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essential university physics
Essential University Physics 3rd Edition Volume 2 Richard Wolfsonby - Solutions
You’re asked to design a concave mirror that will produce a virtual image, enlarged 1.8 times, of an object 22 cm from the mirror. What do you specify for the mirror’s curvature radius?
An object’s image in a 27-cm-focal-length concave mirror is upright and magnified by a factor of 3. Where is the object?
Repeat Problem 37 for a convex mirror, assuming all numbers stay the same.Data from Problem 37A 12-mm-high object is 10 cm from a concave mirror with focal length 17 cm.(a) Where is the image,(b) how high is it, (c) what type is it?
A 12-mm-high object is 10 cm from a concave mirror with focal length 17 cm.(a) Where is the image,(b) how high is it,(c) what type is it?
(a) Find the focal length of a concave mirror if an object placed 38.4 cm in front of the mirror has a real image 55.7 cm from the mirror.(b) Where and what type will the image be if the object is moved to a point 16.0 cm from the mirror?
A compound microscope has objective and eyepiece focal lengths of 6.1 mm and 1.7 cm, respectively. If the lenses are 8.3cm apart, what is the instrument’s magnification?
A particular eye has a focal length of 2.0 cm instead of the 2.2 cm that would put a sharply focused image on the retina.(a) Is this eye nearsighted or farsighted?(b) What corrective lens is needed?
You’re an optometrist helping a nearsighted patient who claims he can’t see clearly beyond 80 cm. Prescribe a lens that will put the images of distant objects at 80 cm, giving your patient clear vision at all distances beyond the normal near point.
What focal length should you specify if you want a magnifying glass with angular magnification 3.2?
You have to hold a book 55 cm from your eyes for the print to be in focus. What power lens would correct your farsightedness?
You?re underwater, looking through a spherical air bubble (Fig. 31.35). What?s its actual diameter if it appears, along your line of sight, to be 1.5cm in diameter? 1.5 cm FIGURE 31.35 Exercise 32
A tiny insect is trapped 1.0 mm from the center of a spherical dewdrop 4.0mm in diameter. As you look straight into the drop, what’s the insect’s apparent distance from the drop’s surface?
The bottom of a swimming pool looks to be 1.5m below the surface. Find the pool’s actual depth.
You’re standing in a wading pool and your feet appear to be 30cm below the surface. How deep is the pool?
You’re writing specifications for a new line of magnifying glasses that have double-convex lenses with equal 32-cm curvature radii, made from glass with n = 1.52. What do you list for the focal length?
A magnifying glass enlarges print by 50% when it’s 9.0 cm from a page. What’s its focal length?
A real image is four times as far from a lens as is the object. What’s the object distance, measured in focal lengths?
By holding a magnifying glass 25 cm from your desk lamp, you can focus an image of the lamp’s bulb on a wall 1.6 m from the lamp. What’s the focal length of your magnifying glass?
A lens with 50-cm focal length produces a real image the same size as the object. How far from the lens are image and object?
By what factor is the image magnified for an object 1.5 focal lengths from a converging lens? Is the image upright or inverted?
A lightbulb is 56 cm from a convex lens. Its image appears on a screen 31 cm from the lens, on the other side. (a) the lens’s focal length(b) how much the image is enlarged or reduced.
(a) Where on the axis of a concave mirror would you place an object to get a half-size image?(b) Where will the image be located?(c) Will the image be real or virtual?
A virtual image is located 40 cm behind a concave mirror with focal length 18 cm.(a) Where is the object?(b) By how much is the image magnified?
An object is five focal lengths from a concave mirror.(a) How do the object and image heights compare?(b) Is the image upright or inverted?
A candle is on the axis of a 15-cm-focal-length concave mirror, 36 cm from the mirror.(a) Where is its image?(b) How do the image and object sizes compare?(c) Is the image real or virtual?
A shoe store uses small floor-level mirrors to let customers view prospective purchases. At what angle should such a mirror be inclined so that a person standing 50cm from the mirror with eyes 140cm off the floor can see her feet?
