Question: A converging lens has a focal length

> (a) How many minutes does it take a photon to travel from the Sun to the Earth? (b) What is the energy in eV of a photon with a wavelength of 558 nm? (c) What is the wavelength of a photon with an energy of 1.00 eV?

> (a) Find a symbolic expression for the wavelength λ of a photon in terms of its energy E, Planck’s constant h, and the speed of light c. (b) What does the equation say about the wavelengths of higher - energy photons?

> Find the energy of (a) A photon having a frequency of 5.00 x 1017 Hz and (b) A photon having a wavelength of 3.00 x 102 nm. Express your answers in units of electron volts, noting that 1 eV = 1.60 x 10-19 J.

> (a) What is the energy in joules of an x-ray photon with wavelength 1.00 x 10-10 m? (b) Convert the energy to electron volts. (c) If more penetrating x - rays are desired, should the wavelength be increased or decreased? (d) Should the frequency be incre

> A virtual image is formed 20.0 cm from a concave mirror having a radius of curvature of 40.0 cm. (a) Find the position of the object. (b) What is the magnification of the mirror?

> To fit a contact lens to a patient’s eye, a kerato-meter can be used to measure the curvature of the cornea—the front surface of the eye. This instrument places an illuminated object of known size at a known distance p from the cornea, which then reflect

> Holding your hand at arm’s length, you can readily block direct sunlight from your eyes. Why can you not block sound from your ears this way?

> A convex spherical mirror, whose focal length has a magnitude of 15.0 cm, is to form an image 10.0 cm behind the mirror. (a) Where should the object be placed? (b) What is the magnification of the mirror?

> An object 10.0 cm tall is placed at the zero mark of a meter-stick. A spherical mirror located at some point on the meter-stick creates an image of the object that is upright, 4.00 cm tall, and located at the 42.0 - cm mark of the meter-stick. (a) Is the

> A glass sphere (n = 1.50) with a radius of 15.0 cm has a tiny air bubble 5.00 cm above its center. The sphere is viewed looking down along the extended radius containing the bubble. What is the apparent depth of the bubble below the surface of the sphere

> A certain Christmas tree ornament is a silver sphere having a diameter of 8.50 cm. (a) If the size of an image created by reflection in the ornament is three - fourth’s the reflected object’s actual size, determine the object’s location. (b) Use a princi

> The lens - maker’s equation applies to a lens immersed in a liquid if n in the equation is replaced by n1/n2. Here n1 refers to the refractive index of the lens material and n2 is that of the medium surrounding the lens. (a) A certain lens has focal leng

> An observer to the right of the mirror–lens combination shown in Figure P23.62 sees two real images that are the same size and in the same location. One image is upright, and the other is inverted. Both images are 1.50 times larger than

> The lens - maker’s equation for a lens with index n1 immersed in a medium with index n2 takes the form A thin diverging glass (index = 1.50) lens with R1 = -3.00 m and R2 = -6.00 m is surrounded by air. An arrow is placed 10.0 m to the

> Find the object distances (in terms of f) for a thin converging lens of focal length f if (a) The image is real and the image distance is four times the focal length and (b) The image is virtual and the absolute value of the image distance is three times

> A dentist uses a mirror to examine a tooth that is 1.00 cm in front of the mirror. The image of the tooth is formed 10.0 cm behind the mirror. Determine (a) The mirror’s radius of curvature and (b) The magnification of the image.

> Figure P23.59 shows a converging lens with radii R1 = 9.00 cm and R2 = -11.00 cm, in front of a concave spherical mirror of radius R = 8.00 cm. The focal points (F1 and F2) for the thin lens and the center of curvature (C) of the mirror are also shown. (

> A person spear fishing from a boat sees a stationary fish a few meters away in a direction about 30° below the horizontal. To spear the fish, and assuming the spear does not change direction when it enters the water, should the person (a) Aim above where

> A “floating strawberry” illusion can be produced by two parabolic mirrors, each with a focal length of 7.5 cm, facing each other so that their centers are 7.5 cm apart (Fig. P23.58). If a strawberry is placed on the bo

> An object 2.00 cm high is placed 40.0 cm to the left of a converging lens having a focal length of 30.0 cm. A diverging lens having a focal length of -20.0 cm is placed 110 cm to the right of the converging lens. (a) Determine the final position and magn

> Consider two thin lenses, one of focal length f1 and the other of focal length f2, placed in contact with each other, as shown in Figure P23.56. Apply the thin - lens equation to each of these lenses and combine the results to show that this combination

> To work this problem, use the fact that the image formed by the first surface becomes the object for the second surface. Figure P23.55 shows a piece of glass with index of refraction n = 1.50 surrounded by air. The ends are hemispheres with radii R1 = 2.

