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physics
light and optics

Questions and Answers of Light and Optics

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
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,
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
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
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
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
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
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)
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
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
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
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
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
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,
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
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
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
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
(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
(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
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
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.
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
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
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)
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
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
(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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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,
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
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
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
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
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
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
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
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
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
(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
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
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
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
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?
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
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
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
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
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
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
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
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
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
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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