Mirages occur when air?s refractive index varies with position as a result of uneven heating. Under such conditions, light undergoes refraction continually and thus follows a curved path. Other examples where a varying refractive index is important include the eye?s lens and Earth?s ionosphere, an
Mirages occur when air?s refractive index varies with position as a result of uneven heating. Under such conditions, light undergoes refraction continually and thus follows a curved path. Other examples where a varying refractive index is important include the eye?s lens and Earth?s ionosphere, an
Mirages occur when air?s refractive index varies with position as a result of uneven heating. Under such conditions, light undergoes refraction continually and thus follows a curved path. Other examples where a varying refractive index is important include the eye?s lens and Earth?s ionosphere, an
Mirages occur when air?s refractive index varies with position as a result of uneven heating. Under such conditions, light undergoes refraction continually and thus follows a curved path. Other examples where a varying refractive index is important include the eye?s lens and Earth?s ionosphere, an
Proposals have been made to ?sail? spacecraft to the outer solar system using the pressure of sunlight, or even to propel interstellar spacecraft with high-powered, Earth-based lasers. Sailing spacecraft would need no fuel?a great advantage because fuel constitutes much of the initial weight of any
Proposals have been made to ?sail? spacecraft to the outer solar system using the pressure of sunlight, or even to propel interstellar spacecraft with high-powered, Earth-based lasers. Sailing spacecraft would need no fuel a great advantage because fuel constitutes much of the initial weight of any
Proposals have been made to ?sail? spacecraft to the outer solar system using the pressure of sunlight, or even to propel interstellar spacecraft with high-powered, Earth-based lasers. Sailing spacecraft would need no fuel a great advantage because fuel constitutes much of the initial weight of any
Proposals have been made to ?sail? spacecraft to the outer solar system using the pressure of sunlight, or even to propel interstellar spacecraft with high-powered, Earth-based lasers. Sailing spacecraft would need no fuel a great advantage because fuel constitutes much of the initial weight of any
The National Ignition Facility at Lawrence Livermore National Laboratory initiates nuclear fusion by converging 192 laser beams on a deuterium tritium target. Each beam has a square cross section 38 cm on a side, and each beam delivers 10.0 kJ of energy in 20.0 ns. Find(a) the peak electric field
Your friend who works for the college radio station must make electric-field measurements for a report to be filed with the station’s application for license renewal. The measurement is made 4.6km from the antenna, where your friend measures the electric field at 380V/m. The station is allowed to
The Voyager 1 spacecraft is now beyond the outer reaches of our solar system, but earthbound scientists still receive data from the spacecraft’s 20-W radio transmitter. Voyager is expected to continue transmitting until about 2025, when it will be some 25 billion km from Earth. What’s the
Your roommate’s father is CEO of a coal company, so your roommate is understandably skeptical of alternative energy proposals. He claims that there’s no future for solar energy, because the power in sunlight is insufficient to meet humankind’s energy demand. Is he right? To find out, compare
A friend buys a used pickup truck that comes with a CB radio. However, the antenna is broken off, and your friend asks you to help make one out of a steel rod that he will affix to the rear bumper. You know that the CB channel frequency is 27.3MHz and that the antenna must be a quarter-wavelength
Maxwell’s equations in a dielectric resemble those in vacuum (Equations 29.6–29.9) but with ε0 replaced by kε0, where k is the dielectric constant introduced in Chapter 23. Show that the speed of electromagnetic waves in a dielectric is c/√k. dA = 0 (Gauss, E) (29.6) B dA = 0 (Gauss, B)
You’re an astronomer studying the origin of the solar system, and you’re evaluating a hypothesis that sufficiently small particles were blown out of the solar system by the force of sunlight. To see how small such particles must be, compare the force of sunlight with the force of solar gravity,
In a stack of polarizing sheets, each sheet has its transmission axis rotated 14° with respect to the preceding sheet. If the stack passes 37% of the incident unpolarized light, how many sheets does it contain?
A cylindrical resistor of length L, radius a, and resistance R carries current I. Calculate the electric and magnetic fields at the surface of the resistor, assuming the electric field is uniform over the surface. Calculate the Poynting vector and show that it points into the resistor. Calculate
A radar system produces pulses consisting of exactly 100 full cycles of a sinusoidal 72.5-GHz electromagnetic wave. The average power while the transmitter is on is 66.0 MW, and the waves are confined to a beam 22.4 cm in diameter. Find(a) the peak electric field,(b) the wavelength,(c) the total
A white dwarf star is approximately the size of Earth but radiates about as much power as the Sun. Estimate the radiation pressure on a light-absorbing object at the white dwarf’s surface.
A photon rocket emits a beam of light instead of hot gas. How powerful a beam would be needed to equal the 40-MN thrust of NASA’s new Space Launch System (SLS)? Compare your answer with humanity’s total electric power-generating capability, about 2 TW.
A 65-kg astronaut is floating in empty space. If she shines a 1.0-W flashlight in a fixed direction, how long will it take her to accelerate to 10m/s?
A 180W/cm2 laser beam shines on a light-absorbing surface. What’s the radiation pressure on the surface?
A laser produces an average power of 7.0W in a 1.0-mm-diameter beam. Find(a) the average intensity (b) the peak electric field of the laser light.
