. Approximately what is the smallest observable detail utilizing 500-MHz radar?Determine the amount of time it takes for X-rays of frequency 31018Hz to travel (a) 1 mm and (b) 1 cm.If you wish to detect details of the size of atoms (about 11010m ) with electromagnetic radiation, it must have a wavelength of about this size. (a) What is its frequency? (b) What type of electromagnetic radiation might this be?If the Sun suddenly turned off, we would not know it until its light stopped coming. How long would that be, given that the Sun is 1.501011m away?Distances in space are often quoted in units of light years, the distance light travels in one year. (a) How many meters is a light year? (b) How many meters is it to Andromeda, the nearest large galaxy, given that it is 2.00106 light years away? (c) The most distant galaxy yet discovered is 12.0109 light years away. How far is this in meters?A certain 50.0-Hz AC power line radiates an electromagnetic wave having a maximum electric field strength of 13.0 kV/m. (a) What is the wavelength of this very low frequency electromagnetic wave? (b) What is its maximum magnetic field strength?During normal bee?ng, the heat creates a maximum 4.00mv potential across 0.300 m of a person’s chest, creating a 1.00-Hz electromagnetic wave. (a) What is the maximum electric field strength created? (b) What is the corresponding maximum magnetic field strength in the electromagnetic wave? (c) What is the wavelength of the electromagnetic wave?(a) The ideal size (most efficient) for a broadcast antenna with one end on the ground is onefourth the wavelength (/4) of the electromagnetic radiation being sent out. If a new radio station has such an antenna that is 50.0 m high, what frequency does it broadcast most efficiently? Is this in the AM or FM band? (b) Discuss the analogy of the fundamental resonant mode of an air column closed at one end to the resonance of currents on an antenna that is one-fourth their wavelength.(a) What is the wavelength of 100MHz radio waves used in an MRI unit? (b) If the frequencies are swept over a (1.00 range centered on 100 MHZ, what is the range of wavelengths broadcast?(a) What is the frequency at the 193-nm ultraviolet radiation used in laser eye surgery? (b) Assuming the accuracy with which this EM radiation can ablate the cornea is directly proportional to wavelength, how much more accurate can this UV be than the shortest visible wavelength of light?TV-reception antennas for VHF are constructed with cross wires supported at their centers, as shown in Figure 24.27. The ideal length for the cross wires is one-half the wavelength to he received, with the more expensive antennas having one for each channel. Suppose you measure the lengths of the wires for particular channels and find them to be 1.94 and 0.753 m long, respectively. What are the frequencies for these channels? Figure 24.27 A television reception antenna has cross wires of various lengths to most efficiently receive different wavelengths.Conversations with astronauts on lunar walks had an echo that was used to estimate the distance to the Moon. The sound spoken by the person on Earth was transformed into a radio signal sent to the Moon, and transformed hack into sound on a speaker inside the astronaut’s space suit. This sound was picked up by the microphone in the space suit (intended tor the astronaut’s voice] and sent back to Earth as a radio echo of sorts. If the round-trip time was 2.60 s, what was the approximate distance to the Moon, neglecting any delays in the electronics?Lunar astronauts placed a reflector on the Moon's Surface, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. (a) To what accuracy in meters can the distance to the Moon be determined, if this time can be measured to 0.100 ns? (b) What percent accuracy is this, given the average distance to the Moon is 3.84108m ?Radar is used to determine distances to various objects by measuring the round-trip time for an echo from the object. (a) How far away is the planet Venus if the echo time is 1000 s? (b) What is the echo time for a car 75.0 m from a Highway Police radar unit? (c) How accurately (in nanoseconds) must you be able to measure the echo time to an airplane 12.0 km away to determine its distance within 10.0 m?Integrated Concepts (a) Calculate the ratio of the highest to lowest frequencies of electromagnetic waves the eye can see, given the wavelength range of visible light is from 380 to 760 nm. (b) Compare this with the ratio of highest to lowest frequencies the ear can hear.Integrated Concepts (a) Calculate the rate in watts at which heat transfer through radiation occurs (almost entirely in the infrared] from 1.0 m2of the Earth’s surface at night. Assume the emissivity is 0.90, the temperature of the Earth is 15°C, and that of outer space is 2.7 K. (b) Compare the intensity at this radiation with that coming to the Earth from the Sun during the day, which averages about 800 W/m2, only hall of which is absorbed. (c) What is the maximum magnetic field strength in the outgoing radiation, assuming it is a continuous wave?What is the intensity of an electromagnetic wave with a peak electric field strength of 125 V/m?Find the intensity of an electromagnetic wave having a peak magnetic field strength of 4.00109T.Assume the