> Two rays traveling parallel to the principal axis strike a large plano - convex lens having a refractive index of 1.60 (Fig. P23.54). If the convex face is spherical, a ray near the edge does not pass through the focal point (spherical aberration occurs)

> A parallel beam of light enters a glass hemisphere perpendicular to the flat face, as shown in Figure P23.53. The radius of the hemisphere is R = 6.00 cm, and the index of refraction is n = 1.56. Determine the point at which the beam is focused. (Assume

> The object in Figure P23.52 is midway between the lens and the mirror, which are separated by a distance d = 25.0 cm. The magnitude of the mirror’s radius of curvature is 20.0 cm, and the lens has a focal length of -16.7 cm. (a) Conside

> The lens and the mirror in Figure P23.51 are separated by 1.00 m and have focal lengths of +80.0 cm and -50.0 cm, respectively. If an object is placed 1.00 m to the left of the lens, where will the final image be located? State whether the image is uprig

> A diverging lens (n = 1.50) is shaped like that in Figure 23.25c. The radius of the first surface is 15.0 cm, and that of the second surface is 10.0 cm. (a) Find the focal length of the lens. Determine the positions of the images for object distances of

> A periscope (Fig. P23.5) is useful for viewing objects that cannot be seen directly. It can be used in submarines and when watching golf matches or parades from behind a crowd of people. Suppose the object is a distance p1 from the upper mirror and the c

> Light can travel from air into water. Some possible paths for the light ray in the water are shown in Figure CQ22.14. Which path will the light most likely follow? (a) A (b) B (c) C (d) D (e) E Figure CQ22.14:

> The magnitudes of the radii of curvature are 32.5 cm and 42.5 cm for the two faces of a biconcave lens. The glass has index of refraction 1.53 for violet light and 1.51 for red light. For a very distant object, locate (a) The image formed by violet light

> A real object’s distance from a converging lens is five times the focal length. (a) Determine the location of the image q in terms of the focal length f. (b) Find the magnification of the image. (c) Is the image real or virtual? Is it upright or inverted

> An object placed 10.0 cm from a concave spherical mirror produces a real image 8.00 cm from the mirror. If the object is moved to a new position 20.0 cm from the mirror, what is the position of the image? Is the final image real or virtual?

> An object is placed 15.0 cm from a first converging lens of focal length 10.0 cm. A second converging lens with focal length 5.00 cm is placed 10.0 cm to the right of the first converging lens. (a) Find the position q1 of the image formed by the first co

> Lens L1 in Figure P23.45 has a focal length of 15.0 cm and is located a fixed distance in front of the film plane of a camera. Lens L2 has a focal length of 13.0 cm, and its distance d from the film plane can be varied from 5.00 cm to 10.0 cm. Determine

> Two converging lenses having focal lengths of f1 = 10.0 cm and f2 = 20.0 cm are placed d = 50.0 cm apart, as shown in Figure P23.44. The final image is to be located between the lenses, at the position x = 31.0 cm indicated. (a) How far to the left of th

> A 1.00 - cm-high object is placed 4.00 cm to the left of a converging lens of focal length 8.00 cm. A diverging lens of focal length -16.00 cm is 6.00 cm to the right of the converging lens. Find the position and height of the final image. Is the image i

> A converging lens is placed at x = 0, a distance d = 10.0 cm to the left of a diverging lens as in Figure P23.42 (where FC and FD locate the focal points for the converging and the diverging lens, respectively). An object is located at x = -2.00 cm to th

> Two converging lenses, each of focal length 15.0 cm, are placed 40.0 cm apart, and an object is placed 30.0 cm in front of the first lens. Where is the final image formed, and what is the magnification of the system?

