Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 37, Problem 50CP
(a)
To determine
Whether the spy satellite can read the license plate or not.
(b)
To determine
Whether the spy satellite can read the date on the dime.
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A new optical imaging satellite is being designed for the Maritime Domain Awareness mission. The satellite will be placed in a circular orbit at 5000 km altitude and be able to look off of nadir, giving a maximum range to the target of 7000 km. The desired resolution is 3 meters. What is the satellite's speed? Express answer in km/s to two significant digits.
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Often in optics scientists take advantage of effects that require very high intensity light. To get the desired effect a scientist uses a laser with power P = 0.0015 W to reach an intensity of I = 350 W/cm2 by focusing it through a lens of focal length f = 0.15 m. The beam has a radius of r = 0.0011 m when it enters the lens.Randomized VariablesP = 0.0015 WI = 350 W/cm2f = 0.15 mr = 0.0011 m
Part (a) Express the radius of the beam, rp, at the point where it reaches the desired intensity in terms of the given quantities. (In other words, what radius does the beam have to have after passing through the lens in order to have the desired intensity?)
Part (b) Give an expression for the tangent of the angle that the edge of the beam exits the lens with with respect to the normal to the lens surface, in terms of r and f? Part (c) Express the distance, D, between the lens's focal point and the illuminated object using tan(α) and rp. Part (d) Find the distance, D, in centimeters.
Chapter 37 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 37.2 - Suppose the slit width in Figure 37.4 is made half...Ch. 37.3 - Cats eyes have pupils that can be modeled as...Ch. 37.3 - Suppose you are observing a binary star with a...Ch. 37.4 - Ultraviolet light of wavelength 350 nm is incident...Ch. 37.6 - A polarizer for microwaves can be made as a grid...Ch. 37.6 - Prob. 37.6QQCh. 37 - Prob. 1PCh. 37 - Prob. 2PCh. 37 - Prob. 3PCh. 37 - In Figure 37.7, show mathematically how many...
Ch. 37 - Prob. 5PCh. 37 - What If? Suppose light strikes a single slit of...Ch. 37 - Prob. 7PCh. 37 - Coherent light of wavelength 501.5 nm is sent...Ch. 37 - Prob. 9PCh. 37 - Prob. 10PCh. 37 - What is the approximate size of the smallest...Ch. 37 - Prob. 12PCh. 37 - Prob. 13PCh. 37 - Prob. 14PCh. 37 - Impressionist painter Georges Seurat created...Ch. 37 - Prob. 16PCh. 37 - Consider an array of parallel wires with uniform...Ch. 37 - Prob. 18PCh. 37 - A grating with 250 grooves/mm is used with an...Ch. 37 - Show that whenever white light is passed through a...Ch. 37 - Light from an argon laser strikes a diffraction...Ch. 37 - Prob. 22PCh. 37 - You are working as a demonstration assistant for a...Ch. 37 - Prob. 24PCh. 37 - Prob. 25PCh. 37 - Prob. 26PCh. 37 - Prob. 27PCh. 37 - Prob. 28PCh. 37 - Prob. 29PCh. 37 - Prob. 30PCh. 37 - Prob. 31PCh. 37 - Prob. 32PCh. 37 - Prob. 33APCh. 37 - Laser light with a wavelength of 632.8 nm is...Ch. 37 - Prob. 35APCh. 37 - Prob. 36APCh. 37 - Prob. 37APCh. 37 - Prob. 38APCh. 37 - Prob. 39APCh. 37 - Prob. 40APCh. 37 - Prob. 41APCh. 37 - Prob. 42APCh. 37 - Prob. 43APCh. 37 - Prob. 44APCh. 37 - Prob. 45APCh. 37 - Prob. 46APCh. 37 - Prob. 47APCh. 37 - Prob. 48APCh. 37 - Two closely spaced wavelengths of light are...Ch. 37 - Prob. 50CPCh. 37 - Prob. 51CPCh. 37 - In Figure P37.52, suppose the transmission axes of...Ch. 37 - Prob. 53CP
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- Lunar astronauts placed a reflector on the Moon’s surface, from which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. What percent error is this, given the average distance to the Moon is 3.84 × 108 m?arrow_forwardOften in optics scientists take advantage of effects that require very high intensity light. To get the desired effect a scientist uses a laser with power P = 0.0065 W to reach an intensity of I = 170 W/cm2 by focusing it through a lens of focal length f = 0.11 m. The beam has a radius of r = 0.0011m when it enters the lens. Randomized VariablesP = 0.0065 WI = 170 W/cm2f = 0.11 mr = 0.0011 Part (a) Express the radius of the beam, rp, at the point where it reaches the desired intensity in terms of the given quantities. (In other words, what radius does the beam have to have after passing through the lens in order to have the desired intensity?) Part (b) Give an expression for the tangent of the angle that the edge of the beam exits the lens with with respect to the normal to the lens surface, in terms of r and f? Part (c) Express the distance, D, between the lens's focal point and the illuminated object using tan(α) and rp. Part (d) Find the distance, D, in centimeters.…arrow_forwardThe resolution of a TEM is limited by diffraction (Rd) as discussed in Chapter 1, Eq. (1.3)), and by the spherical aberration which is expressed as: Rsph =Csα3, where Cs is the spherical aberration coefficient and α is the half-angle of the cone of light entering the objective lens. The TEM resolution is the quadratic sum of the diffraction resolution and spherical aberration resolution, given by the expression: R=√(R_d^2 + R_sph^2 ) The minimum R is obtained when Rd ≅ Rsph. Estimate the optimum value of α and resolution limit of TEM at 100–200 kV. (Cs ≅ 1 mm for an electromagnetic objective lens).arrow_forward