helium-neon lasers commonly used in student physics laboratories have power outputs of 0.250 mw. (a) If such a laser beam is projected onto a circular spot 1.130 mm in diameter, what is its intensity? (b) Find the peak magnetic field strength. (c) Find the peak electric field strength.An AM radio transmitter broadcasts 50.0 kW of power uniformly in all directions. (a) Assuming all of the radio waves that strike the ground are completely absorbed, and that there is no absorption by the atmosphere or other objects, what is the intensity 30.0 km away? (Hint: Half the power will be spread over the area of a hemisphere.) (b) What is the maximum electric field strength at this distance?Suppose the maximum safe intensity of microwaves for human exposure is taken to be 1.00 W/m2. (a) If a radar unit leaks 10.0 W of microwaves (other than those sent by its antenna) uniformly in all directions, how far away must you be to be exposed to an intensity considered to be safe? Assume that the power spreads uniformly over the area of a sphere with no complications from absorption or reflection. (b) What is the maximum electric field strength at the safe intensity? (Note that early radar units leaked more than modern ones do. This caused identi?able health problems, such as cataracts, for people who worked near them.)A 2.50-m-diameter university communications satellite dish receives TV signals that have a maximum electric field strength (for one channel) of 7.50 (V/m. (See Figure 24.28.) (a) What is the intensity of this wave? (b) What is the power received by the antenna? (c) If the orbiting satellite broadcasts uniformly over an area of 1.501013m2 (a large fraction of North America), how much power does it radiate? Figure 24.28 Satellite dishes receive TV signals sent from orbit. Although the signals are quite weak, the receiver can detect them by being tuned to resonate at their frequency.Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time-called pulsed lasers. They are used to ignite nuclear fusion, for example. Such a lager may produce an electromagnetic wave with a maximum electric field strength of 1.001011V/m for a time of 1.00 ns. (a) What is the maximum magnetic field strength in the wave? (b) What is the intensity of the beam? (c) What energy does it deliver on a 1.00-mm2 area?Show that for a continuous sinusoidal electromagnetic wave, the peak intensity is twice the average intensity (I0 = 2Iave), using enter the fact that E0=2Erms, or B0=2Brms, where rms means average (actually root mean square, a type of average).Suppose a source of electromagnetic waves radiates uniformly in all directions in empty space where there are no absorption or interference effects. (a) Show that the intensity is inversely proportional to r2, the distance from the source squared. (b) Show that the magnitudes of the electric and magnetic fields are inversely proportional to r.Integrated Concepts An LC circuit with a 5.00pF capacitor oscillates in such a manner as to radiate at a wavelength of 3.30 m. (a) What is the resonant frequency? (b) What inductance is in series with the capacitor?Integrated Concepts What capacitance is needed in series with an 800H inductor to form a circuit that radiates a wavelength of 196 m?Integrated Concepts Police radar determines the speed of motor vehicles using the same Doppler-shift technique employed for ultrasound in medical diagnostics. Beats are produced by mixing the double Doppler-shifted echo with the original frequency. If 1.50109-Hz microwaves are used and a beat frequency of 150 Hz is produced, what is the speed of the vehicle? (Assume the same Doppler-shift formulas are valid with the speed of sound replaced by the speed of light.)Integrated Concepts Assume the mostly infrared radiation from a heat lamp acts like a continuous wave with wavelength 1.50 (m. (a) If the lamp’s 200W output is focused on a person’s Shoulder, over a circular area 25.0 cm in diameter, what is the intensity in W/m2? (b) What is the peak electric field strength? (c) Find the peak magnetic field strength. (d) How long will it take to increase the temperature of the 4.00-kg shoulder by 2.00°C, assuming no other heat transfer and given that its speci?c heat is 3.47103J/kgC ?Integrated Concepts On its highest power se1ting, a microwave oven increases the temperature of 0.400 kg of spaghetti by 45.0°C in 120 s. (a) What was the rate of power absorption by the spaghetti given that its specific heat is 3.76103J/kgC ? (b) Find the average intensity of the microwaves, given that they are absorbed over a circular area 20.0 cm in diameter. (c) What is the peak electric field strength of the microwave? (d) What is its peak magnetic field strength?Integrated Concepts Electromagnetic radiation from a 5.00-mw laser is concentrated on a 1.00m2 area. (a) What is the intensity in W/m2? (b) Suppose a 2.00nC static charge is in the beam. What is me maximum electric force it experience? (c) If the static charge moves at 400 m/s, what maximum magnetic force can it feel?Integrated Concepts A 200-turn flat coil of wire 30.0 cm in diameter acts as an antenna for FM radio at a frequency of 100 MHz. The magnetic field of the incoming electromagnetic wave is perpendicular to the coil and has a maximum strength of 1.001012T. (a) What power is incident on the coil? (b) What average emf is induced in the coil over one-fourth at a cycle? (c) If the radio receiver has an inductance at 2.50 (H, what capacitance must it have to resonate at 100 MHz?Integrated Concepts If electric and magnetic field strengths vary sinusoidally in time, being zero at t = 0, then E = E0 sin 2ft and B = B0 sin 2 ft. Let f = 1.00 GHz here. (a) When are the field strengths first zero? (b) When do they reach their most negative value? (c) How much time is needed for them to complete one cycle?Unreasonable Results A researcher measures the wavelength of a 1.20-GHz electromagnetic wave to be 0.500 m. (a) Calculate the speed at which this wave propagates. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Unreasonable Results The peak magnetic field strength in a residential microwave oven is 9.20105T. (a) What is the intensity of the microwave? (b) What is unreasonable about this result? (c) What is wrong about the premise?Unreasonable Results An LC circuit containing a 2.00-H inductor oscillates at such a frequency that it radiates at a 1.00m wavelength. (a) What is the capacitance of the circuit? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Unreasonable Results An LC circuit containing a 1.00-pF capacitor oscillates at such a frequency mat it radiates at a 300-nm wavelength. (a) What is the inductance of the circuit? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Create Your Own Problem Consider electromagnetic fields produced by high voltage power lines. Construct a problem in which you calculate the intensity of this electromagnetic radiation in W/m2 based on the measured magnetic field strength of the radiation in a home near the power lines. Assume these magnetic field strengths are known to average less than a T. The intensity is small enough that it is difficult to imagine mechanisms for biological damage due to it. Discuss how much energy may be radiating from a section of power line several hundred meters long and compare this to the power likely to he carried by the lines. An idea of how much power this is can be obtained by calculating the approximate current responsible for T fields at distances of tens of meters.Create Your Own Problem Consider the most recent generation of residential satellite dishes that are a little less than half a meter in diameter. Construct a problem in which you calculate the power received by the dish and the maximum electric field strength of the microwave signals for a single channel received by the dish. Among the things to be considered are the power broadcast by the satellite and the area over which the power is spread, as well as the area of the receiving dish.Using the law of reflection, explain how powder takes the shine off of a person’s nose. What is the name of the optical effect?Diffusion by reflection from a rough surface is described in this chapter. Light can also be diffused by refraction. Describe how this occurs in a speci?c situation, such as light interacting with crushed ice.Why is the index of refraction always greater than or equal to 1?Does the fact that the light flash from lightning teaches you before its sound prove that the speed of light is extremely large or simply that it is greater than the speed at sound? Discuss how you could use this effect to get an estimate of the speed of light.Will light change direction toward or away from the perpendicular when it goes from air to water? Water to glass? Glass to air?Explain why an object in water always appears to be at a depth shallower than it actually is? Why do people sometimes sustain neck and spinal injuries when diving into unfamiliar ponds or waters?Explain why a person’s legs appeal very short when wading in a pool. Justify your explanation with a ray diagram showing the path of rays from the feel to the eye of an observer who is out of the water.Why is the front surface of a thermometer curved as shown? Figure 25.47 The curved surface of the thermometer serves a purpose.Suppose light were incident from air onto a material that had a negative index at retraction, say 1.3; where does the refracted light ray go?A ring with a colorless gemstone is dropped into water. The gemstone becomes invisible when submerged. Can it be a diamond? Explain.A high-quality diamond may be quite clear and colorless, transmitting all visible wavelengths with little absorption. Explain how it can sparkle with flashes of brilliant color when illuminated by white light.Is it possible that total internal reflection plays a role in rainbows? Explain in terms of indices of refraction and angles, perhaps referring to Figure 25.48. Some of us have seen the formation of a double rainbow. Is it physically possible to observe a triple rainbow? Figure 25.48 Double rainbows are not a very common observance. (credit: InvictusOU812, Flickr)The most common type at mirage is an illusion that light from faraway objects is reflected by a pool of water that is not really there. Mirages are generally observed in deserts when there is a hot layer of air near the ground. Given that the reflective index of air is lower for air at higher temperatures, explain how mirages can be formed.It can he argued that a flat piece of glass, such as in a window, is like a lens with an infinite focal length. If so, where does