> (a) Use the thin - lens equation to derive an expression for q in terms of f and p. (b) Prove that for a real object and a diverging lens, the image must always be virtual. Hint: Set f = -|f| and show that q must be less than zero under the given conditi

> Light from an object passes through a lens and forms a visible image on a screen. If the screen is removed, would you be able to see the image (a) If you remained in your present position and (b) If you could look at the lens along its axis, beyond the o

> In a church choir loft, two parallel walls are 5.30 m apart. The singers stand against the north wall. The organist faces the south wall, sitting 0.800 m away from it. So that she can see the choir, a flat mirror 0.600 m wide is mounted on the south wall

> A converging lens is placed 30.0 cm to the right of a diverging lens of focal length 10.0 cm. A beam of parallel light enters the diverging lens from the left, and the beam is again parallel when it emerges from the converging lens. Calculate the focal l

> An object is located 20.0 cm to the left of a diverging lens having a focal length f = -32.0 cm. Determine (a) The location and (b) The magnification of the image. (c) Construct a ray diagram for this arrangement.

> An object of height 8.00 cm is placed 25.0 cm to the left of a converging lens with a focal length of 10.0 cm. Determine (a) The image location, (b) The magnification, and (c) The image height. (d) Is the image real or virtual? (e) Is the image upright o

> The nickel’s image in Figure P23.36 has twice the diameter of the nickel when the lens is 2.84 cm from the nickel. Determine the focal length of the lens. Figure P23.36:

> A transparent photographic slide is placed in front of a converging lens with a focal length of 2.44 cm. An image of the slide is formed 12.9 cm from the slide. How far is the lens from the slide if the image is (a) Real? (b) Virtual?

> A diverging lens has a focal length of 20.0 cm. Use graph paper to construct accurate ray diagrams for object distances of (a) 40.0 cm and (b) 10.0 cm. In each case, determine the location of the image from the diagram and the image magnification, and st

> A diverging lens has a focal length of magnitude 20.0 cm. (a) Locate the images for object distances of (i) 40.0 cm, (ii) 20.0 cm, and (iii) 10.0 cm. For each case, state whether the image is (b) Real or virtual and (c) Upright or inverted. (d) For each

> An object is placed 20.0 cm from a concave spherical mirror having a focal length of magnitude 40.0 cm. (a) Use graph paper to construct an accurate ray diagram for this situation. (b) From your ray diagram, determine the location of the image. (c) What

> Try this simple experiment on your own. Take two opaque cups, place a coin at the bottom of each cup near the edge, and fill one cup with water. Next, view the cups at some angle from the side so that the coin in water is just visible as shown on the lef

> A thin plastic lens with index of refraction n = 1.67 has radii of curvature given by R1 = 212.0 cm and R2 = 40.0 cm. Determine (a) The focal length of the lens, (b) Whether the lens is converging or diverging, and the image distances for object distance

> A person walks into a room that has, on opposite walls, two plane mirrors producing multiple images. Find the distances from the person to the first three images seen in the left - hand mirror when the person is 5.00 ft from the mirror on the left wall a

> A contact lens is made of plastic with an index of refraction of 1.50. The lens has an outer radius of curvature of +2.00 cm and an inner radius of curvature of +2.50 cm. What is the focal length of the lens?

> Figure P23.28 shows a curved surface separating a material with index of refraction n1 from a material with index n2. The surface forms an image I of object O. The ray shown in red passes through the surface along a radial line. Its angles of incidence a

> A jellyfish is floating in a water - filled aquarium 1.00 m behind a flat pane of glass 6.00 cm thick and having an index of refraction of 1.50. (a) Where is the image of the jellyfish located? (b) Repeat the problem when the glass is so thin that its th

> A man inside a spherical diving bell watches a fish through a window in the bell, as in Figure P23.26. If the diving bell has radius R = 1.75 m and the fish is a distance p = 1.00 m from the window, calculate (a) The image distance and (b) The magnificat

> A transparent sphere of unknown composition is observed to form an image of the Sun on its surface opposite the Sun. What is the refractive index of the sphere material?

> The top of a swimming pool is at ground level. If the pool is 2.00 m deep, how far below ground level does the bottom of the pool appear to be located when (a) The pool is completely filled with water? (b) When it is filled halfway with water?

