If a typical eyeball is 2.00 cm long and has a pupil opening that can range from about 2.00 mm to 6.00 mm, what are (a) The focal length of the eye when it is focused on objects 1.00 m away, (b) The smallest f - number of the eye when it is focused on objects 1.00 m away, and (c) The largest f - number of the eye when it is focused on objects 1.00 m away?
> What is the role of a defining contrast, or generator, in fractional factorial experiments? Distinguish between a principal fraction and an alternate fraction.
> Clearly distinguish between the principles of confounding and fractionalization.
> What are the features of a 2k factorial experiment? What are the features of a 2k–2 fractional factorial experiment and how is it constructed?
> What is the utility of contrasts in experimental design? What are orthogonal contrasts and how are they helpful?
> Distinguish between factor, treatment, and treatment levels in the context of a health care facility.
> Distinguish between failure-, time-terminated, and sequential tests for reliability and life testing.
> Explain why it is possible for external failure costs to go up even if the first-pass quality level of a product made by a company remains the same.
> Explain procedures that might improve the reliability of a system. How would you increase the availability of a system? Distinguish between a system with components in parallel and another with standby components.
> Describe the life cycle of a product. What probability distributions would you use to model each phase?
> Define reliability. Explain its role in quality control and improvement.
> Discuss the context in which minimizing the average sample number would be a feasible criterion. Which type of sampling plan (single, double, or multiple) would be preferable and what factors would influence your choice?
> If rectification inspection is used, discuss possible criteria to sampling plans.
> Explain the difference between average sample number and average total inspection. State any assumptions made.
> If you were interested in protection for acceptance of a single lot from a vendor with whom you do not expect to conduct much business, what criteria would you select and why?
> Distinguish between average outgoing quality and acceptable quality level. Explain the meaning and importance of the average outgoing quality limit.
> Discuss the relative advantages and disadvantages of single, double, and multiple sampling plans.
> What is the importance of the OC curve in the selection of sampling plans? Describe the impact of the sample size and the acceptance number on the OC curve. What is the disadvantage of having an acceptance number of zero?
> For a regional hospital in a metropolitan area, what are some of the internal failure and external failure costs? How might they be reduced?
> Consider the following organizations. How would you define quality in each context? Specify attributes/variables that may measure quality. How do you integrate these measures? Discuss the ease or difficulties associated with obtaining values for the vari
> If astronauts could travel at v = 0.950c, we on Earth would say it takes (4.20/0.950) = 4.42 years to reach Alpha Centauri, 4.20 light - years away. The astronauts disagree. (a) How much time passes on the astronauts’ clocks? (b) What is the distance to
> Protons in an accelerator at the Fermi National Laboratory near Chicago are accelerated to a total energy that is 400 times their rest energy. (a) What is the speed of these protons in terms of c? (b) What is their kinetic energy in MeV?
> A proton moves with a speed of 0.950c. Calculate (a) Its rest energy, (b) Its total energy, and (c) Its kinetic energy.
> A rocket moves with a velocity of 0.92c to the right with respect to a stationary observer A. An observer B moving relative to observer A finds that the rocket is moving with a velocity of 0.95c to the left. What is the velocity of observer B relative to
> A pulsar is a stellar object that emits light in short bursts. Suppose a pulsar with a speed of 0.950c approaches Earth, and a rocket with a speed of 0.995c heads toward the pulsar. (Both speeds are measured in Earth’s frame of reference.) If the pulsar
> Spaceship A moves away from Earth at a speed of 0.800c (Fig. P26.25). Spaceship B pursues at a speed of 0.900c relative to Earth. Observers on Earth see B overtaking A at a relative speed of 0.100c. With what speed is B overtaking A as seen by the crew o
> Two identical spaceships with proper lengths of 175 m are launched from Earth. Spaceship A is launched in one direction at 0.500c and spaceship B is launched in the opposite direction at 0.750c. (a) What is the speed of spaceship B relative to spaceship
> A spaceship is moving away from Earth at 0.900c when it fires a small rocket in the forward direction at 0.500c relative to the spaceship. Calculate the rocket’s speed relative to Earth.
