Question: A certain telescope has an objective mirror

> 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

> 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 ob

> 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

> 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 patient has a near point of 45.0 cm and far point of 85.0 cm. (a) Can a single lens correct the patient’s vision? Explain the patient’s options. (b) Calculate the power lens needed to correct the near point so that the patient can see objects 25.0 cm a

> 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?