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physics
light and optics

Fundamentals of Ethics for Scientists and Engineers 1st Edition Edmund G. Seebauer, Robert L. Barry - Solutions

A thin film having an index of refraction of 1.5 is surrounded by air. It is illuminated normally by white light and is viewed by reflection. Analysis of the resulting reflected light shows that the wavelengths 360, 450, and 602 nm are the only missing wavelengths in or near the visible portion of
A drop of oil (n = 1.22) floats on water (n = 1.33). When reflected light is observed from above as shown in Figure, what is the thickness of the drop at the point where the second red fringe, counting from the edge of the drop, is observed? Assume red light has a wavelength of 650nm.
A film of oil of index of refraction n = 1.45 rests on an optically flat piece of glass of index of refraction n = 1.6. When illuminated with white light at normal incidence, light of wavelengths 690 nm and 460 nm is predominant in the reflected light. Determine the thickness of the oil film.
A film of oil of index of refraction n = 1.45 floats on water (n = 1.33). When illuminated with white light at normal incidence, light of wavelengths 700 and 500 nm is predominant in the reflected light. Determine the thickness of the oil film.
A Newton’s-ring apparatus consists of a glass lens with radius of curvature R that rests on a flat glass plate as shown in Figure. The thin film is air of variable thickness. The pattern is viewed by reflected light.(a) Show that for a thickness t the condition for a bright (constructive)
A plano-convex glass lens of radius of curvature 2.0 m rests on an optically flat glass plate. The arrangement is illuminated from above with monochromatic light of 520-nm wavelength. The indexes of refraction of the lens and plate are 1.6. Determine the radii of the first and second bright fringe
Suppose that before the lens of Problem 18 is placed on the plate a film of oil of refractive index 1.82 is deposited on the plate. What will then be the radii of the first and second bright fringes?
Two narrow slits separated by 1 mm are illuminated by light of wavelength 600 nm, and the interference pattern is viewed on a screen 2 m away. Calculate the number of bright fringes per centimeter on the screen.
Using a conventional two-slit apparatus with light of wavelength 589 nm, 28 bright fringes per centimeter are observed on a screen 3 m away. What is the slit separation?
Light of wavelength 633 nm from a helium–neon laser is shone normally on a plane containing two slits. The first interference maximum is 82 cm from the central maximum on a screen 12 m away.(a) Find the separation of the slits.(b) How many interference maxima can be observed?
Two narrow slits are separated by a distance d. Their interference pattern is to be observed on a screen a large distance L away.(a) Calculate the spacing y of the maxima on the screen for light of wavelength 500 nm when L = 1 m and d = 1 cm.(b) Would you expect to observe the interference of light
Light is incident at an angle ф with the normal to a vertical plane containing two slits of separation d (Figure). Show that the interference maxima are located at angles θ given by sin θ + sin ф = mλ/d.
White light falls at an angle of 30° to the normal of a plane containing a pair of slits separated by 2.5 μm. What visible wavelengths give a bright interference maximum in the transmitted light in the direction normal to the plane?
Laser light falls normally on three evenly spaced, very narrow slits. When one of the side slits is covered, the first-order maximum is at 0.60° from the normal. If the center slit is covered and the other two are open, find(a) The angle of the first-order maximum and(b) The order number of the
Equation 35-2, d sin θ = mλ, and Equation 35-11, a sin θ = mλ, are sometimes confused. For each equation, define the symbols and explain the equation’s application.
Light of wavelength 600 nm is incident on a long, narrow slit. Find the angle of the first diffraction minimum if the width of the slit is(a) 1 mm,(b) 0.1 mm, (c) 0.01 mm.
The single-slit diffraction pattern of light is observed on a screen a large distance L from the slit. Note from Equation 35-12 that the width 2y of the central maximum varies inversely with the width a of the slit. Calculate the width 2y for L = 2 m, Î» = 500 nm, and(a) a = 0.1 mm,(b) a = 0.01
For a ruby laser of wavelength 694 nm, the end of the ruby crystal is the aperture that determines the diameter of the light beam emitted. If the diameter is 2 cm and the laser is aimed at the moon, 380,000 km away, find the approximate diameter of the light beam when it reaches the moon, assuming
A two-slit Fraunhofer interference–diffraction pattern is observed with light of wavelength 500 nm. The slits have a separation of 0.1 mm and a width of a.(a) Find the width a if the fifth interference maximum is at the same angle as the first diffraction minimum.(b) For this case, how many
A two-slit Fraunhofer interference–diffraction pattern is observed with light of wavelength 700 nm. The slits have widths of 0.01 mm and are separated by 0.2 mm. How many bright fringes will be seen in the central diffraction maximum?
