The image formed by a microscope objective with a focal length of 5.00 mm is 160 mm from its second focal point. The eyepiece has a focal length of 26.0 mm. a. What is the angular magnification of the microscope? b. The unaided eye can distinguish two points at its near point as separate if they are about 0.10 mm apart. What is the minimum separation between two points that can be observed (or resolved) through this microscope?
> X rays with an initial wavelength of 0.900 * 10-10 m undergo Compton scattering. For what scattering angle is the wavelength of the scattered x rays greater by 1.0% than that of the incident x rays?
> A photon scatters in the backward direction (ɸ = 180°) from a free proton that is initially at rest. What must the wavelength of the incident photon be if it is to undergo a 10.0% change in wavelength as a result of the scattering?
> The human eye is most sensitive to green light of wavelength 505 nm. Experiments have found that when people are kept in a dark room until their eyes adapt to the darkness, a single photon of green light will trigger receptor cells in the rods of the ret
> If a photon of wavelength 0.04250 nm strikes a free electron and is scattered at an angle of 35.0° from its original direction, find a. the change in the wavelength of this photon; b. the wavelength of the scattered light; c. the change in energy of th
> A photon with wavelength λ = 0.1385 nm scatters from an electron that is initially at rest. What must be the angle between the direction of propagation of the incident and scattered photons if the speed of the electron immediately after the collision is
> X rays are produced in a tube operating at 24.0 kV. After emerging from the tube, x rays with the minimum wavelength produced strike a target and undergo Compton scattering through an angle of 45.0°. a. What is the original x-ray wavelength? b. What is
> An x ray with a wavelength of 0.100 nm collides with an electron that is initially at rest. The x ray’s final wavelength is 0.110 nm. What is the final kinetic energy of the electron?
> The average life span in the United States is about 70 years. Does this mean that it is impossible for an average person to travel a distance greater than 70 light-years away from the earth? (A light-year is the distance light travels in a year.) Explain
> A certain very nearsighted person cannot focus on anything farther than 36.0 cm from the eye. Consider the simplified model of the eye described in Exercise 34.50. If the radius of curvature of the cornea is 0.75 cm when the eye is focusing on an object
> In one form of cataract surgery the person’s natural lens, which has become cloudy, is replaced by an artificial lens. The refracting properties of the replacement lens can be chosen so that the person’s eye focuses on distant objects. But there is no ac
> A camera with a 90-mm-focal-length lens is focused on an object 1.30 m from the lens. To refocus on an object 6.50 m from the lens, by how much must the distance between the lens and the sensor be changed? To refocus on the more distant object, is the le
> a. what is the minimum potential difference between the filament and the target of an x-ray tube if the tube is to produce x rays with a wavelength of 0.150 nm? b. What is the shortest wavelength produced in an x-ray tube operated at 30.0 kV?
> The smallest object we can resolve with our eye is limited by the size of the light receptor cells in the retina. In order for us to distinguish any detail in an object, its image cannot be any smaller than a single retinal cell. Although the size depend
> Protons are accelerated from rest by a potential difference of 4.00 kV and strike a metal target. If a proton produces one photon on impact, what is the minimum wavelength of the resulting x rays? How does your answer compare to the minimum wavelength if
> The cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is 15.0 kV, what are the shortest-wavelength x rays produced by the television?
> The photoelectric work function of potassium is 2.3 eV. If light that has a wavelength of 190 nm falls on potassium, find a. the stopping potential in volts; b. the kinetic energy, in electron volts, of the most energetic electrons ejected; c. the spe
> In a photoelectric-effect experiment, the photocurrent i for large positive values of VAC has the same value no matter what the light frequency f (provided that f is higher than the threshold frequency f0). Explain why.
> Human skin is relatively insensitive to visible light, but ultraviolet radiation can cause severe burns. Does this have anything to do with photon energies? Explain.
> A double-convex thin lens has surfaces with equal radii of curvature of magnitude 2.50 cm. Using this lens, you observe that it forms an image of a very distant tree at a distance of 1.87 cm from the lens. What is the index of refraction of the lens?
