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physics
modern physics

Physics 10th edition David Young, Shane Stadler - Solutions

A convex mirror has a focal length of -27.0 cm. Find the magnification produced by the mirror when the object distance is 9.0 cm and 18.0 cm.
A concave mirror has a focal length of 12 cm. This mirror forms an image located 36 cm in front of the mirror. What is the magnification of the mirror?
An object is located 14.0 cm in front of a convex mirror, the image being 7.00 cm behind the mirror. A second object, twice as tall as the first one, is placed in front of the mirror, but at a different location. The image of this second object has the same height as the other image. How far in
A dentist's mirror is placed 2.0 cm from a tooth. The enlarged image is located 5.6 cm behind the mirror.(a) What kind of mirror (plane, concave, or convex) is being used?(b) Determine the focal length of the mirror.(c) What is the magnification?(d) How is the image oriented relative to the object?
A tall tree is growing across a river from you. You would like to know the distance between yourself and the tree, as well as its height, but are unable to make the measurements directly. However, by using a mirror to form an image of the tree and then measuring the image distance and the image
A spherical mirror is polished on both sides. When the concave side is used as a mirror, the magnification is +2.0. What is the magnification when the convex side is used as a mirror, the object remaining the same distance from the mirror?
Consult Multiple-Concept Example 7 to see a model for solving this type of problem. A concave makeup mirror is designed so the virtual image it produces is twice the size of the object when the distance between the object and the mirror is 14 cm. What is the radius of curvature of the mirror?
A concave mirror has a focal length of 30.0 cm. The distance between an object and its image is 45.0 cm. Find the object and image distances, assuming that (a) The object lies beyond the center of curvature and (b) The object lies between the focal point and the mirror.
An object is placed in front of a convex mirror. Draw the convex mirror (radius of curvature = 15 cm) to scale, and place the object 25 cm in front of it. Make the object height 4 cm. Using a ray diagram, locate the image and measure its height. Now move the object closer to the mirror, so the
A concave mirror has a focal length of 42 cm. The image formed by this mirror is 97 cm in front of the mirror. What is the object distance?
Review Conceptual Example 1 before attempting this problem. A person whose eyes are 1.70 m above the floor stands in front of a plane mirror. The top of her head is 0.12 m above her eyes. (a) What is the height of the shortest mirror in which she can see her entire image? (b) How far above the
Suppose that you are walking perpendicularly with a velocity of +0.90 m/s toward a stationary plane mirror. What is the velocity of your image relative to you? The direction in which you walk is the positive direction.
A drop of water on a countertop reflects light from a flower held 3.0 cm directly above it. The flower's diameter is 2.0 cm, and the diameter of the flower's image is 0.10 cm. What is the focal length of the water drop, assuming that it may be treated as a convex spherical mirror?
Identical objects are located at the same distance from two spherical mirrors, A and B. The magnifications produced by the mirrors are mA = 4.0 and mB = 2.0. Find the ratio fA/fB of the focal lengths of the mirrors.
You walk at an angle of Î¸ = 50.0° toward a plane mirror, as in the drawing. Your walking velocity has a magnitude of 0.90 m/s. What is the velocity of your image relative to you (magnitude and direction)?
A candle is placed 15.0 cm in front of a convex mirror. When the convex mirror is replaced with a plane mirror, the image moves 7.0 cm farther away from the mirror. Find the focal length of the convex mirror.
