Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

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In a double-slit experiment, it is found that blue light of wavelength 460nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same location?
Water waves having parallel crests 2.5cm apart pass through two openings 5.0cm apart in a board. At a point 2.0m beyond the board, at what angle relative to the “straight-through” direction would there be little or no wave action?
Suppose a thin piece of glass is placed in front of the lower slit in Fig. 24-7 so that the two waves enter the slits 180o out of phase (Fig. 24-57). Describe in detail the interference pattern on the screen.
In a double-slit experiment, the third-order maximum for light of wavelength 500nm is located 12mm from the central bright spot on a screen 1.6m from the slits. Light of wavelength 650nm is then projected through the same slits. How far from the central bright spot will the second-order maximum of
Two narrow slits separated by 1.0mm are illuminated by 544nm light. Find the distance between adjacent bright fringes on a screen 5.0m from the slits.
Light of wavelength 480nm in air falls on two slits 6.00 x 10-2, apart. The slits are immersed in water, as is a viewing screen 40.0cm away. How far apart are the fringes on the screen?
A very thin sheet of plastic (n = 1.60) covers one slit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?
By what percent, approximately, does the speed of red light (700nm) exceed that of violet light (400nm) in silicate flint glass? (See Fig. 24-14).
A light beam strikes a piece of glass at a 60.00o incident angle. The beam contains two wavelengths, 450.0nm and 700.0nm, for which the index of refraction of the glass is 1.4742, respectively. What is the angle between the two refracted beams?
A parallel beam of light containing two wavelengths, λ1 = 450nm and λ2 = 650nm, enters the silicate flint glass of an equilateral prism as shown in Fig. 24-58. At what angle does each beam leave the prism (give angle with normal to the face?
If 580-nm light falls on a slit 0.0440mm wide, what is the full angular width of the central diffraction peak?
Monochromatic light falls on a slit that is 2.60 x 10-3mm wide. If the angle between the first dark fringes on either side of the central maximum is 35.0o (dark fringe to dark fringe), what is the wavelength of the light used?
Light of wavelength 520nm falls on a slit that is 3.20 x 10-3mm wide, estimate how far the first brightish diffraction fringe is from the strong central maximum if the screen is 10.0m away.
A single slit 1.0mm wide is illuminated by 450-nm light, what is the width of the central maximum (in cm) in the diffraction pattern on a screen 5.0m away?
Monochromatic light of wavelength 653 nm falls on a slit. If the angle between the first bright fringes on either side of the central maximum is 32o, estimate the list width.
How wide is the central diffraction peak on a screen 2.30m behind a 0.048-mm-wide slit illuminated by 589-nm light?
When blue light of wavelength 440nm falls on a single slit, the first dark bands on either side of center are separated by 55.0o. Determine the width of the slit.
When violet light of wavelength 415nm falls on a single slit, it creates a central diffraction peak that is 9.20cm wide on a screen that is 2.55m away. How wide is the slit?
If a slit diffracts 650.nm light so that the diffraction maximum is 4.0cm wide on a screen 1.50m away, what will be the width of the diffraction maximum for light of wavelength 420nm?
For a given wavelength λ, what is the maximum slit width for which there will be no diffraction minima?
At what angle will 560nm light produce a second-order maximum when falling on a grating whose slits are 1.45 x 10-3 cm apart?
A 3500-line/cm grating produces a third-order fringe at a 28.0o angle. What wavelength of light is being used?
How many lines per centimeter does a grating have if the third-order occurs at an 18.0o angle for 630-nm light?
A grating has 8300 lines/cm. How many complete spectral orders can be seen (400nm to 700nm) when it is illuminated by white light?
The first-order line of 589-nm light falling on a diffraction grating is observed at a 15.5o angle. How far apart are the slits? At what angle will the third order be observed?
A diffraction grating has 6.0 x 10-7m lines/m. Find the angular spread in the second-order spectrum between red light of wavelength 7.0 x 10-7 m and blue light of wave length 4.5 x 10-7m.
Light falling normally on a 9700-line/cm grating is revealed to contain three lines in the first –order spectrum at angles of 31.2o, 36.4o, and 47.5o. What wavelengths are these?
What is the highest spectral order that can be seen if a grating with 6000 lines per cm is illuminated with 633-nm laser light? Assume normal incidence.
Two (and only two) full spectral orders can be seen on either side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of lines per cm for the grating?
White light containing wavelengths from 410nm to 750nm falls on a grating with 8500 lines/cm. How wide is the first-order spectrum on a screen 2.30m away?
