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physics
mechanics
Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions
What must be the relative speed between source and receiver if the wavelength of an EM wave as measured by the receiver is twice the wavelength as measured by the source? Are source and observer moving closer together or farther apart?
How fast would you have to drive in order to see a red light as green? Take l = 630 nm for red and l = 530 nm for green
Calculate the frequency of an EM wave with a wavelength the size of (a) The thickness of a piece of paper (60μm), (b) A 91-m-long soccer field, (c) The diameter of Earth, (d) The distance from Earth to the Sun.
The intensity of solar radiation that falls on a detector on Earth is 1.00 kW / m2. The detector is a square that measures 5.00 m on a side and the normal to its surface makes an angle of 30.0° with respect to the Sun's radiation. How long will it take for the detector to measure 420 kJ of energy?
Astronauts on the Moon communicated with mission control in Houston via EM waves. There was a noticeable time delay in the conversation due to the round-trip transit time for the EM waves between the Moon and the Earth. How long was the time delay?
The antenna on a cordless phone radiates microwaves at a frequency of 2.0 GHz. What is the maximum length of the antenna if it is not to exceed half of a wavelength?
Two identical television signals are sent between two cities that are 400.0 km apart. One signal is sent through the air, and the other signal is sent through a fiber optic network. The signals are sent at the same time but the one traveling through air arrives 7.7 × 10−4s before the one
An AM radio station broadcasts at 570 kHz. (a) What is the wavelength of the radio wave in air? (b) If a radio is tuned to this station and the inductance in the tuning circuit is 0.20 mH, what is the capacitance in the tuning circuit? (c) In the vicinity of the radio, the amplitude of the
A 60.0-mW pulsed laser produces a pulse of EM radiation with wavelength 1060 nm (in air) that lasts for 20.0 ps (picoseconds). (a) In what part of the EM spectrum is this pulse? (b) How long (in centimeters) is a single pulse in air? (c) How long is it in water (n = 1.33)? (d) How many
The range of wavelengths allotted to the radio broadcast band is from about 190 m to 550 m. If each station needs exclusive use of a frequency band 10 kHz wide, how many stations can operate in the broadcast band?
At a point due north of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver? An electric dipole antenna used to transmit radio waves is oriented vertically.
Polarized light of intensity I0 is incident on a pair of polarizing sheets. Let θ1 and θ2 be the angles between the direction of polarization of the incident light and the transmission axes of the first and second sheets, respectively. Show that the intensity of the transmitted light is I = I0
An un-polarized beam of light (intensity I0) is moving in the x -direction. The light passes through three ideal polarizers whose transmission axes are (in order) at angles 0.0°, 45.0°, and 30.0° counterclockwise from the y -axis in the yz -plane. (a) What is the intensity and polarization of
What are the three lowest angular speeds for which the wheel in Fizeau's apparatus (see Fig. 22.13) allows the reflected light to pass through to the observer? Assume the distance between the notched wheel and the mirror is 8.6 km and that there are 5 notches in the wheel.
A sinusoidal EM wave has an electric field amplitude Em = 32.0 mV/m. What are the intensity and average energy density?
Energy carried by an EM wave coming through the air can be used to light a bulb that is not connected to a battery or plugged into an electric outlet. Suppose a receiving antenna is attached to a bulb and the bulb is found to dissipate a maximum power of 1.05 W when the antenna is aligned with the
A 10-W laser emits a beam of light 4.0 mm in diameter. The laser is aimed at the Moon. By the time it reaches the Moon, the beam has spread out to a diameter of 85 km. Ignoring absorption by the atmosphere, what is the intensity of the light (a) Just outside the laser (b) Where it hits the
To measure the speed of light, Galileo and a colleague stood on different mountains with covered lanterns. Galileo uncovered his lantern and his friend, seeing the light, uncovered his own lantern in turn. Galileo measured the elapsed time from uncovering his lantern to seeing the light signal
Suppose some astronauts have landed on Mars. (a) When Mars and Earth are on the same side of the Sun and as close as they can be to one another, how long does it take for radio transmissions to travel one way between the two planets? (b) Suppose the astronauts ask a question of mission control
At a point due east of the transmitter, what is the direction of the wave's electric field An electric dipole antenna used to transmit radio waves is oriented horizontally north-south.
