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physics
light and optics

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

A plane monochromatic wave of natural light with intensity Io falls normally on an opaque screen with round hole corresponding to the first Fresnel zone for the observation point P. Find the intensity of light at the point P after the hole was covered with two identical Polaroid’s whose principal
A beam of plane-polarized light falls on a polarizer which rotates about the axis of the ray with angular velocity w = 21 rad/s. Find the energy of light passing through the polarizer per one revolution if the flux of energy of the incident ray is equal to Фo = 4.0mW.
A beam of natural light falls on a system oi N = 6 Nicol prisms whose transmission planes are turned each through an angle ф = 30 ° with respect to that of the foregoing prism. What fraction of luminous flux passes through this system?
Natural light falls on a system of three identical in-line Polaroid’s, the principal direction of the middle Polaroid forming an angle ф = 60° with those of two other Polaroid’s. The maximum transmission coefficient of each Polaroid is equal to τ = 0.81 when plane-polarized light
The degree of polarization of partially polarized light is P = 0.25. Find the ratio of intensities of the polarized component of this light and the natural component.
A Nicol prism is placed in the way of partially polarized beam of light. When the prism is turned from the position of maximum transmission through an angle ф = 60°, the intensity of transmitted light decreased by a factor of η = 3.0. Find the degree of polarization of incident light.
Two identical imperfect polarizer’s are placed in the way of a natural beam of light. When the polarizer’s' planes are parallel, the system transmits η = 10.0 times more light than in the case of crossed planes. Find the degree of polarization of light produced (a) By each polarizer
Two parallel plane-polarized beams of light of equal intensity whose oscillation planes N1 and N2 form a small angle ф between them (Fig. 5.30) fall on a Nicol prism. To equalize the intensities of the beams emerging behind the prism, its principal direction N must be aligned along the
Resorting to the Fresnel equations, demonstrate that light reflected from the surface of dielectric will be totally polarized if the angle of incidence θ1 satisfies the condition tan θ1 = n, where n is the refractive index of the dielectric. What is in this case the angle between the
Natural light falls at the Brewster angle on the surface of glass. Using the Fresnel equations, find (a) The reflection coefficient; (b) The degree of polarization of refracted light.
A plane beam of natural light with intensity Io falls on the surface of water at the Brewster angle. A fraction p = 0.039 of luminous flux is reflected. Find the intensity of the refracted beam.
A beam of plane-polarized light falls on the surface of water at the Brewster angle. The polarization plane of the electric vector of the electromagnetic wave makes an angle ф = 45° with the incidence plane. Find the reflection coefficient.
A narrow beam of natural light falls on the surface of a thick transparent plane-parallel plate at the Brewster angle. As a result, a fraction p = 0.080 of luminous flux is reflected from its top surface. Find the degree of polarization of beams 1-4 (Fig. 5.31)
A narrow beam of light of intensity Io falls on a plane-parallel glass plate (Fig. 5.34) at the Brewster angle. Using the Fresnel equations, find:(a) The intensity of the transmitted beam Io if the oscillation plane of the incident plane-polarized light is perpendicular to the incidence plane;(b)
A narrow beam of natural light falls on a set of N thick plane-parallel glass plates at the Brewster angle. Find: (a) The degree P of polarization of the transmitted beam; (b) What P is equal to when N = l, 2, 5, and 10.
Using the Fresnel equations, find: (a) The reflection coefficient of natural light falling normally on the surface of glass; (b) The relative loss of luminous flux due to reflections of a paraxial ray of natural light passing through an aligned optical system comprising five glass lenses (secondary
A light wave falls normally on the surface of glass coated with a layer of transparent substance. Neglecting secondary reflections, demonstrate that the amplitudes of light waves reflected from the two surfaces of such a laver will be equal under the condition n' = √n, where n' and n are the
A beam of natural light falls on the surface of glass at an angle of 45 °. Using the Fresnel equations, find the degree of polarization of (a) Reflected light; (b) Refracted light.