> Would you expect effects due to the photon nature of light to be generally more important at the low-frequency end of the electromagnetic spectrum (radio waves) or at the high-frequency end (x rays and gamma rays)? Why?
> According to the photon model, light carries its energy in packets called quanta or photons. Why then don’t we see a series of flashes when we look at things?
> There is a certain probability that a single electron may simultaneously absorb two identical photons from a high-intensity laser. How would such an occurrence affect the threshold frequency and the equations of Section 38.1? Explain.
> Some lasers emit light in pulses that are only 10-12 s in duration. The length of such a pulse is (3 * 108 m/s)(10-12 s) = 3 * 10-4 m = 0.3 mm. Can pulsed laser light be as monochromatic as light from a laser that emits a steady, continuous beam? Explain
> Why must engineers and scientists shield against x-ray production in high-voltage equipment?
> The cornea of the eye has a radius of curvature of approximately 0.50 cm, and the aqueous humor behind it has an index of refraction of 1.35. The thickness of the cornea itself is small enough that we shall neglect it. The depth of a typical human eye is
> Can Compton scattering occur with protons as well as electrons? For example, suppose a beam of x rays is directed at a target of liquid hydrogen. (Recall that the nucleus of hydrogen consists of a single proton.) Compared to Compton scattering with elect
> Figure P34.81 shows an object and its image formed by a thin lens. a. What is the focal length of the lens, and what type of lens (converging or diverging) is it? b. What is the height of the image? Is it real or virtual? Figure P34.81 Image Objec
> In a photoelectric-effect experiment, which of the following will increase the maximum kinetic energy of the photoelectrons? a. Use light of greater intensity; b. use light of higher frequency; c. use light of longer wavelength; d. use a metal surfac
> In a particle accelerator a proton moves with constant speed 0.750c in a circle of radius 628 m. What is the net force on the proton?
> A photographic slide is to the left of a lens. The lens projects an image of the slide onto a wall 6.00 m to the right of the slide. The image is 80.0 times the size of the slide. a. How far is the slide from the lens? b. Is the image erect or inverted
> One of the wavelengths of light emitted by hydrogen atoms under normal laboratory conditions is l = 656.3 nm, in the red portion of the electromagnetic spectrum. In the light emitted from a distant galaxy this same spectral line is observed to be Doppler
> a. You want to use a lens with a focal length of 35.0 cm to produce a real image of an object, with the height of the image twice the height of the object. What kind of lens do you need, and where should the object be placed? b. Suppose you want a virtu
> In certain radioactive beta decay processes, the beta particle (an electron) leaves the atomic nucleus with a speed of 99.95% the speed of light relative to the decaying nucleus. If this nucleus is moving at 75.00% the speed of light in the laboratory re
> What should be the index of refraction of a transparent sphere in order for paraxial rays from an infinitely distant object to be brought to a focus at the vertex of the surface opposite the point of incidence?
> A nuclear bomb containing 12.0 kg of plutonium explodes. The sum of the rest masses of the products of the explosion is less than the original rest mass by one part in 104. a. How much energy is released in the explosion? b. If the explosion takes pla
> In our universe, the rest energy of an electron is approximately 8.2 * 10-14 J. What would it be in the alternate universe? a. 8.2 * 10-8 J; b. 8.2 * 10-26 J; c. 8.2 * 10-2 J; d. 0.82 J.
> Scientists working with a particle accelerator determine that an unknown particle has a speed of 1.35 * 108 m/s and a momentum of 2.52 * 10-19 kg.m/s. From the curvature of the particle’s path in a magnetic field, they also deduce that it has a positive
> The Russian physicist P. A. Cerenkov discovered that a charged particle traveling in a solid with a speed exceeding the speed of light in that material radiates electromagnetic radiation. (This is analogous to the sonic boom produced by an aircraft movin
> Physicists and engineers from around the world came together to build the largest accelerator in the world, the Large Hadron Collider (LHC) at the CERN Laboratory in Geneva, Switzerland. The machine accelerates protons to high kinetic energies in an unde
> Inside a spaceship flying past the earth at three-fourths the speed of light, a pendulum is swinging. a. If each swing takes 1.80 s as measured by an astronaut performing an experiment inside the spaceship, how long will the swing take as measured by a
> A spaceship is traveling toward the earth from the space colony on Asteroid 1040A. The ship is at the halfway point of the trip, passing Mars at a speed of 0.9c relative to the Mars frame of reference. At the same instant, a passenger on the spaceship re
> A light bulb is 3.00 m from a wall. You are to use a concave mirror to project an image of the bulb on the wall, with the image 3.50 times the size of the object. How far should the mirror be from the wall? What should its radius of curvature be?