it form an image? That is, how are d1 and d0 related?You can often see a reflection when looking at a sheet of glass, particularly if it is darker on the other side. Explain why you can often see a double image in such circumstances.When you focus a camera, you adjust the distance of the lens from the film. It the camera lens acts like a thin lens, why can it not be a fixed distance from the film for both near and distant objects?A thin lens has two focal points, one on either side, at equal distances from its center, and should behave the same for light entering from either side. Look through your eyeglasses (or those of a friend) backward and forward and comment on whether they are thin lenses.Will the focal length of a lens change when it is submerged in water? Explain.What are the differences between teal and virtual images? How can you tell (by looking) whether an image formed by a single lens or minor is real or virtual?Can you see a virtual image? Can you photograph one? Can one be projected onto a screen with additional lenses or mirrors? Explain your responses.Is it necessary to project a real image onto a screen for it to exist?At what distance is an image always locatedat do, di, or f?Under what circumstances will an image be located at the local point of a lens or mirror?What is meant by a negative magnification? What is meant by a magnification that is less than 1 in magnitude?Can a case 1 image be larger than the object even though its magnification is always negative? Explain.Figure 25.49 shows a light bulb between two mirrors. One minor produces a beam at light with parallel lays; the other keeps light from escaping without being put into the beam. Where is the filament of the light in relation to the focal point or radius of curvature of each mirror? Figure 25.49 The two mirrors trap most of the bulb’s light and form a directional beam as in a headlight.Devise an arrangement of mirrors allowing you to see the back of your head. What is the minimum number of mirrors needed for this task?If you wish to see your entire body in a flat minor (from head to toe), how tall should the minor be? Does its size depend upon your distance away from the mirror? Provide a sketch.It can be argued than a flat mirror has an in?nite focal leng1h. If so, where does it from an image? That is, how are diand d0related?Why are diverging mirrors often used for rear-view mirrors in vehicles? What is the main disadvantage of using such a mirror compared with a flat one?Suppose a man stands in front of a mirror as shown in Figure 25.50. His eyes are 1.65 m above the floor, and the top of his head is 0.13 m higher. Find the height above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet. How is this distance related to the man’s height? Figure 25.50 A full-length mirror is one in which you can see all of yourself. It need not be as big as you, and its size is independent of your distance from it.Show that when light reflects from two mirrors that meet each other at a right angle, the outgoing ray is parallel to the incoming ray, as illustrated in the following figure. Figure 25.51 A corner reflector sends the reflected reflected ray back in a direction parallel to the incident ray, independent of incoming direction.Light shows staged with lasers use moving mirrors to swing beams and create colorful effects. Show that a light ray reflected from a mirror changes direction by 2(when the mirror is rotated by an angle .A flat minor is neither converging nor diverging. To prove this, consider two rays originating from the same point and diverging at an angle . Show that after striking a plane mirror, the angle between their directions remains . Figure 25.52 A flat mirror neither converges nor diverges light rays. Two rays continue to diverge at the same angle after reflection.What is the speed of light in water? In glycerine?What is the speed of light in air? In crown glass?Calculate the index of refraction for a medium in which the speed of light is 2.012108m/s , and identify the most likely substance based on Table 25.1.In what substance in Table 25.1 is the speed of light 2.290108m/s ?There was a major collision of an asteroid with the Moon in medieval times. It was described by monks at Canterbury Cathedral in England as a red glow on and around the Moon. How long after the asteroid hit the Moon, which is 3.84105km away, would the light first arrive on Earth?A scuba diver training in a pool looks at his instructor as shown in Figure 25.53. What angle does the ray from the instructor’s face make with the perpendicular to the water at the point where the ray enters? The angle between the ray in the water and the perpendicular to the water is 25.0°. Figure 25.53 A scuba diver in a pool and his trainer look at each other.Components of some computers communicate with each other through optical fibers having an index of refraction n = 1.55. What time in nanoseconds is required for a signal to travel 0.200 m through such a fiber?