A man holds a double-sided spherical mirror so that he is looking directly into its convex surface, 45 cm from his face. The magnification of the image of his face is +0.20. What will be the image distance when he reverses the mirror (looking into its concave surface), maintaining the same distance
An object is located 7.0 cm in front of a mirror. The virtual image is located 4.5 cm away from the mirror and is smaller than the object. Concepts: (i) Based solely on the fact that the image is virtual, is the mirror concave or convex, or is either type possible? (ii) The image is smaller than
The radius of curvature of a mirror is 24 cm. A diamond ring is placed in front of this mirror. The image is twice the size of the ring. Concepts: (i) Is the mirror concave or convex, or is either type possible? (ii) How many places are there in front of a concave mirror where the ring can be
The drawing shows a laser beam shining on a plane mirror that is perpendicular to the floor. The beam's angle of incidence is 33.0°. The beam emerges from the laser at a point that is 1.10 m from the mirror and 1.80 m above the floor. After reflection, how far from the base of the mirror does the
Review Conceptual Example 1 as an aid in understanding this problem. The drawings show two arrows, A and B, that are located in front of a plane mirror. A person at point P is viewing the image of each arrow. Which images can be seen in their entirety? Determine your answers by drawing a ray from
A small mirror is attached to a vertical wall, and it hangs a distance of 1.80 m above the floor. The mirror is facing due east, and a ray of sunlight strikes the mirror early in the morning and then again later in the morning. The incident and reflected rays lie in a plane that is perpendicular to
In an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 50.0 km due north. A detector is placed 117 m due east of the laser. The mirror is to be aligned so that light from the laser reflects into the detector. (a) When properly aligned, what angle should the
The drawings show two examples in which a ray of light is refracted at the interface between two liquids. In each example the incident ray is in liquid A and strikes the interface at the same angle of incidence. In one case the ray is refracted into liquid B, and in the other it is refracted into
An object is situated to the left of a lens. A ray of light from the object is close to and parallel to the principal axis of the lens. The ray passes through the lens. Which one of the following statements is true? (a) The ray crosses the principal axis at a distance from the lens equal to twice
What type of single lens produces a virtual image that is inverted with respect to the object? (a) Both a converging and a diverging lens can produce such an image. (b) Neither a converging nor a diverging lens produces such an image. (c) A converging lens (d) A diverging lens
Here are a number of statements concerning the refractive power of lenses. A. A positive refractive power means that a lens always creates an image that is larger than the object. B. Two lenses with the same refractive power have the same focal lengths. C. A lens with a positive refractive power is
The table lists the angular sizes in radians and distances from the eye for three objects, A, B, and C. In each case the angular size is small. Object ________Angular Size (in Radians) ________Distance of Object from Eye A ................................... θ
A coin is resting on the bottom of an empty container. The container is then filled to the brim three times, each time with a different liquid. An observer (in air) is directly above the coin and looks down at it. With liquid A in the container, the apparent depth of the coin is 7 cm, with liquid B
The refractive index of material A is greater than the refractive index of material B. A ray of light is incident on the interface between these two materials in a number of ways, as the drawings illustrate. The dashed lines denote the normals to the interfaces. Which one of the drawings shows a $The refractive index of material A is greater than the$
The drawing shows a rectangular block of glass (n = 1.52) surrounded by air. A ray of light starts out within the glass and travels toward point A, where some or all of it is reflected toward point B. At which points does some of the light escape the glass?(a) Only at point A(b) Only at point B(c)
The indices of refraction for red, green, and violet light in glass are nred = 1.520, ngreen = 1.526, and nviolet = 1.538. When a ray of light passes through a transparent slab of glass, the emergent ray is parallel to the incident ray, but can be displaced relative to it. For light passing through
A layer of oil (n = 1.45) fl oats on an unknown liquid. A ray of light originates in the oil and passes into the unknown liquid. The angle of incidence is 64.0°, and the angle of refraction is 53.0°. What is the index of refraction of the unknown liquid?
An amateur astronomer decides to build a telescope from a discarded pair of eyeglasses. One of the lenses has a refractive power of 11 diopters, and the other has a refractive power of 1.3 diopters. (a) Which lens should be the objective? (b) How far apart should the lenses be separated? (c) What
The telescope at Yerkes Observatory in Wisconsin has an objective whose focal length is 19.4 m. Its eyepiece has a focal length of 10.0 cm. (a) What is the angular magnification of the telescope? (b) If the telescope is used to look at a lunar crater whose diameter is 1500 m, what is the size of
The lengths of three telescopes are LA = 455 mm, LB = 615 mm, and LC = 824 mm. The focal length of the eyepiece for each telescope is 3.00 mm. Find the angular magnification of each telescope.
A refracting telescope has an angular magnification of - 83.00. The length of the barrel is 1.500 m. What are the focal lengths of (a) The objective (b) The eyepiece?
An astronomical telescope is being used to examine a relatively close object that is only 114.00 m away from the objective of the telescope. The objective and eyepiece have focal lengths of 1.500 and 0.070 m, respectively. Noting that the expression M ≈ - 2fo / fe is no longer applicable because
A camera uses a lens with a focal length of 0.0500 m and can take clear pictures of objects no closer to the lens than 0.500 m. For closer objects the camera records only blurred images. However, the camera could be used to record a clear image of an object located 0.200 m from the lens, if the
As an aid in understanding this problem, refer to Conceptual Example 4. A swimmer, who is looking up from under the water, sees a diving board directly above at an apparent height of 4.0 m above the water. What is the actual height of the diving board above the water?