> A spaceship travels at 0.750c relative to Earth. If the spaceship fires a small rocket in the forward direction, how fast (relative to the ship) must it be fired for it to travel at 0.950c relative to Earth?
> An electron moves to the right with a speed of 0.90c relative to the laboratory frame. A proton moves to the left with a speed of 0.70c relative to the electron. Find the speed of the proton relative to the laboratory frame.
> True or False: People traveling near the speed of light relative to Earth would measure their lifespans and find them, on the average, longer than the average human lifespan as measured on Earth.
> Spaceship R is moving to the right at a speed of 0.70c with respect to Earth. A second spaceship, L, moves to the left at the same speed with respect to Earth. What is the speed of L with respect to R?
> A spaceship moves past Earth with a speed of 0.900c. As it is passing, a person on Earth measures the spaceship’s length to be 75.0 m. (a) Determine the spaceship’s proper length. (b) Determine the time required for the spaceship to pass a point on Earth
> An unstable particle at rest breaks up into two fragments of unequal mass. The mass of the lighter fragment is equal to 2.50 x 10-28 kg and that of the heavier fragment is 1.67 x 10-27 kg. If the lighter fragment has a speed of 0.893c after the breakup,
> Calculate the classical momentum of a proton traveling at 0.990c, (a) Neglecting relativistic effects. (b) Repeat the calculation while including relativistic effects. (c) Does it make sense to neglect relativity at such speeds?
> An electron has a momentum with magnitude three times the magnitude of its classical momentum. (a) Find the speed of the electron. (b) How would your result change if the particle were a proton?
> At what speed do the classical and relativistic values of a particle’s momentum differ by 10.0%?
> (a) What is the momentum of a proton moving at 0.900c? (b) At what speed will a particle’s relativistic momentum equal twice its classical momentum?
> A box is cubical with sides of proper lengths L1 = L2 = L3, as shown in Figure P26.14, when viewed in its own rest frame. If this block moves parallel to one of its edges with a speed of 0.80c past an observer, (a) What shape does it appear to have to th
> A supertrain of proper length 1.00 x 102 m travels at a speed of 0.95c as it passes through a tunnel having proper length 50.0 m. As seen by a trackside observer, is the train ever completely within the tunnel? If so, by how much?
> A car traveling at 35.0 m/s takes 26.0 minutes to travel a certain distance according to the driver’s clock in the car. How long does the trip take according to an observer at rest on Earth? Hint: The following approximation is helpful: [1 – x]-1/2 ≈ 1 +
> Suppose you are observing a binary star with a telescope and are having difficulty resolving the two stars. Which color filter will better help resolve the stars? (a) Blue (b) Red (c) Neither because colored filters have no effect on resolution
> The proper length of one spaceship is three times that of another. The two spaceships are traveling in the same direction and, while both are passing overhead, an Earth observer measures the two spaceships to have the same length. If the slower spaceship
> A star is 15.0 light - years (ly) from Earth. (a) At what constant speed must a spacecraft travel on its journey to the star so that the Earth–star distance measured by an astronaut onboard the spacecraft is 3.00 ly? (b) What is the journey’s travel time
> The control panel on a spaceship contains a light that blinks every 2.00 s as observed by an astronaut in the ship. If the spaceship is moving past Earth with a speed of 0.750c, determine (a) The proper time interval between blinks and (b) The time inter