(a) Using information in Figure 25.53, find the height of the instructor's head above the water, noting that you will first have to calculate the angle of incidence. (b) Find the apparent depth of the diver’s head below water as seen by the instructor.Suppose you have an unknown clear substance immersed in water, and you wish to identify it by finding its index of refraction. You arrange to have a beam of light enter it at an angle of 45.0°, and you observe the angle of refraction to be 40.3°. What is the index of refraction of the substance and its likely identity?On the Moon’s surface, lunar astronauts placed a corner reflector, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. What percent correction is needed to account for the delay in time due to the slowing of light in Earth’s atmosphere? Assume the distance to the Moon is precisely 3.84108m, and Earth’s atmosphere (which varies in density with altitude) is equivalent to a layer 30.0 km thick with a constant index of refraction n = 1.000293.Suppose Figure 25.54 represents a ray of light going from air through crown glass into waist, such as going into a fish tank. Calculate the amount the ray is displaced by the glass (x) , given mat me incident angle is 40.0° and the glass is 1.00 cm thick.Figure 25.54 shows a ray of light passing from one medium into a second and then a third. Show that 3 is the same as it would be if the second medium were not present (provided total internal reflection does not occur). Figure 25.54 A ray of light passes from one medium to a third by traveling through a second. The final direction is the same as if the second medium were not present, but the ray is displaced by x (Shawn exaggerated).Unreasonable Results Suppose light travels from water to another substance, with an angle of incidence of 10.0° and an angle of refraction of 14.9°. (a) What is the index of refraction of the other substance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Construct Your Own Problem Consider sunlight entering the Earth’s atmosphere at sunrise and sunsetthat is, at a 90° incident angle. Taking the boundary between nearly empty space and the atmosphere to be sudden, calculate the angle of refraction for sunlight. This lengthens the time the Sun appears to be above the horizon, both at sunrise and sunset. Now construct a problem in which you determine the angle of refraction (or different models 01 the atmosphere, such as various layers of varying density. Your instructor may wish to guide you on the level of complexity to consider and on how the index at retraction varies with air density.Unreasonable Results Light traveling from water to a gemstone strikes the surface at an angle of 80.0° and has an angle of refraction of 15.2°. (a) What is the speed at light in the gemstone? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Verify that the critical angle for light going from water to air is 48.6°, as discussed at the end of Example 25.4, regarding the critical angle for light traveling in a polystyrene (a type of plastic) pipe surrounded by air.(a) At the end of Example 25.4, it was stated that the critical angle for light going from diamond to air is 24.4°. Verify this. (b) What is the critical angle for light going from zircon to air?An optical fiber uses flint glass clad with crown glass. What is the critical angle?At what minimum angle will you get total internal reflection of light traveling in water and reflected from ice?Suppose you are using total internal reflection to make an efficient corner reflector. If there is air outside and the incident angle is 45.0°, what must be the minimum index of refraction of the material from which the reflector is made?You can determine me index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle at 68.4° when submerged in water? What is the substance, based on Table 25.1? (b) What would the critical angle be for this substance in air?A ray of light, emitted beneath the surface of an unknown liquid with air above it, undergoes total internal reflection as shown in Figure 25.55. What is the index of retraction for the liquid and its likely identification? Figure 25.55 A tight ray inside a liquid strikes the surface at the critical angle and undergoes total internal reflection.A light ray entering an optical fiber surrounded by air is first refracted and then reflected as shown in Figure 25.55. Show than if the fiber is made from crown glass, any incident ray will be totally internally reflected. Figure 25.55 A light ray enters the end of a fiber, thesurface of which is perpendicular to its sides. Examine the conditions under which it may be totally internally reflected.(a) What is me ratio of the speed of red light to violet light in diamond, based on Table 25.2? (b) What is this ratio in polystyrene? (c) Which is more dispersive?A beam of white light goes from air into water at an incident angle of 75.0°. At what angles are the red (660 nm) and violet (410 nm) parts of the light refracted?By how much do the critical angles for red (660 nm) and violet (410 nm) light differ in a diamond surrounded by air?