A person working on the transmission of a car accidentally drops a bolt into a tray of oil. The oil is 5.00 cm deep. The bolt appears to be 3.40 cm beneath the surface of the oil, when viewed from directly above. What is the index of refraction of the oil?
A camper is trying to start a fire by focusing sunlight onto a piece of paper. The diameter of the sun is 1.39 × 109 m, and its mean distance from the earth is 1.50 × 1011 m. The camper is using a converging lens whose focal length is 10.0 cm. (a) What is the area of the sun's image on the
A dentist is examining a dental filling in a patient's tooth. The diameter of the filling is 2.4 mm, and the dentist's near point is 17.0 cm. To get a better look at the filling, the dentist dons safety goggles fitted with magnifying glasses (f = 6.0 cm). Find the greatest possible angular size (in
A farsighted person has a near point that is 67.0 cm from her eyes. She wears eyeglasses that are designed to enable her to read a newspaper held at a distance of 25.0 cm from her eyes. Find the focal length of the eyeglasses, assuming that they are worn (a) 2.2 cm from the eyes (b) 3.3 cm from
Red light (n = 1.520) and violet light (n = 1.538) traveling in air are incident on a slab of crown glass. Both colors enter the glass at the same angle of refraction. The red light has an angle of incidence of 30.00°. What is the angle of incidence of the violet light?
A converging lens (f = 12.0 cm) is held 8.00 cm in front of a newspaper that has a print size with a height of 2.00 mm. Find (a) The image distance (in cm) (b) The height (in mm) of the magnified print.
To focus a camera on objects at different distances, the converging lens is moved toward or away from the image sensor, so a sharp image always falls on the sensor. A camera with a telephoto lens (f = 200.0 mm) is to be focused on an object located first at a distance of 3.5 m and then at 50.0 m.
A narrow beam of light from a laser travels through air (n = 1.00) and strikes point A on the surface of the water (n = 1.33) in a lake. The angle of incidence is 55°. The depth of the lake is 3.0 m. On the fl at lake-bottom is point B, directly below point A. (a) If refraction did not occur, how
A stamp collector is viewing a stamp with a magnifying glass held next to her eye. Her near point is 25 cm from her eye. (a) What is the refractive power of a magnifying glass that has an angular magnification of 6.0 when the image of the stamp is located at the near point? (b) What is the
An object is in front of a converging lens (f = 0.30 m).The magnification of the lens is m = 4.0.(a) Relative to the lens, in what direction should the object be moved so that the magnification changes to m = - 4.0?(b) Through what distance should the object be moved?
A filmmaker wants to achieve an interesting visual effect by filming a scene through a converging lens with a focal length of 50.0 m. The lens is placed between the camera and a horse, which canters toward the camera at a constant speed of 7.0 m/s. The camera starts rolling when the horse is 40.0 m
Bill is farsighted and has a near point located 125 cm from his eyes. Anne is also farsighted, but her near point is 75.0 cm from her eyes. Both have glasses that correct their vision to a normal near point (25.0 cm from the eyes), and both wear the glasses 2.0 cm from the eyes. Relative to the
A ray of light is incident on a glass-water interface at the critical angle θc¸ as the figure illustrates. The reflected light then passes through a liquid (immiscible with water) and into air. The indices of refraction for the four substances are given in the drawing. Concepts:(i) What
In the figure, a converging lens (f1 = 120.0 cm) and a diverging lens (f2 = 215.0 cm) are separated by a distance of 10.0 cm. An object with a height of ho1 = 5.00 mm is placed at a distance of do1 = 45.0 cm to the left of the first (converging) lens. Concepts: (i) Is the image produced by the
The drawing shows a ray of light traveling through three materials whose surfaces are parallel to each other. The refracted rays (but not the reflected rays) are shown as the light passes through each material. A ray of light strikes the a-b interface at a 50.0° angle of incidence. The index of
Light in a vacuum is incident on a transparent glass slab. The angle of incidence is 35.0°. The slab is then immersed in a pool of liquid. When the angle of incidence for the light striking the slab is 20.3°, the angle of refraction for the light entering the slab is the same as when the slab was
A stone held just beneath the surface of a swimming pool is released and sinks to the bottom at a constant speed of 0.48 m/s. What is the apparent speed of the stone, as viewed from directly above by an observer who is in air?
In an ultra-low-temperature experiment, a collection of sodium atoms enter a special state called a Bose-Einstein condensate in which the index of refraction is 1.57 × 107. What is the speed of light in this condensate?
