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physics
light and optics

College Physics 7th Edition Raymond A. Serway, Jerry S. Faughn, Chris Vuille, Charles A. Bennett - Solutions

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 latter image real or virtual?
In many applications it is necessary to expand or to decrease the diameter of a beam of parallel rays of light. This change can be made by using a converging lens and a diverging lens in combination. Suppose you have a converging lens of focal length 21.0 cm and a diverging lens of focal length
A parallel beam of light enters a glass hemisphere perpendicular to the flat face, as shown in Figure P36.65. The magnitude of the radius is 6.00 cm, and the index of refraction is 1.560. Determine the point at which the beam is focused. (Assume paraxial rays.)
A spherical lightbulb of diameter 3.20 cm radiates light equally in all directions, with power 4.50 W. (a) Find the light intensity at the surface of the bulb. (b) Find the light intensity 7.20 m away from the center of the bulb. (c) At this 7.20-m distance a lens is set up with its axis
An object is placed 12.0 cm to the left of a diverging lens of focal length -6.00 cm. A converging lens of focal length 12.0 cm is placed a distance d to the right of the diverging lens. Find the distance d so that the final image is at infinity. Draw a ray diagram for this case.
An observer to the right of the mirror€“lens combination shown in Figure P36.68 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 object. The lens has a focal length of 10.0 cm.
The disk of the Sun subtends an angle of 0.533° at the Earth. What are the position and diameter of the solar image formed by a concave spherical mirror with a radius of curvature of 3.00 m?
Assume the intensity of sunlight is 1.00 kW/m2 at a particular location. A highly reflecting concave mirror is to be pointed toward the Sun to produce a power of at least 350 W at the image. (a) Find the required radius Ra of the circular face area of the mirror. (b) Now suppose the light
In a darkened room, a burning candle is placed 1.50 m from a white wall. A lens is placed between candle and wall at a location that causes a larger, inverted image to form on the wall. When the lens is moved 90.0 cm toward the wall, another image of the candle is formed. Find (a) The two object
Figure P36.72 shows a thin converging lens for which the radii of curvature are R1 = 9.00 cm and R2 = -11.0 cm. The lens is in front of a concave spherical mirror with the radius of curvature R = 8.00 cm.(a) Assume its focal points F1 and F2 are 5.00 cm from the center of the lens. Determine its
A compound microscope has an objective of focal length 0.300 cm and an eyepiece of focal length 2.50 cm. If an object is 3.40 mm from the objective, what is the magnification? (Suggestion: Use the lens equation for the objective.)
Two converging lenses having focal lengths of 10.0 cm and 20.0 cm are located 50.0 cm apart, as shown in Figure P36.74. The final image is to be located between the lenses at the position indicated.(a) How far to the left of the first lens should the object be?(b) What is the overall
A cataract-impaired lens in an eye may be surgically removed and replaced by a manufactured lens. The focal length required for the new lens is determined by the lens-to-retina distance, which is measured by sonar like device, and by the requirement that the implant provide for correct distant
A floating strawberry illusion is achieved with two parabolic mirrors, each having a focal length 7.50 cm, facing each other so that their centers are 7.50 cm apart (Fig. P36.76). If a strawberry is placed on the lower mirror, an image of the strawberry is formed at the small opening at the center
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 with a focal length of -20.0 cm is placed 110 cm to the right of the converging lens. (a) Determine the position and magnification of the final image. (b) Is the image
Two lenses made of kinds of glass having different refractive indices n1 and n2 are cemented together to form what is called an optical doublet. Optical doublets are often used to correct chromatic aberrations in optical devices. The first lens of a doublet has one flat side and one concave side of
A laser beam (A = 632.8 nm) is incident on two slits 0.200 mm apart. How far apart are the bright interference fringes on a screen 5.00 m away from the double slits?