At a point due east of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver? An electric dipole antenna used to transmit radio waves is oriented horizontally north-south.
Describe the difference between specular and diffuse reflection. Give some examples of each.
Why is the brilliance of an artificial diamond made of cubic zirconium (n = 1.9) distinctly inferior to the real thing (n = 2.4) even if the two are cut exactly the same way? How would an artificial diamond made of glass compare?
The surface of the water in a swimming pool is completely still. Describe what you would see looking straight up toward the surface from under water.
A ray reflects from a spherical mirror at point P. Explain why a radial line from the center of curvature through point P always bisects the angle between the incident and reflected rays.
Is it possible for a plane mirror to produce a real image of an object in front of the mirror? Explain. If it is possible, sketch a ray diagram to demonstrate. If it is not possible, sketch a ray diagram to show which way a curved mirror must curve (concave or convex) to produce a real image.
A slide projector forms a real image of the slide on a screen using a converging lens. If the bottom half of the lens is blocked by covering it with opaque tape, does the bottom half of the image disappear, or does the top half disappear, or is the entire image still visible on the screen? If the
What is the difference between a virtual and a real image? Describe a method for demonstrating the presence of a real image.
A lens is placed at the end of a bundle of optical fibers in an endoscope. The purpose of the lens is to make the light rays parallel before they enter the fibers (in other words, to put the image at infinity). What is the advantage of using a lens with the same index of refraction as the core of
A converging lens made from dense flint glass is placed into a container of transparent glycerine. Describe what happens to the focal length.
Water droplets in air create rainbows. Describe the physical situation that causes a rainbow. Should you look toward or away from the Sun to see a rainbow? Why is the secondary rainbow fainter than the primary rainbow?
Why does a mirror hanging in a vertical plane seem to interchange left and right but not up and down?
A framed poster is covered with glass that has a rougher surface than regular glass. How does a rough surface reduce glare?
Explain how a plane mirror can be thought of as a special case of a spherical mirror. What is the focal length of a plane mirror? Does the spherical mirror equation work for plane mirrors with this choice of focal length? What is the transverse magnification for any image produced by a plane mirror?
If the angle of incidence is greater than the angle of refraction for a light beam passing an interface, what can be said about the relative values of the indices of refraction and the speed of light in the first and second media?
Sketch the wave fronts and rays for the light emitted by an isotropic point source (isotropic = same in all directions). Use Huygens's principle to illustrate the propagation of one of the wave fronts.
Sunlight strikes the surface of a lake at an angle of incidence of 30.0°. At what angle with respect to the normal would a fish see the Sun?
The vertical displacement d of light rays parallel to the axis of a lens is measured as a function of the vertical displacement h of the incident ray from the principal axis as shown in part (a) of the figure. The data are graphed in part (b) of the figure. The distance D from the lens to the
Sunlight strikes the surface of a lake. A diver sees the Sun at an angle of 42.0° with respect to the vertical. What angle do the Sun's rays in air make with the vertical?
A beam of light in air is incident on a stack of four flat transparent materials with indices of refraction 1.20, 1.40, 1.32, and 1.28. If the angle of incidence for the beam on the first of the four materials is 60.0°, what angle does the beam make with the normal when it emerges into the air
At a marine animal park, Alison is looking through a glass window and watching dolphins swim underwater. If the dolphin is swimming directly toward her at 15 m/s, how fast does the dolphin appear to be moving?