Light of wavelength 550 nm illuminates two slits of width 0.03 mm and separation 0.15 mm.(a) How many interference maxima fall within the full width of the central diffraction maximum?(b) What is the ratio of the intensity of the third interference maximum to the side of the centerline (not
Find the resultant of the two waves E1 = 2 sin ωt and E2 = 3 sin (ωt + 270°).
Find the resultant of the two waves E1 = 4 sin ωt and E2 = 3 sin (ωt + 60°).
At the second secondary maximum of the diffraction pattern of a single slit, the phase difference between the waves from the top and bottom of the slit is approximately 5π. The phasors used to calculate the amplitude at this point complete 2.5 circles. If I0 is the intensity at the central
(a) Show that the positions of the interference minima on a screen a large distance L away from three equally spaced sources (spacing d, with d >> λ) are given approximately byY = nλL/3dWhere n = 1, 2, 4, 5, 7, 8, 10, . . .That is, n is not a multiple of 3.(b) For L = 1 m, λ = 5 × 10–7
(a) Show that the positions of the interference minima on a screen a large distance L away from four equally spaced sources (spacing d, with d >> λ) are given approximately byy = nλL/4dWhere n = 1, 2, 3, 5, 6, 7, 9, 10, . . .That is, n is not a multiple of 4.(b) For L = 2 m, λ = 6 ×
Light of wavelength 480 nm falls normally on four slits. Each slit is 2 μm wide and is separated from the next by 6 μm.(a) Find the angle from the center to the first point of zero intensity of the single–slit diffraction pattern on a distant screen.(b) Find the angles of any bright
Three slits, each separated from its neighbor by 0.06 mm, are illuminated by a coherent light source of wavelength 550 nm. The slits are extremely narrow. A screen is located 2.5 m from the slits. The intensity on the centerline is 0.05 W/m2. Consider a location 1.72 cm from the centerline.(a) Draw
Four coherent sources are located on the y axis at +3λ/4, + λ/4, - λ/4, and -3λ/4. They emit waves of wavelength λ and intensity I0.(a) Calculate the net intensity I as a function of the angle θ measured from the +x axis.(b) Make a polar plot of I(θ).
For single-slit diffraction, calculate the first three values of Ñ„ (the total phase difference between rays from each edge of the slit) that produce subsidiary maxima by(a) Using the phasor model and(b) Setting dI/dÑ„ = 0, where I is given by Equation35-20.
Light of wavelength 700 nm is incident on a pinhole of diameter 0.1 mm.(a) What is the angle between the central maximum and the first diffraction minimum for a Fraunhofer diffraction pattern?(b) What is the distance between the central maximum and the first diffraction minimum on a screen 8 m away?
Two sources of light of wavelength 700 nm are 10 m away from the pinhole of Problem 48. How far apart must the sources be for their diffraction patterns to be resolved by Rayleigh’s criterion?
Two sources of light of wavelength 700 nm are separated by a horizontal distance x. They are 5 m from a vertical slit of width 0.5 mm. What is the least value of x for which the diffraction pattern of the sources can be resolved by Rayleigh's criterion?
The headlights on a small car are separated by 112 cm. At what maximum distance could you resolve them if the diameter of your pupil is 5 mm and the effective wavelength of the light is 550 nm?
You are told not to shoot until you see the whites of their eyes. If their eyes are separated by 6.5 cm and the diameter of your pupil is 5 mm, at what distance can you resolve the two eyes using light of wavelength 550 nm?
(a) How far apart must two objects be on the moon to be resolved by the eye? Take the diameter of the pupil of the eye to be 5 mm, the wavelength of the light to be 600 nm, and the distance to the moon to be 380,000 km.(b) How far apart must the objects on the moon be to be resolved by a telescope
The ceiling of your lecture hall is probably covered with acoustic tile, which has small holes separated by about 6 mm.(a) Using light with a wavelength of 500 nm, how far could you be from this tile and still resolve these holes? The diameter of the pupil of your eye is about 5 mm.(b) Could you
The telescope on Mount Palomar has a diameter of 200 inches. Suppose a double star were 4 lightyears away. Under ideal conditions, what must be the minimum separation of the two stars for their images to be resolved using light of wavelength 550 nm?