A He∙ Ne gas laser which produces monochromatic light of a know wavelength λ = 6.328 x 10-7m is used to calibrate a reflection grating in a spectroscope. The first-order diffraction line is found at an angle of 21.5o to the incident beam. How many lines per meter are there on the grating?
Two first-order spectrum lines are measured by a 9500-line/cm spectroscope at angles, on each side of center, of + 26o38`, + 41o08` and –26o48`, –41o19` what are the wavelength?
If a soap bubble 120nm thick, what wavelength is most strongly reflected at the center of the outer surface when illuminated normally by white light? Assume that n = 1.34?
How far apart are the dark fringes in Example 24-8 if the glass plates are each 26.5cm long?
What is the smallest thickness of a soap film (n = 1.42) that would appear black if illuminated with 480-nm light? Assume there is air on both sides of the soap film.
A lens appears greenish yellow (λ = 570nm is strongest) when white light reflects from it. What minimum thickness of coating (n = 1.25) do you think is used on such a glass (n = 1.52) lens, and why?
A total of 31 bright and 31 dark Newton’s rings (not counting the dark spot at the center) are observed when 550-nm light falls normally on a Plano convex lens resting on a flat glass surface (Fig.24-31). How much thicker is the center than the edges?
A fine metal foil separates one end of two pieces of optically flat glass, as in Fig. 24-33. When light of wavelength 670nm is incident normally, 28 dark lines are observed (with one at each end). How thick is the foil?
How thick (minimum) should the air layer be between two flat glass surfaces if the glass is to appear bright when 450-nm light is incident normally? What if the glass is to appear dark?
A piece of material, suspected of being a stolen diamond (n = 2.42), is submerged in oil of refractive index 1.43 and illuminated by Unpolarized light. It is found that the reflected light is completely polarized at an angle of 59o. Is it diamond?
A thin film of alcohol (n = 1.36) lies on a flat glass plate (n = 1.51). When monochromatic light, whose wave-length can be changed, is incident normally, the reflected light is a minimum for λ = 512nm and a maximum for λ = 640nm. What is the minimum thickness of the film?
When a Newton’s ring apparatus (Fig. 24-31) is immersed in a liquid, the diameter of the eighth dark ring decreases from 2.92cm to 2.48cm, what is the refractive index of the liquid?
What is the wavelength of the light entering an interferometer if 644 bright fringes are counted when the movable mirror moves 0.225mm?
A micrometer is connected to the movable mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to the empty micrometer, is 272. What is the thickness of the foil? The wavelength of light used is 589nm.
How far must the mirror M1 in a Michelson interferometer be moved if 850 fringes of 589-nm light are to pass by a reference line?
One of the beams of an interferometer (Fig. 24-59) passes through a small glass container containing a cavity 1.30cm deep. When a gas is allowed to slowly fill the container, a total of 236 dark fringes are counted to move past a reference line. The light used has a wavelength of 610nm. Calculate
Two polarizer’s are oriented at 65o to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?
What is Brewster’s angle for an air-glass (n = 1.52) surface?
What is the Brewster’s angle for a diamond submerged in water if the light is hitting the diamond (n = 2.42) while travelling in the water?
Two Polaroid’s are aligned so that the light passing through them is a maximum. At what angle should one of them be placed so that the intensity is subsequently reduced by half?
At what angle should the aces of two Polaroid’s be placed so as to reduce the intensity of the incident Unpolarized light to? (a) 1/3,(b) 1/10?
Two polarizer’s are oriented at 40o to each other and plane-polarized light is incident on them. If only 15% of the light gets through both of them, what was the initial polarization direction of the incident light?
Two polarizer’s are oriented at 38.0o to one another. Light polarized at a 19.0o angle to each polarizer passes through both. What percent reduction in intensity takes place?
What would Brewster’s angle be for reflections off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angle from above the surface?
Unpolarized light passes through five successive Polaroid sheets, each of whose axis makes a 45o angle with the previous one. What is the intensity of the transmitted beam?
Light of wavelength 5.0 x 10-7m passes through two parallel slits and falls on a screen 4.0m away. Adjacent bright bands of the interference pattern are 2.0cm apart. (a) Find the distance between the slits.(b) The same two slits are next illuminated by light of a different wavelength, and the
Television and radio waves reflecting from mountains or airplanes can interfere with the direct signal from the station. (a) What kind of interference will occur when 75-MHz television signals arrive at a receiver directly from a distant station, and are reflected from a nearby airplane 118m
Red light from three separate sources passes through a diffraction grating with 3.00 x 105 lines/m the wavelengths of the three lines are 6.56 x 10-7m (argon) calculate the angles for the first-order diffraction lines of each of these sources.
