Question: A converging lens forms an image of

> 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

> 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

> 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 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?

> The bottom of the passenger-side mirror on your car notes, “Objects in mirror are closer than they appear.” Is this true? Why?

> A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an erect image with a magnification of 2.00 when the mirror is 1.25 cm from a tooth. (Treat this problem as though the object and image lie along a straight li

> A concave mirror has a radius of curvature of 34.0 cm. a. What is its focal length? b. If the mirror is immersed in water (refractive index 1.33), what is its focal length?

> You hold a spherical salad bowl 60 cm in front of your face with the bottom of the bowl facing you. The bowl is made of polished metal with a 35-cm radius of curvature. a. Where is the image of your 5.0-cm-tall nose located? b. What are the image’s siz

> A student claims that she can start a fire on a sunny day using just the sun’s rays and a concave mirror. How is this done? Is the concept of image relevant? Can she do the same thing with a convex mirror? Explain.

> A coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of 18.0 cm. Reflection from the surface of the shell forms an image of the 1.5-cm-tall coin that is 6.00 cm behind the glass shell. Where is the coin lo

> Repeat Exercise 34.24 for the case in which the end of the rod is ground to a concave hemispherical surface with radius 4.00 cm. From Exercise 34.24: The left end of a long glass rod 8.00 cm in diameter, with an index of refraction of 1.60, is ground an

> An object is 18.0 cm from the center of a spherical silvered-glass Christmas tree ornament 6.00 cm in diameter. What are the position and magnification of its image?

> When a room has mirrors on two opposite walls, an infinite series of reflections can be seen. Discuss this phenomenon in terms of images. Why do the distant images appear fainter?

> For what range of object positions does a concave spherical mirror form a real image? What about a convex spherical mirror?

> If a spherical mirror is immersed in water, does its focal length change? Explain.

> Explain why the focal length of a plane mirror is infinite, and explain what it means for the focal point to be at infinity.

> The image of a tree just covers the length of a plane mirror 4.00 cm tall when the mirror is held 35.0 cm from the eye. The tree is 28.0 m from the mirror. What is its height?

> For the situation shown in Fig. 34.3, is the image distance s′ positive or negative? Is the image real or virtual? Explain your answers. From Fig. 34.3: 34.3 Light rays from the object at point P are refracted at the plane interfac

> A photon of green light has a wavelength of 520 nm. Find the photon’s frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts.

> The negative muon has a charge equal to that of an electron but a mass that is 207 times as great. Consider a hydrogen like atom consisting of a proton and a muon. a. What is the reduced mass of the atom? b. What is the ground-level energy (in electron

> An atom with mass m emits a photon of wavelength λ. a. What is the recoil speed of the atom? b. What is the kinetic energy K of the recoiling atom? c. Find the ratio K/E, where E is the energy of the emitted photon. If this ratio is much less than uni

> You take a lens and mask it so that light can pass through only the bottom half of the lens. How does the image formed by the masked lens compare to the image formed before masking?

> As an amateur astronomer, you are studying the apparent brightness of stars. You know that a star’s apparent brightness depends on its distance from the earth and also on the fraction of its radiated energy that is in the visible region

> In the crystallography lab where you work, you are given a single crystal of an unknown substance to identify. To obtain one piece of information about the substance, you repeat the Davisson–Germer experiment to determine the spacing of

> For your work in a mass spectrometry lab, you are investigating the absorption spectrum of one-electron ions. To maintain the atoms in an ionized state, you hold them at low density in an ion trap, a device that uses a configuration of electric fields to

> Imagine another universe in which the value of Planck’s constant is 0.0663 J.s, but in which the physical laws and all other physical constants are the same as in our universe. In this universe, two physics students are playing catch. They are 12 m apart

> A particle with mass m moves in a potential energy U(x)= A x , where A is a positive constant. In a simplified picture, quarks (the constituents of protons, neutrons, and other particles, as will be described in Chapter 44) have a potential energy of int

> A certain atom has an energy state 3.50 eV above the ground state. When excited to this state, the atom remains for 2.0 µs, on average, before it emits a photon and returns to the ground state. a. What are the energy and wavelength of the photon? b. Wh

> For x rays with wavelength 0.0300 nm, the m = 1 intensity maximum for a crystal occurs when the angle θ in Fig. 39.2 is 35.8°. At what angle u does the m = 1 maximum occur when a beam of 4.50-keV electrons is used instead? Assume

> A certain atom has an energy level 2.58 eV above the ground level. Once excited to this level, the atom remains in this level for 1.64 * 10-7 s (on average) before emitting a photon and returning to the ground level. a. What is the energy of the photon

> If your wavelength were 1.0 m, you would undergo considerable diffraction in moving through a doorway. a. What must your speed be for you to have this wavelength? (Assume that your mass is 60.0 kg.) b. At the speed calculated in part (a), how many year

> The radii of atomic nuclei are of the order of 5.0 * 10-15 m. a. Estimate the minimum uncertainty in the momentum of an electron if it is confined within a nucleus. b. Take this uncertainty in momentum to be an estimate of the magnitude of the momentum

> You can’t see clearly underwater with the naked eye, but you can if you wear a face mask or goggles (with air between your eyes and the mask or goggles). Why is there a difference? Could you instead wear eyeglasses (with water between your eyes and the e

> The radii of atomic nuclei are of the order of 5.0 * 10-15 m. a. Estimate the minimum uncertainty in the momentum of a proton if it is confined within a nucleus. b. Take this uncertainty in momentum to be an estimate of the magnitude of the momentum. U

> a. A particle with mass m has kinetic energy equal to three times its rest energy. What is the de Broglie wavelength of this particle? (Hint: You must use the relativistic expressions for momentum and kinetic energy: E2 =(pc)2 +(mc2)2 and K = E - mc2.)

> An electron beam and a photon beam pass through identical slits. On a distant screen, the first dark fringe occurs at the same angle for both of the beams. The electron speeds are much slower than that of light. a. Express the energy of a photon in term

> Coherent light is passed through two narrow slits whose separation is 20.0 µm. The second-order bright fringe in the interference pattern is located at an angle of 0.0300 rad. If electrons are used instead of light, what must the kinetic energy (in elect