> A paperweight is made of a solid glass hemisphere with index of refraction 1.50. The radius of the circular cross section is 4.0 cm. The hemisphere is placed on its flat surface, with the center directly over a 2.5 - mm - long line drawn on a sheet of pa

> A goldfish is swimming inside a spherical bowl of water having an index of refraction n = 1.333. Suppose the goldfish is p = 10.0 cm from the wall of a bowl of radius |R| = 15.0 cm, as in Figure P23.22. Neglecting the refraction of light caused by the wa

> If a cylinder of solid glass or clear plastic is placed above the words LEAD OXIDE and viewed from the side, as shown in Figure CQ23.10, the word LEAD appears inverted, but the word OXIDE does not. Explain. Figure CQ23.10:

> A cubical block of ice 50.0 cm on an edge is placed on a level floor over a speck of dust. Locate the image of the speck, when viewed from directly above, if the index of refraction of ice is 1.309.

> A ball is dropped from rest 3.00 m directly above the vertex of a concave mirror having a radius of 1.00 m and lying in a horizontal plane. (a) Describe the motion of the ball’s image in the mirror. (b) At what time do the ball and its image coincide?

> Suppose you stand in front of a flat mirror and focus a camera on your image. If the camera is in focus when set for a distance of 3.00 m, how far are you standing from the mirror?

> A spherical mirror is to be used to form an image, five times as tall as an object, on a screen positioned 5.0 m from the mirror. (a) Describe the type of mirror required. (b) Where should the object be positioned relative to the mirror?

> The mirror of a solar cooker focuses the Sun’s rays on a point 25.0 cm in front of the mirror. What is the mirror’s radius?

> At an intersection of hospital hallways, a convex spherical mirror is mounted high on a wall to help people avoid collisions. The magnitude of the mirror’s radius of curvature is 0.550 m. (a) Locate the image of a patient located 10.0 m from the mirror.

> When an object is placed 40.0 cm in front of a convex spherical mirror, a virtual image forms 15.0 cm behind the mirror. Determine (a) The mirror’s focal length and (b) The magnification.

> A man standing 1.52 m in front of a shaving mirror produces an inverted image 18.0 cm in front of it. How close to the mirror should he stand if he wants to form an upright image of his chin that is twice the chin’s actual size?

> A 1.80 - m - tall person stands 9.00 m in front of a large, concave spherical mirror having a radius of curvature of 5.00 m. Determine (a) The mirror’s focal length, (b) The image distance, and (c) The magnification. (d) Is the image real or virtual? (e)

> A concave makeup mirror is designed so that a person 25 cm in front of it sees an upright image magnified by a factor of two. What is the radius of curvature of the mirror?

> Light in medium A undergoes a total internal reflection as it reaches the interface with medium B. Which of the following statements must be true (choose all that apply)? (a) nB < nA (b) nB > nA (c) All light rays that undergo a total internal reflection

> During the Apollo XI Moon landing, a retro-reflecting panel was erected on the Moon’s surface. The speed of light can be found by measuring the time it takes a laser beam to travel from Earth, reflect from the panel, and return to Earth. If this interval

> Babies weighing 5.5 pounds or less at birth are said to have low birth weights, which can be dangerous. Full-term birth weights for single babies (not twins or triplets or other multiple births) are Normally distributed with a mean of 7.5 pounds and a st

> Support for the legalization of marijuana has continued to grow among Americans. A 2017 Gallup poll found that 64% of Americans now say that marijuana use should be legal. Suppose a random sample of 150 Americans is selected. a. Find the probability that

> According to a Pew poll, 67% of Americans believe that jury duty is part of good citizenship. Suppose 500 Americans are randomly selected. a. Find the probability that more than half believe that jury duty is part of good citizenship. b. In a group of 50

> According to the Pew Research Center, 73% of Americans have read at least one book during the past year. Suppose 200 Americans are randomly selected. a. Find the probability that more than 150 have read at least one book during the past year. b. Find the

> Voice-controlled video assistants are being incorporated into a wide variety of consumer products, including smartphones, tablets, and stand-alone devices such as the Amazon Echo or Google Home. A Pew Research poll found that 46% of Americans reported us

> Ignaz Semmelweiss (1818–1865) was the doctor who first encouraged other doctors to wash their hands with disinfectant before touching patients. Before the new procedure was established, the rate of infection at Dr. Semmelweiss’s hospital was about 10%. A