Light of wavelength 590nm passes through two narrow slits 0.60mm apart, the screen is 1.70m away. A second source of unknown wavelength produces its second-order fringe 1.33mm closer to the central maximum than the 590-nm light. What is the wavelength of the unknown light?
A radio station operating at 102.1 MHz broadcasts from two identical antennae at the same elevation but separated by an 8.0-m horizontal distance d, Fig. 24-60. A maximum signal is found along the midline, perpendicular to d at its midpoint and extending horizontally in both directions. If the
A teacher stands well back from an outside doorway 0.88m wide, and blows a whistle of frequency 750Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground outside the doorway?
If parallel light falls on a single slit of width D at a 30o angle to the normal, describe the diffraction pattern.
The wings of a certain beetle have a series of parallel lines across them. When normally incident 460-nm light is reflected from the wing, the wing appears bright when viewed at an angle of 51o. How far apart is the line?
How many lines per centimeter must a grating have if there is to be no second-order spectrum for any visible wavelength?
Show that the second and third-order spectra of white light produced by a diffraction grating always overlap. What wavelengths overlap exactly?
When yellow sodium light, λ = 589nm, falls on a diffraction grating, its first-order peak on a screen 60.0cm away falls 3.32cm from the central peak. What is the wavelength of the new source? How many lines/cm are on the grating?
Light is incident on a diffraction grating with 8600 lines/cm, and the pattern is viewed on a screen 2.5m from the grating. The incident light beam consists of two wavelengths, λ1 = 4.6 x 10-7 m and λ2 = 6.8 x 10-7m. Calculate the linear distance between the first-order bright fringes of
What is the index of refraction of a clear material if a minimum of 150 nm thickness of it, when laid on glass, is needed to reduce reflection to nearly zero when light of 600nm is incident normally upon it? Do you have a choice for an answer?
Monochromatic light of variable wavelength is incident normally on a thin sheet of plastic film in air. The reflected light is a minimum only for λ = 512nm, and λ 640nm in the visible spectrum. What is the thickness of the film (n = 1.58)?
Compare the minimum thickness needed for an antireflective coating (n = 1.38) applied to a glass lens in order to eliminate.(a) Blue (450nm), or (b) Red (700nm) reflections for light at normal incidence.
What is the minimum (non-zero) thickness for the air layer between two flat glass surfaces if the glass is to appear dark when 640-nm light is incident normally? What is the glass is to appear bright?
Suppose you viewed the light transmitted through a thin film layered on a flat piece of glass. Draw a diagram, similar to Fig. 24-30 or 24-36, and describe the conditions required for maxima and minima. Consider all possible values of index of refraction. Discuss the relative size of the minima
At what angle above the horizon is the Sun when light reflecting off a smooth lake is polarized most strongly?
At what angle should the axes of two Polaroid’s be placed so as to reduce the intensity of the incident Unpolarized light by an additional factor (after the first Polaroid cuts it in half) of (a) 4,(b) 10,(c) 100?
Unpolarized light falls on two polarizer sheets whose transmission axes are at right angles. A third polarizer is placed between the first two so that its axis makes a 62o angle with the axis of the first polarizer. (a) What fraction of the incident light intensity is transmitted?(b) What is the
Four polarizer’s are placed in succession with their axes vertical, at 30o to the vertical, at 60o to the vertical, and at 90o to the vertical.(a) Calculate what fraction of the incident Unpolarized light is transmitted by the four polarizer’s.(b) Can the transmitted light be decreased by
A laser beam passes through a slit of width 1.0cm and is pointed at the Moon, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 630nm (the red light of a He∙ Ne laser). Estimate the width of the beam when it reaches the Moon.
A series of polarizer are each placed at a 10o interval from the previous polarizer. Unpolarized light is incident on this series of polarizer’s. How many polarizers’ does the light have to go through before it is ¼ of its original intensity?
A thin film of soap (n = 1.34) coats a piece of flat glass (n = 1.52). How thick is the film if it reflects 643-nm red light most strongly when illuminated normally by white light?
Consider two antennas radiating 6.0-MHz radio waves in phase with each other. They are located at points S1 and S2, separated by a distance d = 175m, Fig. 26-61. What are the first three points on the y axis where the signals from the two sources will be out of phase (crests of one meet troughs of
A parallel beam of light containing two wavelengths, 420nm and 650nm enters silicate flint glass equilateral prism (Fig. 24-58).(a) What is the angle between the two beams leaving the prism?(b) Repeat part (a) for a diffraction grating with 6200 lines/cm?