The star Mizar in Ursa Major is a binary system of stars of nearly equal magnitudes. The angular separation between the two stars is 14 seconds of arc. What is the minimum diameter of the pupil that allows resolution of the two stars using light of wavelength 550 nm?
A diffraction grating with 2000 slits per centimeter is used to measure the wavelengths emitted by hydrogen gas. At what angles θ in the first-order spectrum would you expect to find the two violet lines of wavelengths 434 and 410 nm?
With the grating used in Problem 58, two other lines in the first-order hydrogen spectrum are found at angles θ1 = 9.72 × 10–2 rad and θ2 = 1.32 × 10–1 rad. Find the wavelengths of these lines.
Repeat Problem 58 for a diffraction grating with 15,000 slits per centimeter.
What is the longest wavelength that can be observed in the fifth-order spectrum using a diffraction grating with 4000 slits per centimeter?
A diffraction grating of 2000 slits per centimeter is used to analyze the spectrum of mercury.(a) Find the angular separation in the first-order spectrum of the two lines of wavelength 579.0 and 577.0 nm.(b) How wide must the beam on the grating be for these lines to be resolved?
A diffraction grating with 4800 lines per centimeter is illuminated at normal incidence with white light (wavelength range 400 nm to 700 nm). For how many orders can one observe the complete spectrum in the transmitted light? Do any of these orders overlap? If so, describe the overlapping regions.
A square diffraction grating with an area of 25 cm2 has a resolution of 22,000 in the fourth order. At what angle should you look to see a wavelength of 510 nm in the fourth order?
Sodium light of wavelength 589 nm falls normally on a 2-cm-square diffraction grating ruled with 4000 lines per centimeter. The Fraunhofer diffraction pattern is projected onto a screen at 1.5 m by a lens of focal length 1.5 m placed immediately in front of the grating. Find(a) The positions of the
The spectrum of neon is exceptionally rich in the visible region. Among the many lines are two at wavelengths of 519.313 nm and 519.322 nm. If light from a neon discharge tube is normally incident on a transmission grating with 8400 lines per centimeter and the spectrum is observed in second order,
Mercury has several stable isotopes, among them 198Hg and 202Hg. The strong spectral line of mercury at about 546.07 nm is a composite of spectral lines from the various mercury isotopes. The wavelengths of this line for 198Hg and 202Hg are 546.07532 and 546.07355 nm, respectively. What must be the
A transmission grating is used to study the spectral region extending from 480 to 500 nm. The angular spread of this region is 12° in third order.(a) Find the number of lines per centimeter.(b) How many orders are visible?
White light is incident normally on a transmission grating and the spectrum is observed on a screen 8.0 m from the grating. In the second-order spectrum, the separation between light of 520- and 590-nm wavelength is 8.4 cm.(a) Determine the number of lines per centimeter of the grating.(b) What is
A diffraction grating has n lines per meter. Show that the angular separation of two lines of wavelengths Î» and Î» + Î”Î» meters isapproximately
When assessing a diffraction grating, we are interested not only in its resolving power R, which is the ability of the grating to separate two close wavelengths, but also in the dispersion D of the grating. This is defined by D = Î”Î¸m/Î”Î» in the mth order.(a) Show that D can be
For a diffraction grating in which all the surfaces are normal to the incident radiation, most of the energy goes into the zeroth order, which is useless from a spectroscopic point of view since in zeroth order all the wavelengths are at 0°. Therefore, modern gratings have shaped, or
In this problem you will derive Equation 35-28 for the resolving power of a diffraction grating containing N slits separated by a distance d. To do this you will calculate the angular separation between the maximum and minimum for some wavelength λ and set it equal to the angular separation of the
In a lecture demonstration, laser light is used to illuminate two slits separated by 0.5 mm, and the interference pattern is observed on a screen 5 m away. The distance on the screen from the centerline to the thirty-seventh bright fringe is 25.7 cm. What is the wavelength of the light?