(a) A narrow beam of light containing yellow (580 nm) and green (550 nm} wavelengths goes from polystyrene to air, striking the surface at a 30.0° incident angle. What is the angle between the colors when they emerge? (b) How far would they have to travel to be separated by 1.00 mm?A parallel beam of light containing orange (610 nm) and violet (410 nm) wavelengths goes from fused quartz to water, striking the surface between them an a 60.0° incident angle. What is the angle between the two colors in water?A ray of 610 nm light goes from air into fused quartz at an incident angle of 55.0°. At what incident angle must 470 nm light enter flint glass to have the same angle of refraction?A narrow beam of light containing red (660 nm) and blue (470 nm) wavelengths travels from air through a 1.00 cm thick flat piece of crown glass and back to air again. The beam strikes at a 30.0° incident angle. (a) At what angles do the two colors emerge? (b) By what distance are the red and blue separated when they emerge?A narrow beam of white light enters a prism made of crown glass at a 45.0° incident angle, as shown in Figure 25.57. At what angles, R and V, do the red (660 nm) and violet (410 nm) components of the light emerge from the prism? Figure 25.57 This prism will disperse the while light into a rainbow of colors. The incident angle is 45.0°, and the angles at which the red and violet light emerge are R and V.What is the power in diopters at a camera lens that has a 50.0 mm focal length?Your camera's zoom lens has an adjustable focal leng1h ranging from 80.0 to 200 mm. What is its range of powers?What is the focal length of 1.75 D reading glasses found on the rack in a pharmacy?You note that your prescription for new eyeglasses is 4.50 D. What will their focal leng1h be?How far from the lens must the film in a camera be, if the lens has a 35.0 mm local length and is being used to photograph a flower 75.0 cm away? Explicitly show how you follow the steps in the ProblemSolving Strategy for lenses.A certain slide projector has a 100 mm focal length lens. (a) How far away is the screen, if a slide is placed 103 mm from the lens and produces a sharp image? (b) If the slide is 24.0 by 36.0 mm, what are the dimensions of the image? Explicitly show how you follow the steps in the PreblemSolving Strategy for lenses.A doctor examines a mole with a 15.0 cm focal length magnifying glass held 13.5 cm from the mole (a) Where is the image? (b) What is its magnification? (c) How big is file image of a 5.00 mm diameter mole?How far from a piece of paper must you hold your father’s 2.25 D reading glasses to try to burn a hole in the paper with sunlight?A camera with a 50.0 mm focal length lens is being used to photograph a person standing 3.00 m away. (a) How far from the lens must the film be? (b) If the film is 36.0 mm high, what fraction of a 1.75 m tall person will ?t on it? (c) Discuss how reasonable this seems, based on your experience in taking or posing for photographs.A camera lens used for taking close-up photographs has a focal length of 22.0 mm. The farthest it can be placed from the film is 33.0 mm. (a) What is the closest object that can be photographed? (b) What is the magnification of this closest object?Suppose your 50.00 mm local length camera lens is 51.0 mm away from the film in the camera. (a) How far away is an object that is in focus? (b) What is the height of the object if its image is 2.00 cm high?(a) What is the focal length of a magnifying glass that produces a magnification of 3.00 when held 5.00 cm from an object such as a rare coin? (b) Calculate the power of the magnifier in diopters. (c) Discuss how this power compares to those for store-bought reading glasses (typically 1.0 to 4.0 D). Is the magnifier's power greater, and should it be?What magnification will be produced by a lens of power 4.00 D (such as might be used to correct myopia) if an object is held 25.0 cm away?In Example 25.7, the magnification of a book held 7.50 cm from a 10.0 cm focal length lens was found to be 3.00. (a) Find the magnification for the book when it is held 8.50 cm from the magnifier. (b) Do the same for when it is held 9.50 cm from the magnifier. (c) Comment on the trend in m as the object distance increases as in these two calculations.Suppose a 200 mm focal length telephoto lens is being used to photograph mountains 10.0 km away. (a) Where is file image? (b) What is the height of the image of a 1000 m high cliff on one of the mountains?A camera with a 100 mm focal length lens is used to photograph the sun and mean. What is the height at the image of the sun on the film, given the sun is 1.40106km in diameter and is 1.50108km away?Combine thin lens equations to show that the magnification for a mm lens is determined by its focal length and the object distance and is given by m=f/(fdo).What is the focal length of a makeup mirror that has a power of 1.50 D?Some telephoto cameras use a mirror rather than a lens. What radius of curvature mirror is needed to replace a 800 mm focal length telephoto lens?