A Lucite Plano convex lens has one flat surface and one with R = 18.4cm. It is used to view and object located 66.0cm away from the lens, which is a mixture of red and yellow. The index of refraction of the Lucite is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the
A free electron is located in the field of a monochromatic light wave. The intensity of light is I = 150 W/m 2, its frequency is w = 3.4.1016 s –1. Find: (a) The electron's oscillation amplitude and its velocity amplitude; (b) The ratio Fm/Fe, where Fm and Fe are the amplitudes of forces with
An electromagnetic wave of frequency w propagates in dilute plasma. The free electron concentration in plasma is equal to no. Neglecting the interaction of the wave and plasma ions, find: (a) The frequency dependence of plasma permittivity; (b) How the phase velocity of the electromagnetic wave
Find the free electron concentration in ionosphere if its refractive index is equal to n = 0.90 for radio waves of frequency v = 100 MHz.
Assuming electrons of substance to be free when subjected to hard X-rays, determine by what magnitude the refractive index of graphite differs from unity in the case of X-rays whose wavelength in vacuum is equal to λ = 50 pm.
An electron experiences a quasi-elastic force kx and a "friction force" yx in the field of electromagnetic radiation. The E-component of the field varies as E = E o cos cot. Neglecting the action of the magnetic component of the field, find: (a) The motion equation of the electron; (b) The mean
In some cases permittivity of substance turns out to be a complex or a negative quantity, and refractive index, respectively, a complex (n' = n + ix) or an imaginary (n' = ix) quantity. Write the equation of a plane wave for both of these cases and find out the physical meaning of such refractive
A sounding of dilute plasma by radio waves of various frequencies reveals that radio waves with wave- lengths exceeding λo = 0.75 m experience total internal reflection. Find the free electron concentration in that plasma.
Using the definition of the group velocity u, derive Rayleigh's formula (5.5d).Demonstrate that in the vicinity of λ + λ ' the velocity u is equal to the segment v' cut by the tangent of the curve v (λ) at the point λ' (Fig. 5.36).
In a certain medium the relationship between the group and phase velocities of an electromagnetic wave has the form uv = c2, where c is the velocity of light in vacuum. Find the dependence of permittivity of that medium on wave frequency, ε (w).
The refractive index of carbon dioxide at the wavelengths 509, 534, and 589 nm is equal to 1.647, 1.640, and 1.630 respectively. Calculate the phase and group velocities of light in the vicinity of λ = 534 rim.
A train of plane light waves propagates in the medium where the phase velocity v is a linear function of wavelength: v = bλ, where a and b are some positive constants. Demonstrate that in such a medium the shape of an arbitrary train of light waves is restored after the time interval τ =
A beam of natural light of intensity Io falls on a system of two crossed Nicol prisms between which a tube filled with certain solution is placed in a longitudinal magnetic field of strength H. The length of the tube is l, the coefficient of linear absorption of solution is ×, and the Verdet
A plane monochromatic light wave of intensity Io falls normally on a plane-parallel plate both of whose surfaces has a reflection coefficient p. Taking into account multiple reflections, find the intensity of the transmitted light if (a) The plate is perfectly transparent, i.e. the absorption is
Two plates, one of thickness dl = 3.8 mm and the other of thickness d2 = 9.0 ram, are manufactured from a certain substance. When placed alternately in the way of monochromatic light, the first transmits τ1 = 0.84 fraction of luminous flux and the second, τ2 = 0.70. Find the coefficient
A beam of monochromatic light passes through a pile of N = 5 identical plane-parallel glass plates each of thickness 1 = 0.50 cm. The coefficient of reflection at each surface of the plates is p = 0.050. The ratio of the intensity of light transmitted through the pile of plates to the intensity of
A beam of monochromatic light falls normally on the surface of a plane-parallel plate of thickness l. The absorption coefficient of the substance the plate is made of varies linearly along the normal to its surface from x1 to x2. The coefficient of reflection at each surface of the plate is equal
A beam of light of intensity I o falls normally on a transparent plane-parallel plate of thickness l. The beam contains all the wavelengths in the interval from λ1 to λ2 of equal spectral intensity. Find the intensity of the transmitted beam if in this wavelength interval the absorption
A light filter is a plate of thickness d whose absorption coefficient depends on wavelength λ, as x(λ) = a(1 – λ/ λ0)2cm –1, where a and λo are constants. Find the pass band ∆λ, of this light filter, that is the band at whose edge the attenuation of light is

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Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

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