> A Boy Scout starts a fire by using a lens from his eyeglasses to focus sunlight on kindling 5.0 cm from the lens. The Boy Scout has a near point of 15 cm. When the lens is used as a simple magnifier, (a) What is the maximum magnification that can be achi
> A laboratory (astronomical) telescope is used to view a scale that is 300 cm from the objective, which has a focal length of 20.0 cm; the eyepiece has a focal length of 2.00 cm. Calculate the angular magnification when the telescope is adjusted for minim
> A cataract - impaired lens in an eye may be surgically removed and replaced by a manufactured lens. The focal length required for the new lens is determined by the lens - to - retina distance, which is measured by a sonar - like device, and by the requir
> If the aqueous humor of the eye has an index of refraction of 1.34 and the distance from the vertex of the cornea to the retina is 2.00 cm, what is the radius of curvature of the cornea for which distant objects will be focused on the retina? (For simpli
> The near point of an eye is 75.0 cm. (a) What should be the power of a corrective lens prescribed to enable the eye to see an object clearly at 25.0 cm? (b) If, using the corrective lens, the person can see an object clearly at 26.0 cm but not at 25.0 cm
> An American standard analog television picture (non-HDTV), also known as NTSC, is composed of approximately 485 visible horizontal lines of varying light intensity. Assume your ability to resolve the lines is limited only by the Rayleigh criterion, the p
> Two campers wish to start a fire during the day. One camper is nearsighted and one is farsighted. Whose glasses should be used to focus the Sun’s rays onto some paper to start the fire? (a) Either camper’s (b) The nearsighted camper’s (c) The farsighted
> A person with a nearsighted eye has near and far points of 16 cm and 25 cm, respectively. (a) Assuming a lens is placed 2.0 cm from the eye, what power must the lens have to correct this condition? (b) Suppose contact lenses placed directly on the cornea
> The Yerkes refracting telescope has a 1.00-m-diameter objective lens of focal length 20.0 m. Assume it is used with an eyepiece of focal length 2.50 cm. (a) Determine the magnification of the planet Mars as seen through the telescope. (b) Are the observe
> Estimate the minimum angle subtended at the eye of a hawk flying at an altitude of 50 m necessary to recognize a mouse on the ground.
> A thin sheet of transparent material has an index of refraction of 1.40 and is 15.0 μm thick. When it is inserted in the light path along one arm of an interferometer, how many fringe shifts occur in the pattern? Assume the wavelength (in a vacuum) of th
> The Michelson interferometer can be used to measure the index of refraction of a gas by placing an evacuated transparent tube in the light path along one arm of the device. Fringe shifts occur as the gas is slowly added to the tube. Assume 600.-nm light
> An interferometer is used to measure the length of a bacterium. The wavelength of the light used is 650. nm. As one arm of the interferometer is moved from one end of the cell to the other, 310. fringe shifts are counted. How long is the bacterium?
> Mirror M1 in Figure 25.16 is displaced a distance ΔL. During this displacement, 250 fringe shifts are counted. The light being used has a wavelength of 632.8 nm. Calculate the displacement ΔL. Figure 25.16:
> Light of wavelength 550. nm is used to calibrate a Michelson interferometer. With the use of a micrometer screw, the platform on which one mirror is mounted is moved 0.180 mm. How many fringe shifts are counted?
> Monochromatic light is beamed into a Michelson interferometer. The movable mirror is displaced 0.382 mm, causing the central spot in the interferometer pattern to change from bright to dark and back to bright N = 1 700 times. (a) Determine the wavelength
> A 15.0-cm-long grating has 6.00 x 103 slits per centimeter. Can two lines of wavelengths 600.000 nm and 600.003 nm be separated with this grating? Explain.
> Suppose you’re an astronaut being paid according to the time you spend traveling in space. You take a long voyage traveling at a speed near that of light. Upon your return to Earth, you’re asked how you’d like to be paid: according to the time elapsed on
> The Hα line in hydrogen has a wavelength of 656.20 nm. This line differs in wavelength from the corresponding spectral line in deuterium (the heavy stable isotope of hydrogen) by 0.18 nm. (a) Determine the minimum number of lines a grating must have to r
> A diffraction grating has a second-order resolving power of 1250. (a) Find the number of illuminated lines on the grating. (b) Calculate the smallest difference in wavelengths surrounding 525 nm that can be resolved in the first-order diffraction pattern
> A spy satellite circles Earth at an altitude of 200. km and carries out surveillance with a special high-resolution telescopic camera having a lens diameter of 35 cm. If the angular resolution of this camera is limited by diffraction, estimate the separa
> Suppose a 5.00-m-diameter telescope were constructed on the Moon, where the absence of atmospheric distortion would permit excellent viewing. If observations were made using 500.-nm light, what minimum separation between two objects could just be resolve
> Two stars located 23 light-years from Earth are barely resolved using a reflecting telescope having a mirror of diameter 68 cm. Assuming λ = 575 nm and assuming that the resolution is limited only by diffraction, find the separation between the stars.
> A vehicle with headlights separated by 2.00 m approaches an observer holding an infrared detector sensitive to radiation of wavelength 885 nm. What aperture diameter is required in the detector if the two headlights are to be resolved at a distance of 10
> (a) Calculate the limiting angle of resolution for the eye, assuming a pupil diameter of 2.00 mm, a wavelength of 500 nm in air, and an index of refraction for the eye of 1.33. (b) What is the maximum distance from the eye at which two points separated
> To increase the resolving power of a microscope, the object and the objective are immersed in oil (n = 1.5). If the limiting angle of resolution without the oil is 0.60 μrad, what is the limiting angle of resolution with the oil? Hint: The oil changes th
> While flying at an altitude of 9.50 km, you look out the window at various objects on the ground. If your ability to distinguish two objects is limited only by diffraction, find the smallest separation between two objects on the ground that are distingui
> A converging lens with a diameter of 30.0 cm forms an image of a satellite passing overhead. The satellite has two green lights (wavelength 500. nm) spaced 1.00 m apart. If the lights can just be resolved according to the Rayleigh criterion, what is the
> True or False: If you were traveling in a spaceship at a speed of c/2 relative to Earth and you fired a laser beam in the direction of the spaceship’s motion, the light from the laser would travel at a speed of 3c/2 relative to Earth.
> Galileo devised a simple terrestrial telescope that produces an upright image. It consists of a converging objective lens and a diverging eyepiece at opposite ends of the telescope tube. For distant objects, the tube length is the objective focal length
> A person decides to use an old pair of eyeglasses to make some optical instruments. He knows that the near point in his left eye is 50.0 cm and the near point in his right eye is 100. cm. (a) What is the maximum angular magnification he can produce in a
> An elderly sailor is shipwrecked on a desert island, but manages to save his eyeglasses. The lens for one eye has a power of +1.20 diopters, and the other lens has a power of +9.00 diopters. (a) What is the magnifying power of the telescope he can constr
> Astronomers often take photographs with the objective lens or mirror of a telescope alone, without an eyepiece. (a) Show that the image size h’ for a telescope used in this manner is given by h’ = fh/(f - p), where h is the object size, f is the objectiv
> A certain telescope has an objective of focal length 1500 cm. If the Moon is used as an object, a 1.0-cm-long image formed by the objective corresponds to what distance, in miles, on the Moon? Assume 3.8 x 108 m for the Earth–Moon distance.