A light ray in the core (n = 1.40) of a cylindrical optical fiber travels at an angle θ1 = 49.0° with respect to the axis of the fiber. A ray is transmitted through the cladding (n = 1.20) and into the air. What angle θ2 does the exiting ray make with the outside
A glass lens has a scratch-resistant plastic coating on it. The speed of light in the glass is 0.67 c and the speed of light in the coating is 0.80 c. A ray of light in the coating is incident on the plastic-glass boundary at an angle of 12.0 ° with respect to the normal. At what angle with
In Figure 23.12, a coin is right up against the far edge of the mug. In picture (a) the coin is just hidden from view and in picture (b) we can almost see the whole coin. If the mug is 6.5 cm in diameter and 8.9 cm tall, what is the diameter of the coin?
A horizontal light ray is incident on a crown glass prism as shown in the figure where b = 30.0°. Find the angle of deviation d of the ray-the angle that the ray emerging from the prism makes with the incident ray.
Apply Huygens's principle to a 5-cm-long planar wave front approaching a reflecting wall at normal incidence. The wavelength is 1 cm and the wall has a wide opening (width = 4cm). The center of the incoming wave front approaches the center of the opening. Repeat the procedure until you have wave
A diamond in air is illuminated with white light. On one particular facet, the angle of incidence is 26.00°. Inside the diamond, red light (λ = 660.0 nm in vacuum) is refracted at 10.48° with respect to the normal; blue light (λ = 470.0 nm in vacuum) is refracted at 10.33°. (a) What are the
The prism in the figure is made of crown glass. Its index of refraction ranges from 1.517 for the longest visible wavelengths to 1.538 for the shortest. Find the range of refraction angles for the light transmitted into air through the right side of the prism.
Calculate the critical angle for a sapphire surrounded by air.
(a) Calculate the critical angle for a diamond surrounded by air. (b) Calculate the critical angle for a diamond under water. (c) Explain why a diamond sparkles less under water than in air.
Is there a critical angle for a light ray coming from a medium with an index of refraction 1.2 and incident on a medium that has an index of refraction 1.4? If so, what is the critical angle that allows total internal reflection in the first medium?
The figure shows some light rays reflected from a small defect in the glass toward the surface of the glass. (a) If θc = 40.00°, what is the index of refraction of the glass? (b) Is there any point above the glass at which a viewer would not be able to see the defect? Explain.
A 45 ° prism has an index of refraction of 1.6. Light is normally incident on the left side of the prism. Does light exit the back of the prism (for example, at point P)? If so, what is the angle of refraction with respect to the normal at point P? If not, what happens to the light?
Light incident on a 45.0° prism as shown in the figure undergoes total internal reflection at point P. What can you conclude about the index of refraction of the prism?
The angle of incidence q of a ray of light in air is adjusted gradually as it enters a shallow tank made of Plexiglas and filled with carbon disulfide. Is there an angle of incidence for which light is transmitted into the carbon disulfide but not into the Plexiglas at the bottom of the tank? If
Repeat Problem 28 for a Plexiglas tank filled with carbon tetrachloride instead of carbon disulfide. In Problem 28 The angle of incidence q of a ray of light in air is adjusted gradually as it enters a shallow tank made of Plexiglas and filled with carbon disulfide. Is there an angle of incidence
Repeat Problem 2 for an opening of width 0.5 cm.
What is the index of refraction of the core of an optical fiber if the cladding has n = 1.20 and the critical angle at the core-cladding boundary is 45.0°?
Some glasses used for viewing 3D movies are polarized, one lens having a vertical transmission axis and the other horizontal. While standing in line on a winter afternoon for a 3D movie and looking through his glasses at the road surface, Maurice notices that the left lens cuts down reflected glare
(a) Sunlight reflected from the still surface of a lake is totally polarized when the incident light is at what angle with respect to the horizontal? (b) In what direction is the reflected light polarized? (c) Is any light incident at this angle transmitted into the water? If so, at what angle
Light travels in a medium with index n1 toward a boundary with another material of index n2 < n1. (a) Which is larger, the critical angle or Brewster's angle? Does the answer depend on the values of n1 and n2 (other than assuming n2 < n1)? (b) What can you say about the critical angle and
A defect in a diamond appears to be 2.0 mm below the surface when viewed from directly above that surface. How far beneath the surface is the defect?