(a) Calculate the focal length of the mirror formed by the shiny back of a spoon that has a 3.00 cm radius of curvature. (b) What is its power in diopters?Find the magnification of the heater element in Example 25.9. Note that its large magnitude helps spread out the reflected energy.What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s face is 12.0 cm away? Explicitly show how you follow the steps in the ProblemSolving Strategy for Mirrors.A shopper standing 3.00 m from a convex security minor sees his image with a magnification of 0.250. (a) Where is his image? (b) What is the focal length of the mirror? (c) What is its radius of curvature? Explicitly show how you follow the steps in the Problem-Solving Strategy for Mirrors.An object 1.50 cm high is held 3.00 cm from a person’s cornea, and its reflected image is measured to be 0.16? cm high. (a) What is the magnification? (b) Where is the image? (c) Find the radius of curvature of the convex mirror formed by the cornea. (Note that this technique is used by optometrists to measure the curvature of the cornea for contact lens ?tting. The instrument used is called a keratometer, or curve measurer.)Ray tracing for a flat mirror shows that the image is located a distance behind the mirror equal to the distance of the object from the mirror. This is stated di=do, since this is a negative image distance (it is a virtual image). (a) What is the focal length of a flat mirror? (b) What is its power?Show that for a flat mirror hi= ho, knowing that the image is a distance behind the mirror equal in magnitude to the distance of the object from the mirror.Use the law of reflection to prove that the focal length of a mirror is hall its radius of curvature. That is, prove that f = R/2. Note this is true for a spherical mirror only if its diameter is small compared with its radius of curvature.Referring to the electric room heater considered in the first example in this section, calculate the intensity of IR radiation in W/m2 projected by the concave mirror on a person 3.00 m away. Assume that the healing element radiates 1500 W and has an area of 100 cm2, and that half of the radiated power is reflected and focused by the mirror.Consider a 250-W heat lamp fixed to the ceiling in a bathroom. If the filament in one light burns out then the remaining three still work. Construct a problem in which you determine the resistance of each filament in order to obtain a certain intensity projected on the bathroom floor. The ceiling is 3.0 m high. The problem will need to involve concave miners behind the filaments. Your instructor may wish to guide you on the level of complexity to consider in the electrical components.If the lens of a person’s eye is removed because of cataracts (as has been done since ancient times), why would you expect a spectacle lens of about 16 D to be prescribed?A cataract is cloudiness in the lens of the eye. Is light dispersed or diffused by it?When laser light is shone into a relaxed normalvision eye to repair a tear by spot-welding the retina to the back of the eye. The rays entering the eye must be parallel. Why?How does the power of a dry contact lens compare with its power when resting on the tear layer of the eye? Explain.Why is your vision so blurry when you open your eyes while swimming under water? How does a face mask enable clear vision?It has become common to replace the cataractclouded lens of the eye with an internal lens. This intraocular lens can be chosen so that the person has perfect distant vision. Will the person be able to read without glasses? If the person was nearsighted, is the power of the intraocular lens greater or less than the removed lens?If the cornea is to be reshaped (this can be done surgically or with contact lenses) to correct myopia, should its curvature be made greater or smaller? Explain. Also explain how hyperopia can be corrected.If there is a fixed percent uncertainty in LASIK reshaping of the cornea, why would you expect those people with the greatest correction to have a poorer chance of normal distant vision after the procedure?A person with presbyopia has lost some or all of the ability to accommodate the power of the eye. If such a person’s distant vision is corrected with LASIK, will she still need reading glasses? Explain.A pure red object on a black background seems to disappear when illuminated with pure green light. Explain why.What is color constancy, and what are its limitations?There are different types of color blindness related to the malfunction of different types of cones. Why would one particularly useful to study those role individuals who are color blind only in one eye or who have a different type of color blindness in each eye?Propose a way to study the function of the rods alone, given they can sense light about 1000 times dimmer than the cones.Geometric optics describes the interaction of light with macroscopic objects. Why, then, is it correct to use geometric optics to analyse a microscope’s image?The image produced by the microscope in Figure 25.16 cannot be projected. Could extra lenses or mirrors project if? Explain.Why not have the objective at a microscope form a case 2 image with a large magnification? (Hint: Consider the location of that image and the difficulty that would pose tor using the eyepiece as a magnifier.)What advantages do oil immersion objectives offer?How does the NA of a microscope compare wi1h the NA of an optical liber?If you want your microscope or telescope to project a real image onto a screen, how would you change the placement of the eyepiece relative to the objective?List the various types of aberrations. What causes them and how can each be reduced?What is the power of the eye when viewing an object 50.0 cm away?Calculate the power at the eye when viewing an object 3.00 m away.