A Young’s interference experiment is performed with monochromatic light. The separation between the slits is 0.500 mm, and the interference pattern on a screen 3.30 m away shows the first side maximum 3.40 mm from the center of the pattern. What is the wavelength?
Two radio antennas separated by 300 m as shown in Figure P37.3 simultaneously broadcast identical signals at the same wavelength. A radio in a car traveling due north receives the signals.(a) If the car is at the position of the second maximum, what is the wavelength of the signals?(b) How much
In a location where the speed of sound is 354 m/s, a 2 000-Hz sound wave impinges on two slits 30.0 cm apart. (a) At what angle is the first maximum located? (b) What If? If the sound wave is replaced by 3.00-cm microwaves, what slit separation gives the same angle for the first maximum? (c)
Young’s double-slit experiment is performed with 589-nm light and a distance of 2.00 m between the slits and the screen. The tenth interference minimum is observed 7.26 mm from the central maximum. Determine the spacing of the slits.
The two speakers of a boom box are 35.0 cm apart. A single oscillator makes the speakers vibrate in phase at a frequency of 2.00 kHz. At what angles, measured from the perpendicular bisector of the line joining the speakers, would a distant observer hear maximum sound intensity? Minimum sound
Two narrow, parallel slits separated by 0.250 mm are illuminated by green light (& # 546.1 nm). The interference pattern is observed on a screen 1.20 m away from the plane of the slits. Calculate the distance (a) From the central maximum to the first bright region on either side of the central
Light with wavelength 442 nm passes through a double-slit system that has a slit separation d = 0.400 mm. Determine how far away a screen must be placed in order that a dark fringe appear directly opposite both slits, with just one bright fringe between them.
A riverside warehouse has two open doors as shown in Figure P37.9. Its walls are lined with sound-absorbing material. A boat on the river sounds its horn. To person A the sound is loud and clear. To person B the sound is barely audible. The principal wavelength of the sound waves is 3.00 m.
Two slits are separated by 0.320 mm. A beam of 500-nm light strikes the slits, producing an interference patterns determine the number of maxima observed in the angular range -30.0° < θ < 30.0°.
Young€™s double-slit experiment underlies the Instrument Landing System used to guide aircraft to safe landings when the visibility is poor. Although real systems are more complicated than the example described here, they operate on the same principles. A pilot is trying to align her
A student holds a laser that emits light of wavelength 633 nm. The beam passes though a pair of slits separated by 0.300 mm, in a glass plate attached to the front of the laser. The beam then falls perpendicularly on a screen, creating an interference pattern on it. The student begins to walk
In Figure 37.5 let L = 1.20 m and d = 0.120 mm and assume that the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) θ = 0.500° and (b) y = 5.00 mm. (c) What is the value of θ for which the
Coherent light rays of wavelength A strike a pair of slits separated by distance d at an angle θ1 as shown in Figure P37.14. Assume an interference maximum is formed at an angle θ2 a great distance from the slits. Show that d (sin θ2 - sin θ1) = mA, where m is an integer.
In a double-slit arrangement of Figure 37.5, d = 0.150 mm, L = 140 cm, A = 643 nm, and y = 1.80 cm. (a) What is the path difference = for the rays from the two slits arriving at P? (b) Express this path difference in terms of A. (c) Does P correspond to a maximum, a minimum, or an
The intensity on the screen at a certain point in a double slit interference pattern is 64.0% of the maximum value. (a) What minimum phase difference (in radians) between sources produces this result? (b) Express this phase difference as a path difference for 486.1-nm light.
In Figure 37.5, let L = 120 cm and d = 0.250 cm. The slits are illuminated with coherent 600-nm light. Calculate the distance y above the central maximum for which the average intensity on the screen is 75.0% of the maximum.
Two slits are separated by 0.180 mm. An interference pattern is formed on a screen 80.0 cm away by 656.3-nm light. Calculate the fraction of the maximum intensity 0.600 cm above the central maximum.