> A concave mirror is to form an image of the filament of a headlight lamp on a screen 8.00 m from the mirror. The filament is 6.00 mm tall, and the image is to be 24.0 cm tall. a. How far in front of the vertex of the mirror should the filament be placed
> Where must you place an object in front of a concave mirror with radius R so that the image is erect and 2 1 2 times the size of the object? Where is the image?
> A spacecraft of the Trade Federation flies past the planet Coruscant at a speed of 0.600c. A scientist on Coruscant measures the length of the moving spacecraft to be 74.0 m. The spacecraft later lands on Coruscant, and the same scientist measures the le
> a. Through what potential difference does an electron have to be accelerated, starting from rest, to achieve a speed of 0.980c? b. What is the kinetic energy of the electron at this speed? Express your answer in joules and in electron volts.
> A reflecting telescope (Fig. E34.63) is to be made by using a spherical mirror with a radius of curvature of 1.30 m and an eyepiece with a focal length of 1.10 cm. The final image is at infinity. a. What should the distance between the eyepiece and the
> The eyepiece of a refracting telescope (see Fig. 34.53) has a focal length of 9.00 cm. The distance between objective and eyepiece is 1.20 m, and the final image is at infinity. What is the angular magnification of the telescope? From Fig. 34.53 34
> When a particle meets its antiparticle, they annihilate each other and their mass is converted to light energy. The United States uses approximately 1.0 * 1020 J of energy per year. a. If all this energy came from a futuristic antimatter reactor, how mu
> What is the speed of a particle whose kinetic energy is equal to a. its rest energy and b. five times its rest energy?
> A person swimming 0.80 m below the surface of the water in a swimming pool looks at the diving board that is directly overhead and sees the image of the board that is formed by refraction at the surface of the water. This image is a height of 5.20 m abov
> The laws of optics also apply to electromagnetic waves invisible to the eye. A satellite TV dish is used to detect radio waves coming from orbiting satellites. Why is a curved reflecting surface (a “dish”) used? The dish is always concave, never convex;
> You want to view through a magnifier an insect that is 2.00 mm long. If the insect is to be at the focal point of the magnifier, what focal length will give the image of the insect an angular size of 0.032 radian?
> The focal length of a simple magnifier is 8.00 cm. Assume the magnifier is a thin lens placed very close to the eye. a. How far in front of the magnifier should an object be placed if the image is formed at the observer’s near point, 25.0 cm in front of
> A thin lens with a focal length of 6.00 cm is used as a simple magnifier. a. What angular magnification is obtainable with the lens if the object is at the focal point? b. When an object is examined through the lens, how close can it be brought to the
> An electron is acted upon by a force of 5.00 * 10-15 N due to an electric field. Find the acceleration this force produces in each case: a. The electron’s speed is 1.00 km/s. b. The electron’s speed is 2.50 * 108 m/s and the force is parallel to the ve
> How fast must a rocket travel relative to the earth so that time in the rocket “slows down” to half its rate as measured by earth based observers? Do present-day jet planes approach such speeds?
> a. At what speed is the momentum of a particle twice as great as the result obtained from the nonrelativistic expression mv? Express your answer in terms of the speed of light. b. A force is applied to a particle along its direction of motion. At what
> Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or image) is the same as the distance from the lens to that object (or image). A certain person can see distant objects well, but his near point is 45.0 cm from hi
> As you have seen, relativistic calculations usually involve the quantity γ. When γ is appreciably greater than 1, we must use relativistic formulas instead of Newtonian ones. For what speed v (in terms of c) is the value of γ a. 1.0% greater than 1; b.