A long, narrow, horizontal slit lies 1 mm above a plane mirror, which is in the horizontal plane. The interference pattern produced by the slit and its image is viewed on a screen 1 m from the slit. The wavelength of the light is 600 nm.(a) Find the distance from the mirror to the first maximum.(b)
In a lecture demonstration, a laser beam of wavelength 700 nm passes through a vertical slit 0.5 mm wide and hits a screen 6 m away. Find the horizontal length of the principal diffraction maximum on the screen; that is, find the distance between the first minimum on the left and the first minimum
What minimum aperture, in millimeters, is required for opera glasses (binoculars) if an observer is to be able to distinguish the soprano’s individual eyelashes (separated by 0.5 mm) at an observation distance of 25 m? Assume the effective wavelength of the light to be 550 nm.
The diameter of the aperture of the radio telescope at Arecibo, Puerto Rico, is 300 m. What is the resolving power of the telescope when tuned to detect microwaves of 3.2 cm wavelength?
A thin layer of a transparent material with an index of refraction of 1.30 is used as a nonreflective coating on the surface of glass with an index of refraction of 1.50. What should the thickness of the material be for it to be nonreflecting for light of wavelength 600 nm?
A Fabry–Perot interferometer consists of two parallel, half-silvered mirrors separated by a small distance a. Show that when light is incident on the interferometer with an angle of incidence θ, the transmitted light will have maximum intensity when a = (mλ/2) cos θ.
A mica sheet 1.2 μm thick is suspended in air. In reflected light, there are gaps in the visible spectrum at 421, 474, 542, and 633 nm. Find the index of refraction of the mica sheet.
A camera lens is made of glass with an index of refraction of 1.6. This le ns is coated with a magnesium fluoride film (n = 1.38) to enhance its light transmission. This film is to produce zero reflection for light of wavelength 540 nm. Treat the lens surface as a flat plane and the film as a
In a pinhole camera, the image is fuzzy because of geometry (rays arrive at the film through different parts of the pinhole) and because of diffraction. As the pinhole is made smaller, the fuzziness due to geometry is reduced, but the fuzziness due to diffraction is increased. The optimum size of
The Impressionist painter Georges Seurat used a technique called “pointillism,” in which his paintings are composed of small, closely spaced dots of pure color, each about 2 mm in diameter. The illusion of the colors blending together smoothly is produced in the eye of the viewer by diffraction
A Jamin refractometer is a device for measuring or comparing the indexes of refraction of fluids. A beam of monochromatic light is split into two parts, each of which is directed along the axis of a separate cylindrical tube before being recombined into a single beam that is viewed through a
Light of wavelength λ is diffracted through a single slit of width a, and the resulting pattern is viewed on a screen a long distance L away from the slit.(a) Show that the width of the central maximum on the screen is approximately 2Lλ/a.(b) If a slit of width 2Lλ/a is cut in the screen and is
Television viewers in rural areas often find that the picture flickers (fades in and out) as an airplane flies across the sky in the vicinity. The flickering arises from the interference between the signal directly from the transmitter and that reflected to the antenna from the airplane. Suppose
For the situation described in Problem 88, show that the rate of oscillation of the picture’s intensity is a minimum when the airplane is directly above the midpoint between the transmitter and receiving antenna.
A double-slit experiment uses a helium–neon laser with a wavelength of 633 nm and a slit separation of 0.12 mm. When a thin sheet of plastic is placed in front of one of the slits, the interference pattern shifts by 5.5 fringes. When the experiment is repeated under water, the shift is 3.5
Two coherent sources are located on the y axis at +λ/4 and – λ/4. They emit waves of wavelength λ and intensity I0.(a) Calculate the net intensity I as a function of the angle θ measured from the +x axis.(b) Make a polar plot of I(θ).
(Multiple choice)(1)Which of the following pairs of light sources are coherent:(a) Two candles;(b) One point source and its image in a plane mirror;(c) Two pinholes uniformly illuminated by the same point source;(d) Two headlights of a car;(e) Two images of a point source due to reflection from the
1.When destructive interference occurs, what happens to the energy in the light waves?2.The spacing between Newton’s rings decreases rapidly as the diameter of the rings increases. Explain qualitatively why this occurs.
1. If the angle of a wedge-shaped air film such as that in Example 35-2 is too large, fringes are not observed. Why?2. Plane microwaves are incident on a long, narrow metal slit of width 5 cm. The first diffraction minimum is observed at θ = 37°. What is the wavelength of the microwaves?