- (a) A small light fixture on the bottom of a swimming pool is 0.72 m below the surface. The light emerging from the still water forms a circle on the water surface. What is the diameter of this circle? (Give your answer, in m, to at least two decimal places.) (b) What If? If a 2.13 cm thick layer of oil (n = 1.35) is spread uniformly over the surface of the water, what is the diameter of the circle of light emerging from the swimming pool? (Give your answer, in m, to at least two decimal places.)arrow_forwardEstimate the linear separation (in kilometers) of two objects at a distance of 1.9 × 10° km that can just be resolved by an observer on Earth (a) using the naked eye and (b) using a telescope with a 7.4-m diameter mirror. Use the following data: diameter of pupil = 5.0 mm; wavelength of light = 550 nm. %3D (a) Number i 2.5E8 Units km (b) Number i 1.7E5 Units kmarrow_forwardWhen the sun is either rising or setting and appears to be just on the horizon, it is in fact below the horizon. The explanation for this seeming paradox is that light from the sun bends slightly when entering the earth’s atmosphere, as shown in Fig. Since our perception is based on the idea that light travels in straight lines, we perceive the light to be coming from an apparent position that is an angle d above the sun’s true position. (a) Make the simplifying assumptions that the atmosphere has uniform density, and hence uniform index of refraction n, and extends to a height h above the earth’s surface, at which point it abruptly stops. Show that the angle d is given by as attached. where R = 6378 km is the radius of the earth. (b) Calculate d using n = 1.0003 and h = 20 km. How does this compare to the angular radius of the sun, which is about one quarter of a degree? (In actuality a light ray from the sun bends gradually, not abruptly, since the density and refractive index of the…arrow_forward
- On a clear day a tiny fish hides under water (nwater =1.38) from an osprey under a circular leaf that has a diameter of 0.215 m. What is the maximum depth below the leaf that the fish can be so that it could not be spotted by the ospray? h Provide your answer in meters with a precision of four places after the decimal.arrow_forwardAs sunlight enters the Earth’s atmosphere, it changes direction due to the small difference between the speeds of light in vacuum and in air. The duration of an optical day is defined as the time interval between the instant when the top of the rising Sun is just visible above the horizon andthe instant when the top of the Sun just disappears below the horizontal plane. The duration of the geometric day is defined as the time interval between the instant a mathematically straight line between an observer and the top of the Sun just clears the horizon and the instant this linejust dips below the horizon. (a) Explain which is longer, an optical day or a geometric day. (b) Find the difference between these two time intervals. Model the Earth’s atmosphere as uniform, with index of refraction 1.000 293, a sharply defined upper surface, and depth 8 614 m. Assume the observer is at the Earth’s equator so that the apparent path of the rising and setting Sun is perpendicular to the horizon.arrow_forwardEstimate the linear separation (in kilometers) of two objects at a distance of 1.4 x 106 km that can just be resolved by an observer on Earth (a) using the naked eye and (b) using a telescope with a 5.4-m diameter mirror. Use the following data: diameter of pupil = 5.0 mm; wavelength of light = 550 nm. (a) Number i Units (b) Number i Unitsarrow_forward
- The mass of a solid hemisphere is measured once with a digital balance whose resolution is 1 g. The result is m = 50 g. With a caliper, the resolution of which is 0.05 mm, repeated measurements of the diameter D of the hemisphere are carried out. The values obtained for D: 100.30 mm; 100.00 mm; 100.60 mm; 100.10 mm; 100.25 mm; 100.50 mm; 100.40 mm; 100.20 mm; 100.30 mm; 100.35 mm. Knowing that the standard deviation of the set of diameter values is 0.18 mm, the result of measuring the diameter d is: (a) (1002.30 ± 0.05) mm (b) (100.300 ± 0.029) mm (c) (100.30 ± 0.18) mm (d)(100.300 ± 0.057) mmarrow_forwardIn an experiment to monitor the Moon’s surface with a light beam, pulsed radiation from a ruby laser (wave = 0.69 mm) was directed to the Moon through a reflecting telescope with a mirror radius of 1.3 m. A reflector on the Moon behaved like a circular flat mirror with radius 10 cm, reflecting the light directly back toward the telescope on Earth.The reflected light was then detected after being brought to a focus by this telescope. Approximately what fraction of the original light energy was picked up by the detector? Assume that for each direction of travel all the energy is in the central diffraction peak.arrow_forwardIn an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 56.0 km due north. A detector is placed 146 m due east of the laser. The mirror is to be aligned so that light from the laser refelects into the detector. (a) When properly aligned, what angle should the normal to the surface of the mirror make with due south? (b) Suppose the mirror is misaligned, so that the actual angle between the normal to the surface and due south is too large by 0.0050°. By how many meters (due east) will the reflected ray miss the detector? (a) Number i (b) Number i Units Mirror Units Laser ◄► W N S E Detectorarrow_forward
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