(a) The print in many books averages 3.50 mm in height. How high is the image at the print on the retina when the book is held 30.0 cm from the eye? (b) Compare the size of the print to the sizes of rods and cones in the fovea and discuss the possible details observable in the letters. (The eye-brain system can perform better because of interconnections and higher order image processing.)Suppose a certain person’s visual acuity is such that he can see objects clearly that term an image 4.00 m high on his retina. What is the maximum distance at which he can read the 75.0 cm high letters on the side of an airplane?People who do very detailed work close up, such as jewellers, often can see objects clearly at much closer distance than the normal 25 cm. (a) What is the power of the eyes of a woman who can see an object clearly at a distance of only 8.00 cm? (b) What is 1J1e size of an image of a 1.00 mm object, such as lettering inside a ring, held at this distance? (c) What would the size of the image be if the object were held at the normal 25.0 cm distance?What is the far point of a person whose eyes have a relaxed power of 50.5 D?What is the near point of a person whose eyes have an accommodated power of 53.5 D?(a) A laser vision correction reshaping the cornea of a myopic patient reduces the power of his eye by 9.00 D, with a 5.0 uncertainty in the final correction. What is the range of diopters for spectacle lenses that this person might need after LASIK procedure? (b) Was the person nearsighted or farsighted before the procedure? How do you know?In a LASIK vision correction, the power of a patient’s eye is increased by 3.00 D. Assuming this produces normal close vision, what was the patient’s near point before the procedure?What was the previous far point of a patient who had laser vision correction that reduced me power of her eye by 7.00 D, producing normal distant vision for her?A severely myopic patient has a far point of 5.00 cm. By how many diopters should the power of his eye be reduced in laser vision correction to obtain normal distant vision for him?A student’s eyes, while reading the blackboard, have a power of 51.0 D. How far is the board from his eyes?The power of a physician’s eyes is 53.0 D while examining a patient. How far from her eyes is the feature being examined?A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?The far point of a myopic administrator is 50.0 cm. (a) What is the relaxed power of his eyes? (b) If he has the normal 8.00% ability to accommodate, what is the closest object he can see clearly?A very myopic man has afar point of 20.0 cm. What power contact lens (when on the eye) will correct his distant vision?Repeat the previous problem for eyeglasses held 1.50 cm from the eyes.A myopic person sees that her contact lens prescription is 4.00 D. What is her far point?Repeat the previous problem for glasses that are 1.75 cm from the eyes.The contact lens prescription for a mildly farsighted person is 0.750 D, and the person has a near point of 29.0 cm. What is the power of the tear layer between the cornea and the lens if the correction is ideal, taking the tear layer into account?A nearsighted man cannot see objects clearly beyond 20 cm from his eyes. How close must he stand to a mirror in order to see what he is doing when he shaves?A mother sees that her child's contact lens prescription is 0.750 D. What is me child's near point?Repeat the previous problem for glasses that are 2.20 cm from the eyes.The contact lens prescription for a nearsighted person is 4.00 D and the person has a far point of 22.5 cm. What is the power of the tear layer between the cornea and the lens if the correction is ideal, taking the tear layer into account?Unreasonable Results A boy has a near point of 50 cm and a far point of 500 cm. Will a 4.00 D lens correct his far point to infinity?A microscope with an overall magnification of 800 has an objective that magnifies by 200. (a) What is the magnification of the eyepiece? (b) If mere are two other objectives that can be used, having magnifications of 100 and 400, what other total magnifications are possible?(a) What magnification is produced by a 0.150 cm local length microscope objective than is 0.155 cm from the object being viewed? (b) What is the overall magnification if an 8 eyepiece (one that produces a magnification of 8.00) is used?(a) Where does an object need to be placed relative to a microscope for its 0.500 cm focal leng1h objective to produce a magnification of 400? (b) Where should the 5.00 cm focal length eyepiece be placed to produce a further fourfold (4.00) magnification?You switch from a 1.40NA60X oil immersion objective to a 1.40NA60X oil immersion objective. What are the acceptance angles for each? Compare and comment on the values. Which would you use first to locate the target area on your specimen?An amoeba is 0.305 cm away from the 0.300 cm focal length objective lens of a microscope. (a) Where is the image formed by the objective lens? (b) What is this image's magnification? (c) An eyepiece with a 2.00 cm focal length is placed 20.0 cm from the objective. Where is the final image? (c) What magnification is produced by the eyepiece? (e) What is the overall magnification? (See Figure 26.16.)You are using a standard microscope with a 0.10NA4X objective and switch to a 0.65NA40X objective. What are the acceptance angles for each? Compare and comment on the values. Which would you use first to locate the target area on of your specimen? (See Figure 26.17.)