A camera flash delivers 2.5 kW of light power for 1.0ms. Find(a) the total energy(b) the total momentum carried by the flash.
A typical fluorescent lamp is a little more than 1 m long and a few cm in diameter. How do you expect the light intensity to vary with distance(a) near the lamp but not near either end and(b) far from the lamp?
Find the peak electric and magnetic fields 1.5m from a 60-W lightbulb that radiates equally in all directions.
At 1.5 km from a radio transmitter, the peak electric field is 350 mV/m. Assuming the transmitter broadcasts equally in all directions, find(a) the transmitted power(b) the peak electric field 10 km from the transmitter.
Lasers are classified according to the eye-damage danger they pose. Class 2 lasers, including many laser pointers, produce visible light with no greater than 1 mW total power. They’re relatively safe because the eye’s blink reflex limits exposure time to 250 ms. Find(a) the intensity of a 1-mW
A quasar 10 billion light-years from Earth appears the same brightness as a star 50,000 light-years away. How do the power outputs of quasar and star compare?
Use the fact that sunlight intensity at Earth’s orbit is 1364 W/m2 to calculate the Sun’s total power output.
High microwave intensities can cause biological damage through heating of tissue; a particular concern is cataract formation. The U.S. Food and Drug Administration limits microwave radiation near the door of a microwave oven to 5.0 mW/m2 . The window in a particular oven door measures 40 cm by 17
Show that it’s impossible for an electromagnetic wave in vacuum to have a time-varying component of its electric field in the direction of its magnetic field.
Vertically polarized light passes through two polarizers, the first at 60° to the vertical and the second at 90° to the vertical. What fraction of the light gets through?
Unpolarized light of intensity S0 passes first through a polarizer with its axis vertical and then through one with its axis at 35° to the vertical. Find the intensity after the second polarizer.
An electro-optic modulator is a device that switches a laser beam rapidly from off to on by switching the polarization direction through 90° when a voltage is applied. But a brownout results in only enough voltage for a 72° rotation. What fraction of the light is transmitted during the brownout
A polarizer blocks 75% of a polarized light beam. What’s the angle between the beam’s polarization and the polarizer’s axis?
A radio receiver can detect signals with electric fields as weak as 320μV/m. Find the corresponding magnetic field.
Dielectric breakdown in air occurs when the electric field is approximately 3 MV/m. What would be the peak magnetic field in an electromagnetic wave with this peak electric field?
The medical profession divides the ultraviolet region of the electromagnetic spectrum into three bands: UVA (320 nm–420 nm), UVB (290 nm–320 nm), and UVC (100 nm–290 nm). UVA and UVB promote skin cancer and premature skin aging; UVB also causes sunburn, but helpfully fosters production of
An electric field points into the page and occupies a circular region of radius 1.0 m, as shown in Fig. 29.14. There are no electric charges in the region, but there is a magnetic field forming closed loops pointing clockwise, as shown. X. х х х x/B -1 m- FIGURE 29.14 Problem 36 х х х x, х
You’re engineering a new cell phone, and you’d like to incorporate the antenna entirely within the phone, which is 9 cm long when closed. The antenna is to be a quarter-wavelength long a common design for vertically oriented antennas. If the cell-phone frequency is 2.4 GHz, will the antenna fit?
A parallel-plate capacitor has circular plates with radius 50.0 cm and spacing 1.0mm. A uniform electric field between the plates is changing at the rate of 1.0 MV/ms. Find the magnetic field between the plates(a) on the symmetry axis,(b) 15 cm from the axis,(c) 150 cm from the axis.
Your university radio station has a 5.0-kW radio transmitter that broadcasts uniformly in all directions; listeners within 15 km have reliable reception. You want to increase the power to double that range. What should be a new power?
A laser pointer delivers 0.10-mW average power in a beam 0.90mm in diameter. Find(a) the average intensity,(b) the peak electric field, (c) the peak magnetic field.
Your new radio says it can pick up signals with peak electric fields as weak as 450μV/m. Will it work if you take it to your remote cabin, where the intensity of your favorite radio station is 0.35 nW/m2 ?
Estimate the peak electric field inside a 1.1-kW microwave oven under the simplifying approximation that the microwaves propagate as a plane wave through the oven’s 750cm2 cross-sectional area.
What would be the average intensity of a laser beam so strong that its electric field produced dielectric breakdown of air (which requires Ep = 3 MV/m)?
A typical laboratory electric field is 1500 V/m. Find the average intensity of an electromagnetic wave with this value for its peak field.
Vertically polarized light passes through a polarizer with its axis at 70° to the vertical. What fraction of the incident intensity emerges from the polarizer?
