A spy satellite can consist essentially of a large-diameter concave mirror forming an image on a digital-camera detector and sending the picture to a ground receiver by radio waves. In effect, it is an astronomical telescope in orbit, looking down instead of up. Can a spy satellite read a license plate? Can it read the date on a dime? Argue for your answers by making an order-of-magnitude calculation, specifying the data you estimate.
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A spy satellite can consist essentially of a large-diameter concave mirror forming an image on a digital-camera detector and sending the picture to a ground receiver by radio waves. In effect, it is an astronomical telescope in orbit, looking down instead of up. Can a spy satellite read a license plate? Can it read the date on a dime? Argue for your answers by making an order-of-magnitude calculation, specifying the data you estimate.
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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 = 0.0065 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.…As 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.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.
- (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.)Q blem 9: Two mirrors are held at an angle of y-130 degrees with respect to one another. A ray of light is incident of the first mirror at an angle of 8. When it reflects off of the mirror next to it makes an angle of o-13.5 degrees. Randomized Variables i -130 t(a) Write an expression for the angle of incidence 8. a V d i m Submit B 0 8 P Part (b) Numerically what is this angle? Hent 9 a h k t ( INH + NO 4 7 89 BO 4 5 6 1 2 3 0 A END CLEAR ACKUACE I give up!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?
- 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.Estimate 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 kmThe 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).
- In 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 0.074688971 (b) Number i 10.3819 Mirror Laser Units (degrees) Units m ◄► W N S E DetectorIn an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 50.0 km due north. A detector is placed 117 m due east of the laser. The mirror is to be aligned so that light from the laser reflects 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 0.0048. By how many meters (due east) will the reflected ray miss the detector?In 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 Detector