The drawing shows a rectangular block of glass (n = 1.52) surrounded by liquid carbon disulfide (n = 1.63). A ray of light is incident on the glass at point A with a 30.0° angle of incidence. At what angle of refraction does the ray leave the glass at point B?
The back wall of a home aquarium is a mirror that is a distance of 40.0 cm away from the front wall. The walls of the tank are negligibly thin. A fish, swimming midway between the front and back walls, is being viewed by a person looking through the front wall. The index of refraction of air is
Refer to Figure 26.4b and assume the observer is nearly above the submerged object. For this situation, derive the expression for the apparent depth: d' = d(n2/n1), Equation 26.3.Figure 26.4b
A paperweight consists of a 9.00-cm-thick plastic cube. Within the plastic a thin sheet of paper is embedded, parallel to opposite faces of the cube. On each side of the paper is printed a different joke that can be read by looking perpendicularly straight into the cube. When read from one side
A small logo is embedded in a thick block of crown glass (n = 1.52), 3.20 cm beneath the top surface of the glass. The block is put under water, so there is 1.50 cm of water above the top surface of the block. The logo is viewed from directly above by an observer in air. How far beneath the top
For the liquids in Table 26.1, determine the smallest critical angle for light that originates in one of them and travels toward the air-liquid interface.
A point source of light is submerged 2.2 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have?
A ray of light is traveling in glass and strikes a glass-liquid interface. The angle of incidence is 58.0°, and the index of refraction of glass is n = 1.50. (a) What must be the index of refraction of the liquid so that the direction of the light entering the liquid is not changed? (b) What is
The refractive indices of materials A and B have a ratio of nA/nB = 1.33. The speed of light in material A is 1.25 × 108 m/s. What is the speed of light in material B?
The drawing shows three layers of different materials, with air above and below the layers. The interfaces between the layers are parallel. The index of refraction of each layer is given in the drawing. Identical rays of light are sent into the layers, and light zigzags through each layer,
The drawing shows a crown glass slab with a rectangular cross section. As illustrated, a laser beam strikes the upper surface at an angle of 60.0°. After reflecting from the upper surface, the beam reflects from the side and bottom surfaces.(a) If the glass is surrounded by air, determine where
The drawing shows three materials, a, b, and c. A ray of light strikes the a-b interface at an angle that just barely exceeds its critical angle of 40.0°. The reflected ray then strikes the a-c interface at an angle of incidence that just barely exceeds its critical angle (which is not 40.0°).
The drawing shows a ray of light traveling from point A to point B, a distance of 4.60 m in a material that has an index of refraction n1. At point B, the light encounters a different substance whose index of refraction is n2 = 1.63. The light strikes the interface at the critical angle of θc =
A layer of liquid B fl oats on liquid A. A ray of light begins in liquid A and undergoes total internal reflection at the interface between the liquids when the angle of incidence exceeds 36.5°. When liquid B is replaced with liquid C, total internal reflection occurs for angles of incidence
For light that originates within a liquid and strikes the liquid-air interface, the critical angle is 39°. What is Brewster's angle for this light?
Light is incident from air onto the surface of a liquid. The angle of incidence is 53.0°, and the angle of refraction is 34.0°. At what angle of incidence would the reflected light be 100% polarized?
The frequency of a light wave is the same when the light travels in ethyl alcohol or in carbon disulfide. Find the ratio of the wavelength of the light in ethyl alcohol to that in carbon disulfide.
A laser is mounted in air, at a distance of 0.476 m above the edge of a large, horizontal pane of crown glass, as shown in the drawing. The laser is aimed at the glass in such a way that the reflected beam is 100% polarized. Determine the distance d between the edge of the pane and the point at
In Figure 26.17 light strikes the surface of a liquid at the Brewster angle, and the reflected light is 100% polarized. Suppose the light originates in air and the angle of refraction in Figure 26.17 is θ2 = 33.7°. Find the value of the index of refraction n2 of the liquid.Figure 26.17
A ray of sunlight is passing from diamond into crown glass; the angle of incidence is 35.00°. The indices of refraction for the blue and red components of the ray are: blue (ndiamond = 2.444, ncrown glass = 1.531), and red (ndiamond = 2.410, ncrown glass = 1.520). Determine the angle between the
Violet light and red light travel through air and strike a block of plastic at the same angle of incidence. The angle of refraction is 30.400° for the violet light and 31.200° for the red light. The index of refraction for violet light in plastic is greater than that for red light by 0.0400.