Using Huygens's principle, construct the wave fronts and the propagation directions of the ordinary and extraordinary rays in a positive uniaxial crystal whose optical axis (a) Is perpendicular to the incidence plane and parallel to the surface of the crystal; (b) Lies in the incidence plane and is
A narrow beam of natural light with wavelength λ = 589 nm falls normally on the surface of a Wollaston polarizing prism made of Iceland spar as shown in Fig. 5.32. The optical axes of the two parts of the prism are mutually perpendicular. Find the angle 6 between the directions of the beams
What kind of polarization has a plane electromagnetic wave if the projections of the vector E on the x and y axes are perpendicular to the propagation direction and are defined by the following equations: (a) Ex = E cos (wt – kz), Ey = E sin (wt – kz); (b) Ex = E cos (wt – kz), Ey = E cos
One has to manufacture a quartz plate cut parallel to its optical axis and not exceeding 0.50 mm in thickness. Find the maximum thickness of the plate allowing plane-polarized light with wavelength λ = 589 nm (a) To experience only rotation of polarization plane; (b) To acquire circular
A quartz plate cut parallel to the optical axis is placed between two crossed Nicol prisms. The angle between the principal directions of the Nicol prisms and the plate is equal to 45°. The thickness of the plate is d = 0.50 ram. At what wavelengths in the interval from 0.50 to 0.60μm is the
White natural light falls on a system of two crossed Nicol prisms having between them a quartz plate 1.50 mm thick, cut parallel to the optical axis. The axis of the plate forms an angle of 45° with the principal directions of the Nicol prisms. The light transmitted through that system was split
A crystalline plate cut parallel to its optical axis is 0.25 mm thick and serves as a quarter-wave plate for a wavelength λ = 530 rim. At what other wavelengths of visible spectrum will it also serve as a quarter-wave plate? The difference of refractive indices for extraordinary and ordinary
A quartz plate cut parallel to its optical axis is placed between two crossed Nicol prisms so that their principle directions form an angle of 45° with the optical axis of the plate. What is the minimum thickness of that plate transmitting light of wavelength λ1 = 643 nm with maximum
A quartz wedge with refracting angle O = 3.5° is inserted between two crossed Polaroids. The optical axis of the wedge is parallel to its edge and forms an angle of 45° with the principal directions of the Polaroids. On transmission of light with wavelength λ = 550 nm through this system, an
Natural monochromatic light of intensity-I o falls on a system of two Polaroids between which a crystalline plate is inserted, cut parallel to its optical axis.The plate introduces a phase difference δ between the ordinary and extraordinary rays. Demonstrate that the intensity of light
Monochromatic light with circular polarization falls normally on a crystalline plate cut parallel to the optical axis. Behind the plate there is a Nicol prism whose principal direction forms an angle ф with the optical axis of the plate. Demonstrate that the intensity of light transmitted
Explain how, using a Polaroid and a quarter-wave plate made of positive uniaxial crystal (ne > no), to distinguish (a) Light with left-hand circular polarization from that with right-hand polarization; (b) Natural light from light with circular polarization and from the composition of natural light
Light with wavelength λ falls on a system of crossed polarizer P and analyzer A between which a Babinet compensator C is inserted (Fig. 5.33). The compensator consists of two quartz wedges with the optical axis of one of them being parallel to the edge, and of the other, perpendicular to it.
Using the tables of the Appendix, calculate the difference of refractive indices of quartz for light of wavelength λ = 589.5 nm with right-hand and left-hand circular polarizations.
Plane-polarized light of wavelength 0.59μm falls on a trihedral quartz prism P (Fig. 5.34) with refracting angle Θ = 30o. Inside the prism light propagates along the optical axis whose direction is shown by hatching. Behind the Polaroid Pol an interference pattern of bright and dark
Natural monochromatic light falls on a system of two crossed Nicol prisms between which a quartz plate cut at right angles to its optical axis is inserted. Find the minimum thickness of the plate at which this system will transmit η = 0.30 of luminous flux if the specific rotation constant of
Light passes through a system of two crossed Nicol prisms between which a quartz plate cut at right angles to its optical axis is placed. Determine the minimum thickness of the plate which allows light of wavelength 436 nm to be completely cut off by the system and transmits half the light of
Plane-polarized light of wavelength 589 nm propagates along the axis of a cylindrical glass vessel filled with slightly turbid sugar solution of concentration 500 g/1. Viewing from the side, one can see a system of helical fringes, with 50 cm between neighbouring dark fringes along the axis.
A Kerr cell is positioned between two crossed Nicol prisms so that the direction of electric field E in the capacitor forms an angle of 45 ° with the principal directions of the prisms. The capacitor has the length l = 10 cm and is filled up with nitrobenzene. Light of wavelength λ =
Monochromatic plane-polarized light with angular frequency w passes through a certain substance along a uniform magnetic field H. Find the difference of refractive indices for right-hand and left-hand components of light beam with circular polarization if the Verdet constant is equal to V.
A certain substance is placed in a longitudinal magnetic field of a solenoid located between two Polaroids. The length of the tube with substance is equal to l = 30 cm. Find the Verdet constant if at a field strength H = 56.5 kA/m the angle of rotation of polarization plane is equal to ф1 = +
A narrow beam of plane-polarized light passes through dextrorotatory positive compound placed into a longitudinal magnetic field as shown in Fig. 5.35. Find the angle through which the polarization plane of the transmitted beam will turn if the length of the tube with the compound is equal to l,
A tube of length l = 26 cm is filled with benzene and placed in a longitudinal magnetic field of a solenoid positioned between two Polaroids. The angle between the principle directions of the Polaroids is equal to 45°. Find the minimum strength of the magnetic field at which light of the
Experience shows that a body irradiated with light with circular polarization acquires a torque. This happens because such a light possesses an angular momentum whose flow density in vacuum is equal to M = I/w), where I is the intensity of light, w is the angular oscillation frequency. