Question: A patient has a near point of

> 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

> Imagine an astronaut on a trip to Sirius, which lies 8 light - years from Earth. Upon arrival at Sirius, the astronaut finds that the trip lasted 6 years. If the trip was made at a constant speed of 0.8c, how can the 8 - light - year distance be reconcil

> During LASIK eye surgery (laser - assisted in situ keratomileusis), the shape of the cornea is modified by vaporizing some of its material. If the surgery is performed to correct for nearsightedness, how does the cornea need to be reshaped?

> Two identically constructed clocks are synchronized. One is put into orbit around Earth, and the other remains on Earth. (a) Which clock runs more slowly? (b) When the moving clock returns to Earth, will the two clocks still be synchronized? Discuss from

> A lens with a certain power is used as a simple magnifier. If the power of the lens is doubled, does the angular magnification increase or decrease?

> It is said that Einstein, in his teenage years, asked the question, “What would I see in a mirror if I carried it in my hands and ran at a speed near that of light?” How would you answer this question?

> You observe a rocket moving away from you. (i) Compared with its length when it was at rest on the ground, will you measure its length to be (a) Shorter, (b) Longer, or (c) The same? Compared to the passage of time measured by the watch on your wrist, is

> Large telescopes are usually reflecting rather than refracting. List some reasons for this choice.

> With regard to reference frames, how does general relativity differ from special relativity?

> Choose the option from each pair that makes the following statement correct. For a farsighted person, the (a) Near point; (b) Far point is always located farther than (c) 1 m; (d) 25 cm from the eye and the corrective lens is (e) Converging; (f) Divergin

> What two speed measurements will two observers in relative motion always agree upon?

> Compare and contrast the eye and a camera. What parts of the camera correspond to the iris, the retina, and the cornea of the eye?

> A camera is being used with a correct exposure at f/4 and a shutter speed of 1/15 s. In addition to the f - numbers listed in Section 25.1, this camera has f - numbers f/1, f/1.4, and f/2. To photograph a rapidly moving subject, the shutter speed is chan

> A digital camera equipped with an f = 50.0 - mm lens uses a CCD sensor of width 8.70 mm and height 14.0 mm. Find the closest distance from the camera to a 1.80 - m - tall person if the person’s full image is to fit on the CCD sensor.

> An f/2.80 CCD camera has a 105 - mm focal length lens and can focus on objects from infinity to as near as 30.0 cm from the lens. (a) Determine the camera’s aperture diameter. Determine the (b) Minimum and (c) Maximum distances from the CCD sensor over w

> A certain camera has f - numbers that range from 1.2 to 22. If the focal length of the lens is 55 mm, what is the range of aperture diameters for the camera?

> A particular patient’s eyes are unable to focus on objects closer than 35.0 cm and corrective lenses are to be prescribed so that the patient can focus on objects 20.0 cm from their eyes. (a) Is the patient nearsighted or farsighted? (b) If contact lense

> A particular nearsighted patient can’t see objects clearly beyond 15.0 cm from their eye. Determine (a) The lens power required to correct the patient’s vision and (b) The type of lens required (converging or diverging). Neglect the distance between the

> An individual is nearsighted; his near point is 13.0 cm and his far point is 50.0 cm. (a) What lens power is needed to correct his nearsightedness? (b) When the lenses are in use, what is this person’s near point?

> Choose the option from each pair that makes the following statement correct. Because ( for an object in relative motion is always [(a) greater; (b) less] than 1, a proper time interval Δtp is always [(c) longer; (d) shorter] than the time interval Δt and

> A certain child’s near point is 10.0 cm; her far point (with eyes relaxed) is 125 cm. Each eye lens is 2.00 cm from the retina. (a) Between what limits, measured in diopters, does the power of this lens–cornea combination vary? (b) Calculate the power of

> The accommodation limits for Nearsighted Nick’s eyes are 18.0 cm and 80.0 cm. When he wears his glasses, he is able to see faraway objects clearly. At what minimum distance is he able to see objects clearly?

> A patient can’t see objects closer than 40.0 cm and wishes to clearly see objects that are 20.0 cm from his eye. (a) Is the patient nearsighted or farsighted? (b) If the eye–lens distance is 2.00 cm, what is the minimum object distance p from the lens? (

> The near point of a person’s eye is 60.0 cm. To see objects clearly at a distance of 25.0 cm, what should be the (a) Focal length and (b) Power of the appropriate corrective lens? (Neglect the distance from the lens to the eye.)

> A certain camera lens has a focal length of 175 mm. Its position can be adjusted to produce images when the lens is between 180. mm and 210. mm from the plane of the film. Over what range of object distances is the lens useful?

> A certain type of film requires an exposure time of 0.010 s with an f/11 lens setting. Another type of film requires twice the light energy to produce the same level of exposure. What f - number does the second type of film need with the 0.010 - s exposu

> (a) Use conceptual arguments to show that the intensity of light (energy per unit area per unit time) reaching the film in a camera is proportional to the square of the reciprocal of the f - number as (b) The correct exposure time for a camera set to f/

> A muon formed high in Earth’s atmosphere travels toward Earth at a speed v = 0.990c for a distance of 4.60 km as measured by an observer at rest with respect to Earth. It then decays into an electron, a neutrino, and an antineutrino. (a) How long does th

> An astronaut is traveling in a space vehicle that has a speed of 0.500c relative to Earth. The astronaut measures his pulse rate at 75.0 beats per minute. Signals generated by the astronaut’s pulse are radioed to Earth when the vehicle is moving perpendi

> The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 x 10-8 s. If the meson moves with a speed of 0.98c, what is (a) Its mean lifetime as measured by an observer on Earth, and (b) The average distance it tra

> Suppose you are observing the interference pattern formed by a Michelson interferometer in a laboratory and a joking colleague holds a lit match in the light path of one arm of the interferometer. Will this match have an effect on the interference patter

> An astronaut at rest on Earth has a heart rate of 70. beats/min. When the astronaut is traveling in a spaceship at 0.90c, what will this rate be as measured by (a) An observer also in the ship and (b) An observer at rest on Earth?

> An alien spaceship traveling 0.600c toward Earth launches a landing craft with an advance guard of purchasing agents. The lander travels in the same direction with a velocity 0.800c relative to the spaceship. As observed on Earth, the spaceship is 0.200

> An observer moving at a speed of 0.995c relative to a rod (Fig. P26.55) measures its length to be 2.00 m and sees its length to be oriented at 30.0° with respect to its direction of motion. (a) What is the proper length of the rod? (b) What is

> An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 70.0% of the speed of light. Its nuclear - powered batteries supply the energy to keep its data transmitter active continuously.

> The identical twins Speedo and Goslo join a migration from Earth to Planet X, which is 20.0 light - years away in a reference frame in which both planets are at rest. The twins, of the same age, depart at the same time on different spacecraft. Speedo’s c

> Imagine that the entire Sun collapses to a sphere of radius Rg such that the work required to remove a small mass m from the surface would be equal to its rest energy mc2. This radius is called the gravitational radius for the Sun. Find Rg. (It is believ

> The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a reference frame in which the muons are stationary, if the number of muons at t = 0 is N0, the number at time t is given by N = N0e-t/τ, where τ is the mea

> (a) Show that a potential difference of 1.02 x 106 V would be sufficient to give an electron a speed equal to twice the speed of light if Newtonian mechanics remained valid at high speeds. (b) What speed would an electron actually acquire in falling thro

> The length of a moving spaceship is 28.0 m according to an astronaut on the spaceship. If the spaceship is contracted by 15.0 cm according to an Earth observer, what is the speed of the spaceship?

> The nonrelativistic expression for the momentum of a particle, p = mv, can be used if v

> Choose the option that makes the following statement correct. Two events at a single location define a time interval. The proper time interval Δtp is measured by an observer [(a) at rest; (b) moving] relative to the location where the two events occur.

> The cosmic rays of highest energy are protons that have kinetic energy on the order of 1013 MeV. (a) From the point of view of the proton, how many kilometers across is the galaxy? (b) How long would it take a proton of this energy to travel across the M

> A spaceship of proper length 300. m takes 0.75 µs to pass an Earth observer. Determine the speed of this spaceship as measured by the Earth observer.

> An observer in a coasting spacecraft moves toward a mirror at speed v relative to the reference frame labeled by S in Figure P26.46. The mirror is stationary with respect to S. A light pulse emitted by the spacecraft travels toward the mirror and is refl

> Owen and Dina are at rest in frame S', which is moving with a speed of 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P26.45). Owen throws the ball to Dina with a speed of 0.800c (accordin

> An alarm clock is set to sound in 10.0 h. At t = 0, the clock is placed in a spaceship moving with a speed of 0.75c (relative to Earth). What distance, as determined by an Earth observer, does the spaceship travel before the alarm clock sounds?

> An astronaut wishes to visit the Andromeda galaxy, making a one - way trip that will take 30.0 years in the spaceship’s frame of reference. Assume the galaxy is 2.00 million light - years away and his speed is constant. (a) How fast mus

> An electron has a total energy equal to five times its rest energy. (a) What is its momentum? (b) Repeat for a proton.

> A star is 5.00 ly from the Earth. At what speed must a spacecraft travel on its journey to the star such that the Earth–star distance measured in the frame of the spacecraft is 2.00 ly?

> A spring of force constant k is compressed by a distance x from its equilibrium length. (a) Does the mass of the spring change when the spring is compressed? Explain. (b) Find an expression for the change in mass of the spring in terms of k, x, and c. (c

> A meter-stick moving at 0.900c relative to the Earth’s surface approaches an observer at rest with respect to the Earth’s surface. (a) What is the meter-stick’s length as measured by the observer? (b) Qualitatively, how would the answer to part (a) chang

> A CCD camera is equipped with a lens with constant focal - length. As the f - number is decreased, determine whether the following quantities increase, decrease, or remain unchanged. Indicate your answers with I, D, or U. (a) The aperture (b) The depth o

> The rest energy of an electron is 0.511 MeV. The rest energy of a proton is 938 MeV. Assume both particles have kinetic energies of 2.00 MeV. Find the speed of (a) The electron and (b) The proton. (c) By how much does the speed of the electron exceed tha

> An electron has a speed of 0.750c. (a) Find the speed of a proton that has the same kinetic energy as the electron. (b) Find the speed of a proton that has the same momentum as the electron.

> Consider electrons accelerated to a total energy of 20.0 GeV in the 3.00 - km - long Stanford Linear Accelerator. (a) What is the ( factor for the electrons? (b) How long does the accelerator appear to the electrons? Electron mass energy: 0.511 MeV.

> Consider the reaction 92235U + 01n ( 57148La + 3587Br + 01n. (a) Write the conservation of relativistic energy equation symbolically in terms of the rest energy and the kinetic energy, setting the initial total energy equal to the final total energy. (b)

> Starting with the definitions of relativistic energy and momentum, show that E2 = p2c2 + m2c4 (Eq. 26.13).

> An unstable particle with a mass equal to 3.34 x 10-27 kg is initially at rest. The particle decays into two fragments that fly off with velocities of 0.987c and -0.868c, respectively. Find the masses of the fragments. Hint: Conserve both mass – energy a

> A chain of nuclear reactions in the Sun’s core converts four protons into a helium nucleus. (a) What is the mass difference between four protons and a helium nucleus? (b) How much energy in MeV is released during the conversion of four protons into a hel

> Determine the energy required to accelerate an electron from (a) 0.500c to 0.900c and (b) 0.900c to 0.990c.

> What speed must a particle attain before its kinetic energy is double the value predicted by the nonrelativistic expression KE = ½ mv2?

> A proton in a large accelerator has a kinetic energy of 175 GeV. (a) Compare this kinetic energy to the rest energy of the proton, and find an approximate expression for the proton’s kinetic energy. (b) Find the speed of the proton.

> A lens has a focal length of 28 cm and a diameter of 4.0 cm. What is the f - number of the lens?

> You are packing for a trip to another star, and on your journey you will be traveling at a speed of 0.99c. Can you sleep in a smaller cabin than usual, because you will be shorter when you lie down? Explain your answer.

> Refer to the following two histograms and two QQ plots of the same data. a. Match each of the histograms with the corresponding QQ plot. Histogram A goes with QQ plot ______. Histogram B goes with QQ plot ______. b. Describe the shape of the histograms.

> Refer to the following two histograms and two QQ plots of the same data. a. Match each of the histograms with the corresponding QQ plot. Histogram A goes with QQ plot ______. Histogram B goes with QQ plot ______. b. Describe the shape of the histograms.