Two narrow parallel slits separated by 0.850 mm are illuminated by 600-nm light, and the viewing screen is 2.80 m away from the slits. (a) What is the phase difference between the two interfering waves on a screen at a point 2.50 mm from the central bright fringe? (b) What is the ratio of the
Monochromatic coherent light of amplitude E0 and angular frequency - passes through three parallel slits each separated by a distance d from its neighbor. (a) Show that the time-averaged intensity as a function of the angle θ is (b) Determine the ratio of the intensities of the primary
Marie Cornu, a physicist at the Polytechnic Institute in Paris, invented phasors in about 1880. This problem helps you to see their utility. Find the amplitude and phase constant of the sum of two waves represented by the expressions E1 = (12.0 kN/C) sin (15x - 4.5t) And E2 = (12.0 kN/C) sin
The electric fields from three coherent sources are described by E1 = E0 sin -t, E2 = E0 sin (wt + ǿ), and E3 = E0 sin (wt + 2ǿ). Let the resultant field be represented by EP = ER sin (wt + a). Use phasors to find ER and 1 when (a) Ǿ = 20.0°, (b) Ǿ = 60.0°, and (c)
Determine the resultant of the two waves given by E1 = 6.0 sin (100 π t) and E2 = 8.0 sin (100 πt + (π/2).
Suppose the slit openings in a Young’s double-slit experiment have different sizes so that the electric fields and intensities from each slit are different. With E1 = E01 sin (wt) and E 2 = E02 sin (wt + ǿ), show that the resultant electric field is E = E0 sin (wt + ǿ), where
Use phasors to find the resultant (magnitude and phase angle) of two fields represented by E1 = 12 sin wt and E2 = 18 sin (wt + 60°). (Note that in this case the amplitudes of the two fields are unequal.)
Two coherent waves are described byDetermine the relationship between x1 and x2 that produces constructive interference when the two waves are superposed.
When illuminated, four equally spaced parallel slits act as multiple coherent sources, each differing in phase from the adjacent one by an angle ǿ Use a phasor diagram to determine the smallest value of ǿ for which the resultant of the four waves (assumed to be of equal amplitude) is zero.
Sketch a phasor diagram to illustrate the resultant of E1 = E01 sin wt and E2 = E02 sin (wt + ǿ), where E02 = 1.50E01 and π/6 < ǿ < π/3. Use the sketch and the law of cosines to show that, for two coherent waves, the resultant intensity can be written in the form IR = I1 + I2 +
Consider N coherent sources described as follows: E1 = E0sin (wt + ǿ), E2 = E0sin (wt + 2 ǿ), E3 = E0sin (wt + 3 ǿ). . . EN = E0 sin (wt (Nǿ). Find the minimum value of ǿ for which ER = E1 + E2 + E3 + . . . + EN is zero.
A soap bubble (n = 1.33) is floating in air. If the thickness of the bubble wall is 115 nm, what is the wavelength of the light that is most strongly reflected?
An oil film (n = 1.45) floating on water is illuminated by white light at normal incidence. The film is 280 nm thick. Find (a) The color of the light in the visible spectrum most strongly reflected and (b) The color of the light in the spectrum most strongly transmitted. Explain your reasoning.
A thin film of oil (n = 1.25) is located on a smooth wet pavement. When viewed perpendicular to the pavement, the film reflects most strongly red light at 640 nm and reflects no blue light at 512 nm. How thick is the oil film?
A possible means for making an airplane invisible to radar is to coat the plane with an antireflective polymer. If radar waves have a wavelength of 3.00 cm and the index of refraction of the polymer is n = 1.50, how thick would you make the coating?
A material having an index of refraction of 1.30 is used as an antireflective coating on a piece of glass (n = 1.50). What should be the minimum thickness of this film in order to minimize reflection of 500-nm light?