> According to studies done in the 1940s, 29% of people dream in color. Assuming this is still true, find the probability that in a random sample of 200 independent people, 50% or more will report dreaming in color. Start by checking the conditions to see

> The distribution of spring high temperatures in Los Angeles is approximately Normal, with a mean of 75 degrees and a standard deviation of 2.5 degrees. a. What is the probability that the high temperature is less than 70 degrees in Los Angeles on a day i

> Systolic blood pressures are approximately Normal with a mean of 120 and a standard deviation of 8. a. What percentage of people have a systolic blood pressure above 130? b. What is the range of systolic blood pressures for the middle 60% of the populati

> A Gallup poll conducted in 2017 found that 648 out of 1011 people surveyed supported same-sex marriage. An NBC News/Wall Street Journal poll conducted the same year surveyed 1200 people and found 720 supported same-sex marriage. a. Find both sample propo

> a. From your answers in Exercise 6.7, find the probability of getting 0 ups, 1 up, or 2 ups when flipping two thumbtacks, and report the distribution in a table. b. Make a probability distribution graph of this.

> Medical school graduates who want to become doctors must pass the U.S. Medical Licensing Exam (USMLE). Scores on this exam are approximately Normal with a mean of 225 and a standard deviation of 15. Use the Empirical Rule to answer these questions. a. Ro

> In a 2018 survey conducted by Northeastern University, 28% of working adults with education levels less than a bachelor’s degree worried that their job would be eliminated due to new technology or automation. This was based on a 95% confidence interval w

> According to the Bureau of Labor Statistics, 10.1% of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that

> In the Pew Research social media survey, television viewers were asked if it would be very hard to give up watching television. In 2002, 38% responded yes. In 2018, 31% said it would be very hard to give up watching television. a. Assume that both polls

> According to a Gallup poll, 45% of Americans actively seek out organic foods when shopping. Suppose a random sample of 500 Americans is selected and the proportion who actively seek out organic foods is recorded. a. What value should we expect for the sa

> In a game of chance, players draw one cube out of a bag containing 3 red cubes, 2 white cubes, and 1 blue cube. The player wins $5 if a blue cube is drawn, the player loses $2 if a white cube is drawn. If a red cube is drawn, the player does not win or l

> Pew Research conducts polls on social media use. In 2012, 66% of those surveyed reported using Facebook. In 2018, 76% reported using Facebook. a. Assume that both polls used samples of 100 people. Do a test to see whether the proportion of people who rep

> A student was tested to see if he could tell the difference between two different brands of cola. He was presented with 20 samples of cola and correctly identified 12 of the samples. Since he was correct 60 percent of the time, can we conclude that he ca

> In Toronto, Canada, 55% of people pass the drivers’ road test. Suppose that every day, 100 people independently take the test. a. What is the number of people who are expected to pass? b. What is the standard deviation for the number expected to pass? c.

> The 2017 Chapman University Survey of American Fears asked a random sample of 1207 adults Americans if they believed that aliens had come to Earth in modern times, and 26% responded yes. a. What is the standard error for this estimate of the percentage o

> Make a list of all possible outcomes for gender when a family has two children. Assume that the probability of having a boy is 0.50 and the probability of having a girl is also 0.50. Find the probability of each outcome in your list.

> A random sample of likely voters showed that 55% planned to vote for Candidate X, with a margin of error of 2 percentage points and with a 95% confidence level. a. Use a carefully worded sentence to report the 95% confidence interval for the percentage o

> According to a study by the Colorado Department of Transportation, 25% of Colorado drivers admit to using their cell phones to send texts while driving. Suppose two Colorado drivers are randomly selected. a. If the driver texts while driving, record a T.

> According to a report by the American Academy of Orthopedic Surgeons, 29% of pedestrians admit to texting while walking. Suppose two pedestrians are randomly selected. a. If the pedestrian texts while walking, record a T. If not, record an N. List all po

> A Gallup poll asked a random samples of Americans in 2016 and 2018 if they were satisfied with the quality of the environment. In 2016, 543 were satisfied with the quality of the environment and 440 were dissatisfied. In 2018, 461 were satisfied and 532

> A Gallup poll asked college students in 2016 and again in 2017 whether they believed the First Amendment guarantee of freedom of the press was secure or threatened in the country today. In 2016, 2489 out of 3072 students surveyed said that freedom o