An insect is trapped inside a piece of amber (n = 1.546). Looking at the insect from directly above, it appears to be 7.00 mm below a smooth surface of the amber. How far below the surface is the insect?
A penny is at the bottom of a bowl full of water. When you look at the water surface from the side, with your eyes at the water level, the penny appears to be just barely under the surface and a horizontal distance of 3.0 cm from the edge of the bowl. If the penny is actually 8.0 cm below the water
Daniel's eyes are 1.82 m from the floor when he is wearing his dress shoes, and the top of his head is 1.96 m from the floor. Daniel has a mirror that is 0.98 m in length. How high from the floor should the bottom edge of the mirror be located if Daniel is to see a full-length image of himself?
A plane wave reflects from the surface of a sphere. Draw a ray diagram and sketch some wave fronts for the reflected wave.
A rose in a vase is placed 0.250 m in front of a plane mirror. Nagar looks into the mirror from 2.00 m in front of it. How far away from Nagar is the image of the rose?
Entering a darkened room, Gustav strikes a match in an attempt to see his surroundings. At once he sees what looks like another match about 4 m away from him. As it turns out, a mirror hangs on one wall of the room. How far is Gustav from the wall with the mirror?
In an amusement park maze with all the walls covered with mirrors, Pilar sees Hernando's reflection from a series of three mirrors. If the reflected angle from mirror 3 is 55 ° for the mirror arrangement shown in the figure, what is the angle of incidence on mirror 1?
Maurizio is standing in a rectangular room with two adjacent walls and the ceiling all covered by plane mirrors. How many images of himself can Maurizio see?
Hannah is standing in the middle of a room with two opposite walls that are separated by 10.0 m and covered by plane mirrors. There is a candle in the room 1.50 m from one mirrored wall. Hannah is facing the opposite mirrored wall and sees many images of the candle. How far from Hannah are the
A point source of light is in front of a plane mirror.(a) Prove that all the reflected rays, when extended back behind the mirror, intersect in a single point.(b) Show that the image point lies on a line through the object and perpendicular to the mirror, and that the object and image distances are
An object 2.00 cm high is placed 12.0 cm in front of a convex mirror with radius of curvature of 8.00 cm. Where is the image formed? Draw a ray diagram to illustrate.
A 1.80-cm-high object is placed 20.0 cm in front of a concave mirror with a 5.00-cm focal length. What is the position of the image? Draw a ray diagram to illustrate.
In her job as a dental hygienist, Kathryn uses a concave mirror to see the back of her patient's teeth. When the mirror is 1.20 cm from a tooth, the image is upright and 3.00 times as large as the tooth. What are the focal length and radius of curvature of the mirror?
An object is placed in front of a concave mirror with a 25.0-cm radius of curvature. A real image twice the size of the object is formed. At what distance is the object from the mirror? Draw a ray diagram to illustrate.
A spherical wave (from a point source) reflects from a planar surface. Draw a ray diagram and sketch some wave fronts for the reflected wave.
An object is placed in front of a convex mirror with a 25.0-cm radius of curvature. A virtual image half the size of the object is formed. At what distance is the object from the mirror? Draw a ray diagram to illustrate.
The right-side rearview mirror of Mike's car says that objects in the mirror are closer than they appear. Mike decides to do an experiment to determine the focal length of this mirror. He holds a plane mirror next to the rearview mirror and views an object that is 163 cm away from each mirror. The
A concave mirror has a radius of curvature of 5.0 m. An object, initially 2.0 m in front of the mirror, is moved back until it is 6.0 m from the mirror. Describe how the image location changes
Derive the magnification equation, m = h ′ / h = − q / p, for a convex mirror. Draw a ray diagram as part of the solution.