A film of MgF2 (n = 1.38) having thickness 1.00 x 10-5 cm is used to coat a camera lens. Are any wavelengths in the visible spectrum intensified in the reflected light?
Astronomers observe the chromo sphere of the Sun with a filter that passes the red hydrogen spectral line of wavelength 656.3 nm, called the H1 line. The filter consists of a transparent dielectric of thickness d held between two partially aluminized glass plates. The filter is held at a constant
A beam of 580-nm light passes through two closely spaced glass plates, as shown in Figure P37.37, for what minimum nonzero value of the plate separation d is the transmitted light bright ?
When a liquid is introduced into the air space between the lens and the plate in a Newton’s-rings apparatus, the diameter of the tenth ring changes from 1.50 to 1.31 cm, find the index of refraction of the liquid.
An air wedge is formed between two glass plates separated at one edge by a very fine wire, as shown in Figure P37.39. When the wedge is illuminated from above by 600-nm light and viewed from above, 30 dark fringes are observed. Calculate the radius of the wire.
Two glass plates 10.0 cm long are in contact at one end and separated at the other end by a thread 0.050 0 mm in diameter (Fig. P37.39). Light containing the two wavelengths 400 nm and 600 nm is incident perpendicularly and viewed by reflection. At what distance from the contact point is the next
Mirror M1 in Figure 37.22 is displaced a distance ∆L. During this displacement, 250 fringe reversals (formation of successive dark or bright bands) are counted. The light being used has a wavelength of 632.8 nm. Calculate the displacement ∆L.
Monochromatic light is beamed into a Michelson interferometer. The movable mirror is displaced 0.382 mm, causing the interferometer pattern to reproduce itself 1 700 times. Determine the wavelength of the light. What color is it?
One leg of a Michelson interferometer contains an evacuated cylinder of length L, having glass plates on each end. A gas is slowly leaked into the cylinder until a pressure of 1 atm is reached. If N bright fringes pass on the screen when light of wavelength A is used, what is the index of
In the What If? Section of Example 37.2, it was claimed that overlapping fringes in a two-slit interference pattern for two different wavelengths obey the following relationship even for large values of the angle θ: A/ A = m`/m (a) Prove this assertion. (b) Using the data in Example 37.2,
One radio transmitter A operating at 60.0 MHz is 10.0 m from another similar transmitter B that is 180° out of phase with A. How far must an observer move from A toward B along the line connecting A and B to reach the nearest point where the two beams are in phase?
This problem extends the result of Problem 12 in Chapter 18. Figure P37.46 shows two adjacent vibrating balls dipping into a tank of water. At distant points they produce an interference pattern of water waves, as shown in Figure 37.3. Let A represent the wavelength of the ripples. Show that the
Raise your hand and hold it flat. Think of the space between your index finger and your middle finger as one slit, and think of the space between middle finger and ring finger as a second slit. (a) Consider the interference resulting from sending coherent visible light perpendicularly through
In a Young’s double-slit experiment using light of wavelength A, a thin piece of Plexiglas having index of refraction n covers one of the slits. If the center point on the screen is a dark spot instead of a bright spot, what is the minimum thickness of the Plexiglas?
A flat piece of glass is held stationary and horizontal above the flat top end of a 10.0-cm-long vertical metal rod that has its lower end rigidly fixed. The thin film of air between the rod and glass is observed to be bright by reflected light when it is illuminated by light of wavelength 500 nm.
A certain crude oil has an index of refraction of 1.25. A ship dumps 1.00 m3 of this oil into the ocean, and the oil spreads into a thin uniform slick. If the film produces a first-order maximum of light of wavelength 500 nm normally incident on it, how much surface area of the ocean does the oil
Astronomers observe a 60.0-MHz radio source both directly and by reflection from the sea. If the receiving dish is 20.0 m above sea level, what is the angle of the radio source above the horizon at first maximum?