> In a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the bending occurs at the cornea, whose vertex is 2.60 cm from the retina. What should be the radius of curvature of the cor
> A proton has momentum with magnitude p0 when its speed is 0.400c. In terms of p0, what is the magnitude of the proton’s momentum when its speed is doubled to 0.800c?
> A speck of dirt is embedded 3.50 cm below the surface of a sheet of ice (n = 1.309). What is its apparent depth when viewed at normal incidence?
> Consider the simple model of the zoom lens shown in Fig. 34.43a. The converging lens has focal length f1 = 12 cm, and the diverging lens has focal length f2 = -12 cm. The lenses are separated by 4 cm as shown in Fig. 34.43a. a. For a distant
> When a camera is focused, the lens is moved away from or toward the digital image sensor. If you take a picture of your friend, who is standing 3.90 m from the lens, using a camera with a lens with an 85-mm focal length, how far from the sensor is the le
> You wish to project the image of a slide on a screen 9.00 m from the lens of a slide projector. a. If the slide is placed 15.0 cm from the lens, what focal length lens is required? b. If the dimensions of the picture on a 35-mm color slide are 24 mm *
> A camera lens has a focal length of 200 mm. How far from the lens should the subject for the photo be if the lens is 20.4 cm from the sensor?
> Electromagnetic radiation from a star is observed with an earth-based telescope. The star is moving away from the earth at a speed of 0.520c. If the radiation has a frequency of 8.64 * 1014 Hz in the rest frame of the star, what is the frequency measured
> An observer in frame S′ is moving to the right (+x-direction) at speed u = 0.600c away from a stationary observer in frame S. The observer in S′ measures the speed v′ of a particle moving to the right away from her. What speed v does the observer in S me
> A meter stick moves past you at great speed. Its motion relative to you is parallel to its long axis. If you measure the length of the moving meter stick to be 1.00 ft (1 ft = 0.3048 m)—for example, by comparing it to a 1-foot ruler that is at rest relat
> A 1.20-cm-tall object is 50.0 cm to the left of a converging lens of focal length 40.0 cm. A second converging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. a. Find the loc
> An object is 16.0 cm to the left of a lens. The lens forms an image 36.0 cm to the right of the lens. a. What is the focal length of the lens? Is the lens converging or diverging? b. If the object is 8.00 mm tall, how tall is the image? Is it erect or
> Compute the kinetic energy of a proton (mass 1.67 * 10-27 kg) using both the nonrelativistic and relativistic expressions, and compute the ratio of the two results (relativistic divided by nonrelativistic) for speeds of a. 8.00 * 107 m/s and b. 2.85 *
> The thin glass shell shown in Fig. E34.15 has a spherical shape with a radius of curvature of 12.0 cm, and both of its surfaces can act as mirrors. A seed 3.30 mm high is placed 15.0 cm from the center of the mirror along the optic axis, as shown in the
> A converging lens with a focal length of 12.0 cm forms a virtual image 8.00 mm tall, 17.0 cm to the right of the lens. Determine the position and size of the object. Is the image erect or inverted? Are the object and image on the same side or opposite si
> For each thin lens shown in Fig. E34.37, calculate the location of the image of an object that is 18.0 cm to the left of the lens. The lens material has a refractive index of 1.50, and the radii of curvature shown are only the magnitudes. Figure E34
> A lensmaker wants to make a magnifying glass from glass that has an index of refraction n = 1.55 and a focal length of 20.0 cm. If the two surfaces of the lens are to have equal radii, what should that radius be?
> The theory of relativity sets an upper limit on the speed that a particle can have. Are there also limits on the energy and momentum of a particle? Explain.
> A converging lens with a focal length of 9.00 cm forms an image of a 4.00-mm-tall real object that is to the left of the lens. The image is 1.30 cm tall and erect. Where are the object and image located? Is the image real or virtual?
> You are holding an elliptical serving platter. How would you need to travel for the serving platter to appear round to another observer?