Horizontal rays of red light (λ = 660 nm, in vacuum) and violet light (λ = 410 nm, in vacuum) are incident on the flint-glass prism shown in the drawing. The indices of refraction for the red and violet light are nred = 1.662 and nviolet = 1.698. The prism is surrounded by air. What is the angle
The drawing shows a horizontal ray of white light incident perpendicularly on the vertical face of a prism (crown glass). The light enters the prism, and part of it undergoes refraction at the slanted face and emerges into the surrounding material. The rest of it is totally internally reflected and
The owner of a van installs a rear-window lens that has a focal length of -0.300 m. When the owner looks out through the lens at a person standing directly behind the van, the person appears to be just 0.240 m from the back of the van, and appears to be 0.34 m tall. (a) How far from the van is the
A camera is supplied with two interchangeable lenses, whose focal lengths are 35.0 and 150.0 mm. A woman whose height is 1.60 m stands 9.00 m in front of the camera. What is the height (including sign) of her image on the image sensor, as produced by (a) The 35.0-mm lens and (b) The 150.0-mm lens?
When a diverging lens is held 13.0 cm above a line of print, as in Figure 26.29, the image is 5.0 cm beneath the lens.(a) Is the image real or virtual?(b) What is the focal length of the lens?Figure 26.29
A slide projector has a converging lens whose focal length is 105.00 mm. (a) How far (in meters) from the lens must the screen be located if a slide is placed 108.00 mm from the lens? (b) If the slide measures 24.0 mm × 36.0 mm, what are the dimensions (in mm) of its image?
(a) For a diverging lens (f = -20.0 cm), construct a ray diagram to scale and find the image distance for an object that is 20.0 cm from the lens. (b) Determine the magnification of the lens from the diagram.
A tourist takes a picture of a mountain 14 km away using a camera that has a lens with a focal length of 50 mm. She then takes a second picture when she is only 5.0 km away. What is the ratio of the height of the mountain's image on the camera's image sensor for the second picture to its height on
An object is placed to the left of a lens, and a real image is formed to the right of the lens. The image is inverted relative to the object and is one-half the size of the object. The distance between the object and the image is 90.0 cm. (a) How far from the lens is the object? (b) What is the
A converging lens has a focal length of 88.00 cm. An object 13.0 cm tall is located 155.0 cm in front of this lens. (a) What is the image distance? (b) Is the image real or virtual? (c) What is the image height? Be sure to include the proper algebraic sign.
The distance between an object and its image formed by a diverging lens is 49.0 cm. The focal length of the lens is -233.0 cm. Find (a) The image distance and (b) The object distance.
Light has a wavelength of 340.0 nm and a frequency of 5.403 Ã— 1014 Hz when traveling through a certain substance. What substance from Table 26.1 could this be? Show your calculations.
When a converging lens is used in a camera (as in Figure 26.26b), the film must be at a distance of 0.210 m from the lens to record an image of an object that is 4.00 m from the lens. The same lens and film are used in a projector (see Figure 26.27b), with the screen 0.500 m from the lens. How far
An object is placed in front of a converging lens in such a position that the lens (f = 12.0 cm) creates a real image located 21.0 cm from the lens. Then, with the object remaining in place, the lens is replaced with another converging lens (f = 16.0 cm). A new, real image is formed. What is the
A converging lens (f = 25.0 cm) is used to project an image of an object onto a screen. The object and the screen are 125 cm apart, and between them the lens can be placed at either of two locations. Find the two object distances.
The equation given below1/do + 1/di = 1fis called the Gaussian form of the thin-lens equation. The drawing shows the variables do, di, and f. The drawing also shows the distances x and x', which are, respectively, the distance from the object to the focal point on the left of the lens and the
Two identical diverging lenses are separated by 16 cm. The focal length of each lens is -8.0 cm. An object is located 4.0 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.
Two systems are formed from a converging lens and a diverging lens, as shown in parts a and b of the drawing. (The point labeled "Fconverging" is the focal point of the converging lens.) An object is placed inside the focal point of lens 1 at a distance of 10.00 cm to the left of lens 1. The focal
Two converging lenses are separated by 24.00 cm. The focal length of each lens is 12.00 cm. An object is placed 36.00 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.
A converging lens (f1 = 24.0 cm) is located 56.0 cm to the left of a diverging lens (f2 = -28.0 cm). An object is placed to the left of the converging lens, and the final image produced by the two-lens combination lies 20.7 cm to the left of the diverging lens. How far is the object from the
In a certain time, light travels 6.20 km in a vacuum. During the same time, light travels only 3.40 km in a liquid. What is the refractive index of the liquid?

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