> Suppose an astronomical telescope is being designed to have an angular magnification of 34.0. If the focal length of the objective lens being used is 86.0 cm, find (a) The required focal length of the eyepiece and (b) The distance between the two lenses
> (a) Find an equation for the length L of a refracting telescope in terms of the focal length of the objective fo and the magnification m. (b) A knob adjusts the eyepiece forward and backward. Suppose the telescope is in focus with an eyepiece giving a ma
> A certain telescope has an objective mirror with an aperture diameter of 200. mm and a focal length of 2.00 x 103 mm. It captures the image of a nebula on photographic film at its prime focus with an exposure time of 1.50 min. To produce the same light e
> An inquiring student makes a refracting telescope by placing an objective lens and an eyepiece at opposite ends of a 47.5-cm-long tube. If the eyepiece has a focal length of 1.50 cm, calculate (a) The required focal length of the objective lens and (b) T
> The two lenses of a compound microscope are separated by a distance of 20.0 cm. If the objective lens produces a lateral magnification of 10.0x and the overall magnification is 115x, determine (a) The angular magnification of the eyepiece, (b) The focal
> A photon is reflected from a mirror. True or False: (a) Because a photon has zero mass, it does not exert a force on the mirror. (b) Although the photon has energy, it can’t transfer any energy to the surface because it has zero mass. (c) The photon carr
> A microscope has an objective lens with a focal length of 16.22 mm and an eyepiece with a focal length of 9.50 mm. With the length of the barrel set at 29.0 cm, the diameter of a red blood cell’s image subtends an angle of 1.43 mrad with the eye. If the
> Find the magnification of a telescope that uses a 2.75-diopter objective lens and a 35.0-diopter eyepiece.
> The distance between the eyepiece and the objective lens in a certain compound microscope is 20.0 cm. The focal length of the objective is 0.500 cm, and that of the eyepiece is 1.70 cm. Find the overall magnification of the microscope.
> The desired overall magnification of a compound microscope is 140x. The objective alone produces a lateral magnification of 12x. Determine the required focal length of the eyepiece.
> (a) What is the maximum angular magnification of an eyeglass lens having a focal length of 18.0 cm when used as a simple magnifier? (b) What is the magnification of this lens when the eye is relaxed?
> A leaf of length h is positioned 71.0 cm in front of a converging lens with a focal length of 39.0 cm. An observer views the image of the leaf from a position 1.26 m behind the lens, as shown in Figure P25.25. (a) What is the magnitude of the lateral mag
> A jeweler’s lens of focal length 5.0 cm is used as a magnifier. With the lens held near the eye, determine (a) The angular magnification when the object is at the focal point of the lens and (b) The angular magnification when the image formed by the lens
> A biology student uses a simple magnifier to examine the structural features of an insect’s wing. The wing is held 3.50 cm in front of the lens, and the image is formed 25.0 cm from the eye. (a) What is the focal length of the lens? (b) What angular magn
> When a drop of water is placed on a flat, clear surface such as a glass slide or plastic sheet, surface tension pulls the top surface into a curved, lens-like shape so that the drop functions as a simple magnifier. Suppose a drop of water has a maximum a
> A stamp collector uses a lens with 7.5-cm focal length as a simple magnifier. The virtual image is produced at the normal near point (25 cm). (a) How far from the lens should the stamp be placed? (b) What is the expected angular magnification?
> True or False: Because the speed of a particle cannot exceed the speed of light, there is an upper limit to its momentum and kinetic energy.
> A person sees clearly wearing eyeglasses that have a power of -4.00 diopters when the lenses are 2.00 cm in front of the eyes. (a) What is the focal length of the lens? (b) Is the person nearsighted or farsighted? (c) If the person wants to switch to con
> A nearsighted woman can’t see objects clearly beyond 40.0 cm (her far point). If she has no astigmatism and contact lenses are prescribed, what power and type of lens are required to correct her vision?
> A person is to be fitted with bifocals. She can see clearly when the object is between 30. cm and 1.5 m from the eye. (a) The upper portions of the bifocals (Fig. P25.18) should be designed to enable her to see distant objects clearly. What power should
> An artificial lens is implanted in a person’s eye to replace a diseased lens. The distance between the artificial lens and the retina is 2.80 cm. In the absence of the lens, an image of a distant object (formed by refraction at the cornea) falls 5.33 cm
> Suppose a photon, proton, and electron all have the same total energy E. Rank the magnitude of their momenta from smallest to greatest. (a) Photon, electron, proton (b) Proton, photon, electron (c) Electron, photon, proton (d) Electron, proton, photon (e