Polarized light is incident on a sheet of polarizing material, and only 20% of the light gets through. Find the angle between the electric field and the material’s transmission axis.
An electromagnetic wave is propagating in the z-direction. What’s its polarization direction if its magnetic field is in the y-direction?
An electromagnetic wave is propagating in the z-direction. What’s its polarization direction if its magnetic field is in the y-direction?
Microwave ovens for consumers’ use operate at 2.45 GHz. What’s the distance between wave crests in such a microwave?
A 60-Hz power line emits electromagnetic radiation. What’s the wavelength?
What are the wavelengths of(a) a 100-MHz FM radio wave,(b) a 5.0-GHz WiFi signal,(c) a 600-THz light wave,(d) a 1.0-EHz X ray?
If you speak via radio from Earth to an astronaut on the Moon, how long is it before you can receive a reply?
Your intercontinental telephone call is carried by electromagnetic waves routed via a satellite in geostationary orbit at 36,000 km altitude. Approximately how long does it take before your voice is heard at the other end?
A light-minute is the distance light travels in 1 minute. Show that the Sun is about 8 light-minutes from Earth.
A radio wave’s electric field is given by the expression E(vector)) = E sin (kz – ωt) x (î + ĵ).(a) Find the peak electric field.(b) Give a unit vector in the direction of the magnetic field at a place and time where sin(kz – ωt) is positive.
The fields of an electromagnetic wave are E(vector) = Ep sin(kz + ωt)ĵ and B(vector) = Bp sin(kz + ωt)î. Give a unit vector in the wave’s propagation direction.
A parallel-plate capacitor has square plates 10 cm on a side and 0.50 cm apart. The voltage across the plates is increasing at 220V/ms. What’s the displacement current in the capacitor?
A uniform electric field is increasing at 1.5 (V/m)/μs. Find the displacement current through a 1 cm2 area perpendicular to the field.
A filter is a circuit designed to pass AC signals in some frequency range and to attenuate others. Common filters include low-pass filters, which allow low-frequency signals to pass but attenuate high frequencies; high-pass filters, which do the opposite; and band-pass filters, which pass a range
A filter is a circuit designed to pass AC signals in some frequency range and to attenuate others. Common filters include low-pass filters, which allow low-frequency signals to pass but attenuate high frequencies; high-pass filters, which do the opposite; and band-pass filters, which pass a range
A filter is a circuit designed to pass AC signals in some frequency range and to attenuate others. Common filters include low-pass filters, which allow low-frequency signals to pass but attenuate high frequencies; high-pass filters, which do the opposite; and band-pass filters, which pass a range
A filter is a circuit designed to pass AC signals in some frequency range and to attenuate others. Common filters include low-pass filters, which allow low-frequency signals to pass but attenuate high frequencies; high-pass filters, which do the opposite; and band-pass filters, which pass a range
Your professor tells you about the days before digital computers when engineers used electric circuits to model mechanical systems. Suppose a 5.0-kg mass is connected to a spring with k = 1.44 kN/m. This is then modeled by an LC circuit with L = 2.5 H. What should C be in order for the LC circuit
Substitute the expression for q1t2 in Equation 28.11 into the differential equation for an LC circuit with resistance, and find an expression for the angular frequency of the damped oscillations in terms of R, L, and C. -Rt/2L q(1) : = 9pe cos wt (28.11)
A triangle wave swings linearly between voltages -Vp and +Vp. Show that the rms voltage of a triangle wave is Vp √3.
For RLC circuits in which the resistance isn’t too high, the Q factor may be defined as the ratio of the resonant frequency to the difference between the two frequencies where the power dissipated in the circuit is half the power dissipated at resonance. Using suitable approximations, show that
A sine-wave generator with 20-V peak output is applied across a series RLC circuit. At the resonant frequency of 2.0 kHz, the peak current is 50 mA; at 1.0 kHz, it’s 15 mA. Find R, L, and C.
A series RLC circuit with R = 47 Ω, L = 250mH, and C = 4.0 μF is connected across a sine-wave generator whose peak output voltage is independent of frequency. Find the frequency range over which the peak current will exceed half its value at resonance.
A “black box” has two input connections and two output connections. With a 12-V rms, 60-Hz sine wave across the inputs, the output is a 6.0-V, 60-Hz sine wave leading the input voltage by 45°. Design a circuit that could be in the “black box.”
Two capacitors are connected in parallel across a 24-V rms, 7.5-kHz sine-wave generator, and the generator supplies a total rms current of 56mA. With capacitors rewired in series, the rms current drops to 2.8mA. What are the two capacitances?
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