Interference effects are produced at point P on a screen as a result of direct rays from a 500-nm source and reflected rays from the mirror, as shown in Figure P37.52. Assume the source is 100 m to the left of the screen and 1.00 cm above the mirror. Find the distance y to the first dark band above
The waves from a radio station can reach a home receiver by two paths. One is a straight-line path from transmitter to home, a distance of 30.0 km. The second path is by reflection from the ionosphere (a layer of ionized air molecules high in the atmosphere). Assume this reflection takes place at a
Many cells are transparent and colorless. Structures of great interest in biology and medicine can be practically invisible to ordinary microscopy. An interference microscope reveals a difference in index of refraction as a shift in interference fringes, to indicate the size and shape of cell
Measurements are made of the intensity distribution in a Young’s interference pattern (see Fig. 37.7). At a particular value of y, it is found that I/Imax = 0.810 when 600-nm light is used. What wavelength of light should be used to reduce the relative intensity at the same location to 64.0% of
Our discussion of the techniques for determining constructive and destructive interference by reflection from a thin film in air has been confined to rays striking the film at nearly normal incidence. What If? Assume that a ray is incident at an angle of 30.0° (relative to the normal) on a film
The condition for constructive interference by reflection from a thin film in air as developed in Section 37.6 assumes nearly normal incidence. What If? Show that if the light is incident on the film at a nonzero angle .1 (relative to the normal), then the condition for constructive interference is
(a) Both sides of a uniform film that has index of refraction n and thickness d are in contact with air. For normal incidence of light, an intensity minimum is observed in the reflected light at A2 and an intensity maximum is observed at A1, where A1 - A2. Assuming that no intensity minima are
Figure P37.59 shows a radio-wave transmitter and a receiver separated by a distance d and both a distance h above the ground. The receiver can receive signals both directly from the transmitter and indirectly from signals that reflect from the ground. Assume that the ground is level between the
A piece of transparent material having an index of refraction n is cut into the shape of a wedge as shown in Figure P37.60. The angle of the wedge is small. Monochromatic light of wavelength A is normally incident from above, and viewed from above. Let h represent the height of the wedge and
Consider the double-slit arrangement shown in Figure P37.61, where the slit separation is d and the slit to screen distance is L. A sheet of transparent plastic having an index of refraction n and thickness t is placed over the upper slit. As a result, the central maximum of the interference
A plano-convex lens has index of refraction n. The curved side of the lens has radius of curvature R and rests on a flat glass surface of the same index of refraction, with a film of index nfilm between them, as shown in Fig. 37.18a. The lens is illuminated from above by light of wavelength &. Show
In a Newton’s-rings experiment, a plano-convex glass (n = 1.52) lens having diameter 10.0 cm is placed on a flat plate as shown in Figure 37.18a. When 650-nm light is incident normally, 55 bright rings are observed with the last one right on the edge of the lens. (a) What is the radius of
A plano-concave lens having index of refraction 1.50 is placed on a flat glass plate, as shown in Figure P37.64. Its curved surface, with radius of curvature 8.00 m, is on the bottom. The lens is illuminated from above with yellow sodium light of wavelength 589 nm, and a series of concentric bright
A plano-convex lens having a radius of curvature of r = 4.00m is placed on a concave glass surface whose radius of curvature is R= 12.0 m, as shown in Figure P37.65. Determine the radius of the 100th bright ring, assuming 500-nm light is incident normal to the flat surface of the lens.
Use phasor addition to find the resultant amplitude and phase constant when the following three harmonic functions are combined: E1 = sin (wt (π/6), E2 = 3.0 sin (wt + 7π /2), and E3 = 6.0 sin (wt + 4π/3).