> When a monochromatic light source moves toward an observer, its wavelength appears to be shorter than the value measured when the source is at rest. Does this contradict the hypothesis that the speed of light is the same for all observers? Explain.
> A converging lens forms an image of an 8.00-mm-tall real object. The image is 12.0 cm to the left of the lens, 3.40 cm tall, and erect. What is the focal length of the lens? Where is the object located?
> A converging lens with a focal length of 70.0 cm forms an image of a 3.20-cm-tall real object that is to the left of the lens. The image is 4.50 cm tall and inverted. Where are the object and image located in relation to the lens? Is the image real or vi
> A converging meniscus lens (see Fig. 34.32a) with a refractive index of 1.52 has spherical surfaces whose radii are 7.00 cm and 4.00 cm. What is the position of the image if an object is placed 24.0 cm to the left of the lens? What is the magnification?
> An insect 3.75 mm tall is placed 22.5 cm to the left of a thin planoconvex lens. The left surface of this lens is flat, the right surface has a radius of curvature of magnitude 13.0 cm, and the index of refraction of the lens material is 1.70. a. Calcul
> A lens forms an image of an object. The object is 16.0 cm from the lens. The image is 12.0 cm from the lens on the same side as the object. a. What is the focal length of the lens? Is the lens converging or diverging? b. If the object is 8.50 mm tall,
> The speed of light relative to still water is 2.25 * 108 m/s. If the water is moving past us, the speed of light we measure depends on the speed of the water. Do these facts violate Einstein’s second postulate? Explain.
> The glass rod of Exercise 34.25 is immersed in a liquid. An object 14.0 cm from the vertex of the left end of the rod and on its axis is imaged at a point 9.00 cm from the vertex inside the liquid. What is the index of refraction of the liquid? From Exe
> A student asserts that a material particle must always have a speed slower than that of light, and a massless particle must always move at exactly the speed of light. Is she correct? If so, how do massless particles such as photons and neutrinos acquire
> The left end of a long glass rod 8.00 cm in diameter, with an index of refraction of 1.60, is ground and polished to a convex hemispherical surface with a radius of 4.00 cm. An object in the form of an arrow 1.50 mm tall, at right angles to the axis of t
> The glass rod of Exercise 34.22 is immersed in oil (n = 1.45). An object placed to the left of the rod on the rod’s axis is to be imaged 1.20 m inside the rod. How far from the left end of the rod must the object be located to form the image? From Exerc
> The left end of a long glass rod 6.00 cm in diameter has a convex hemispherical surface 3.00 cm in radius. The refractive index of the glass is 1.60. Determine the position of the image if an object is placed in air on the axis of the rod at the followin
> According to the discussion in Section 34.2, light rays are reversible. Are the formulas in the table in this chapter’s Summary still valid if object and image are interchanged? What does reversibility imply with respect to the forms of the various formu
> A person is lying on a diving board 3.00 m above the surface of the water in a swimming pool. She looks at a penny that is on the bottom of the pool directly below her. To her, the penny appears to be a distance of 7.00 m from her. What is the depth of t
> The diameter of Mars is 6794 km, and its minimum distance from the earth is 5.58 * 107 km. When Mars is at this distance, find the diameter of the image of Mars formed by a spherical, concave telescope mirror with a focal length of 1.75 m.
> For a concave spherical mirror that has focal length f = +18.0 cm, what is the distance of an object from the mirror’s vertex if the image is real and has the same height as the object?
> A transparent liquid fills a cylindrical tank to a depth of 3.60 m. There is air above the liquid. You look at normal incidence at a small pebble at the bottom of the tank. The apparent depth of the pebble below the liquid’s surface is 2.45 m. What is th
> Repeat Exercise 34.5 for the case in which the mirror is convex. From Exercise 34.5 An object 0.600 cm tall is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 22.0 cm. a. Draw a principal-ray diag
> The focal length of a simple lens depends on the color (wavelength) of light passing through it. Why? Is it possible for a lens to have a positive focal length for some colors and negative for others? Explain.
> For a convex spherical mirror that has focal length f = -12.0 cm, what is the distance of an object from the mirror’s vertex if the height of the image is half the height of the object?