1. Why must a film used to observe interference colors be thin?2. Suppose that the central diffraction maximum for two slits contains 17 interference fringes for some wavelength of light. How many interference fringes would you expect in the first secondary diffraction maximum?
1. How many interference maxima will be contained in the central diffraction maximum in the diffraction– interference pattern of two slits if the separation d of the slits is 5 times their width a? How many will there be if d = Na for any value of N?2. As the width of a slit producing a single
Sketch(a) The wave function and(b) The probability distribution for the n = 4 state for the finite square-well potential.
Sketch(a) The wave function and(b) The probability distribution for the n = 5 state for the finite square-well potential.
Show that the expectation value = ∫x|ψ|2 dx is zero for both the ground and the first excited states of the harmonic oscillator.
Use the procedure of Example 36-1 to verify that the energy of the first excited state of the harmonic oscillator is E1 = 3/2 hω0.
Show that the normalization constant A0 of Equation 36-23 is A0 = (2mω0/h)1/4.
Find the normalization constant A1 for the wave function of the first excited state of the harmonic oscillator, Equation36-25.
Find the expectation value = ∫x2|ψ|2 dx for the ground state of the harmonic oscillator. Use it to show that the average potential energy equals half the total energy.
Verify that ψ1(x) = A1xe–ax2 is the wave function corresponding to the first excited state of a harmonic oscillator by substituting it into the time-independent Schrödinger equation and solving for a and E.
Find the expectation value = ∫ x2 |ψ|2 dx for the first excited state of the harmonic oscillator.
Classically, the average kinetic energy of the harmonic oscillator equals the average potential energy. We may assume that this is also true for the quantum mechanical harmonic oscillator. Use this condition to determine the expectation value of p2 for the ground state of the harmonic oscillator.
We know that for the classical harmonic oscillator, pav = 0. It can be shown that for the quantum mechanical harmonic oscillator, = 0. Use the results of Problems 4, 6, and 11 to determine the uncertainty product Δx Δp for the ground state of the harmonic oscillator.
A free particle of mass m with wave number k1 is traveling to the right. At x = 0, the potential jumps from zero to U0 and remains at this value for positive x.(a) If the total energy is E = h2k21/2m = 2U0, what is the wave number k2 in the region x > 0? Express your answer in terms of k1 and in
Suppose that the potential jumps from zero to − U0 at x = 0 so that the free particle speeds up instead of slowing down. The wave number for the incident particle is again k1, and the total energy is 2U0.(a) What is the wave number for the particle in the region of positive x?(b) Calculate
Work Problem 13 for the case in which the energy of the incident particle is 1.01U0 instead of 2U0.
Use Equation 36-29 to calculate the order of magnitude of the probability that a proton will tunnel out of a nucleus in one collision with the nuclear barrier if it has energy 6 MeV below the top of the potential barrier and the barrier thickness is 10-15m.
A 10-eV electron is incident on a potential barrier of height 25 eV and width of 1 nm.(a) Use Equation 36-29 to calculate the order of magnitude of the probability that the electron will tunnel through the barrier.(b) Repeat your calculation for a width of 0.1 nm.
A particle is confined to a three-dimensional box that has sides L1, L2 = 2L1, and L3 = 3L1. Give the quantum numbers n1, n2, n3 that correspond to the lowest ten quantum states of this box.
(a) Repeat Problem 19 for the case L2 = 2L1 and L3 = 4L1.(b) What quantum numbers correspond to degenerate energy levels?
A particle moves in a potential well given by U(x, y, z) = 0 for –L/2 < x < L/2, 0 < y < L, and 0 < z < L, and U = ∞ outside these ranges.(a) Write an expression for the ground-state wave function for this particle.(b) How do the allowed energies compare
A particle moves freely in the two-dimensional region defined by 0 ≤ x ≤ L and 0 ≤ y ≤ L.(a) Find the wave function satisfying Schrödinger’s equation.(b) Find the corresponding energies.(c) Find the lowest two states that are degenerate. Give the quantum numbers for this case.(d) Find
What is the next energy level above those found in Problem 24c for a particle in a two-dimensional square box for which the degeneracy is greater than 2?
Show that Equation 36-37 satisfies Equation 36-35 with U = 0, and find the energy of this state.
What is the ground-state energy of ten noninteracting fermions, such as neutrons, in a one-dimensional box of length L?

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