In a subway station, a convex mirror allows the attendant to view activity on the platform. A woman 1.64 m tall is standing 4.5 m from the mirror. The image formed of the woman is 0.500 m tall. (a) What is the radius of curvature of the mirror? (b) The mirror is 0.500 m in diameter. If the woman's
Show that when rays parallel to the principal axis reflect from a concave mirror, the reflected rays all pass through the focal point at a distance R /2 from the vertex. Assume that the angles of incidence are small.
(a) For a converging lens with a focal length of 3.50 cm, find the object distance that will result in an inverted image with an image distance of 5.00 cm. Use a ray diagram to verify your calculations. (b) Is the image real or virtual? (c) What is the magnification?
Sketch a ray diagram to show that when an object is placed more than twice the focal length away from a converging lens, the image formed is inverted, real, and diminished in size
Sketch a ray diagram to show that when an object is placed at twice the focal length from a converging lens, the image formed is inverted, real, and the same size as the object.
Light rays from the Sun, which is at an angle of 35° above the western horizon, strike the still surface of a pond. (a) What is the angle of incidence of the Sun's rays on the pond? (b) What is the angle of reflection of the rays that leave the pond surface? (c) In what direction and at what
Sketch a ray diagram to show that when an object is placed between twice the focal length and the focal length from a converging lens, the image formed is inverted, real, and enlarged in size.
Sketch a ray diagram to show that when an object is a distance equal to the focal length from a converging lens, the emerging rays from the lens are parallel to each other, so the image is at infinity.
When an object is placed 6.0 cm in front of a converging lens, a virtual image is formed 9.0 cm from the lens. What is the focal length of the lens?
An object of height 3.00 cm is placed 12.0 cm from a diverging lens of focal length − 12.0 cm. Draw a ray diagram to find the height and position of the image.
A diverging lens has a focal length of − 8.00 cm. (a) What are the image distances for objects placed at these distances from the lens: 5.00 cm, 8.00 cm, 14.0 cm, 16.0 cm, 20.0 cm? In each case, describe the image as real or virtual, upright or inverted, and enlarged or diminished in size. (b) If
A converging lens has a focal length of 8.00 cm. (a) What are the image distances for objects placed at these distances from the thin lens: 5.00 cm, 14.0 cm, 16.0 cm, 20.0 cm? In each case, describe the image as real or virtual, upright or inverted, and enlarged or diminished in size. (b) If the
Sketch a ray diagram to show that if an object is placed less than the focal length from a converging lens, the image is virtual and upright
For each of the lenses in the figure, list whether the lens is converging or diverging.
In order to read his book, Stephen uses a pair of reading glasses. When he holds the book at a distance of 25 cm from his eyes, the glasses form an upright image a distance of 52 cm from his eyes. (a) Is this a converging or diverging lens? (b) What is the magnification of the lens? (c) What is the
A standard "35-mm" slide measures 24.0 mm by 36.0 mm. Suppose a slide projector produces a 60.0-cm by 90.0-cm image of the slide on a screen. The focal length of the lens is 12.0 cm. (a) What is the distance between the slide and the screen? (b) If the screen is moved farther from the projector,
A light ray reflects from a plane mirror as shown in the figure. What is the angle of deviation δ?
An object that is 6.00 cm tall is placed 40.0 cm in front of a diverging lens. The magnitude of the focal length of the lens is 20.0 cm. Find the image position and size. Is the image real or virtual? Upright or inverted?
Samantha puts her face 32.0 cm from a makeup mirror and notices that her image is magnified by 1.80 times. (a) What kind of mirror is this? (b) Where is her face relative to the radius of curvature or focal length? (c) What is the radius of curvature of the mirror?
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