A soap film (n = 1.33) is contained within a rectangular wire frame. The frame is held vertically so that the film drains downward and forms a wedge with flat faces. The thickness of the film at the top is essentially zero. The film is viewed in reflected white light with near-normal incidence,
Compact disc (CD) and digital video disc (DVD) players use interference to generate a strong signal from a tiny bump. The depth of a pit is chosen to be one quarter of the wavelength of the laser light used to read the disc. Then light reflected from the pit and light reflected from the adjoining
Interference fringes are produced using Lloyd’s mirror and a 606-nm source as shown in Figure 37.15. Fringes 1.20 mm apart are formed on a screen 2.00 m from the real source S. Find the vertical distance h of the source above the reflecting surface.
Monochromatic light of wavelength 620 nm passes through a very narrow slit S and then strikes a screen in which are two parallel slits, S1 and S2, as in Figure P37.70. Slit S1 is directly in line with S and at a distance of L = 1.20 m away from S, whereas S2 is displaced a distance d to one side.
Slit 1 of a double slit is wider than slit 2, so that the light from 1 has amplitude 3.00 times that of the light from 2. Show that for this situation, Equation 37.11 is replaced by the equation I = (4Imax/9) (1 + 3 cos2 ǿ/2).
The Apollo 11 astronauts set up a panel of efficient corner cube retro reflectors on the Moon’s surface. The speed of light can be found by measuring the time interval required for a laser beam to travel from Earth, reflect from the panel, and return to Earth. If this interval is measured to be
As a result of his observations, Roemer concluded that eclipses of Io by Jupiter were delayed by 22 min during a 6 month period as the Earth moved from the point in its orbit where it is closest to Jupiter to the diametrically opposite point where it is farthest from Jupiter. Using 1.50 x 108 km as
In an experiment to measure the speed of light using the apparatus of Fizeau (see Fig. 35.2), the distance between light source and mirror was 11.45 km and the wheel had 720 notches. The experimentally determined value of c was 2.998 x 108 m/s. Calculate the minimum angular speed of the wheel for
Figure P35.4 shows an apparatus used to measure the speed distribution of gas molecules. It consists of two slotted rotating disks separated by a distance d, with the slots displaced by the angle &. Suppose the speed of light is measured by sending a light beam from the left through this
A dance hall is built without pillars and with a horizontal ceiling 7.20 m above the floor. A mirror is fastened flat against one section of the ceiling. Following an earthquake, the mirror is in place and unbroken. An engineer makes a quick check of whether the ceiling is sagging by directing a
The two mirrors illustrated in Figure P35.6 meet at a right angle. The beam of light in the vertical plane P strikes mirror 1 as shown.(a) Determine the distance the reflected light beam travels before striking mirror 2.(b) In what direction does the light beam travel after being reflected from
Two flat rectangular mirrors, both perpendiculars to a horizontal sheet of paper, are set edge to edge with their reflecting surfaces perpendicular to each other. (a) A light ray in the plane of the paper strikes one of the mirrors at an arbitrary angle of incidence θ 1. Prove that the final
How many times will the incident beam shown in Figure P35.8 be reflected by each of the parallel mirrors?
The distance of a lightbulb from a large plane mirror is twice the distance of a person from the plane mirror. Light from the bulb reaches the person by two paths. It travels to the mirror at an angle of incidence θ, and reflects from the mirror to the person. It also travels directly to the
A narrow beam of sodium yellow light, with wavelength 589 nm in vacuum, is incident from air onto a smooth water surface at an angle of incidence of 35.0°. Determine the angle of refraction and the wavelength of the light in water.
Compare this problem with the preceding problem. A plane sound wave in air at 20°C, with wavelength 589 mm, is incident on a smooth surface of water at 25°C, at an angle of incidence of 3.50°. Determine the angle of refraction for the sound wave and the wavelength of the sound in water.
The wavelength of red helium–neon laser light in air is 632.8 nm. (a) What is its frequency? (b) What is its wavelength in glass that has an index of refraction of 1.50? (c) What is its speed in the glass?
An underwater scuba diver sees the Sun at an apparent angle of 45.0° above the horizon. What is the actual elevation angle of the Sun above the horizon?

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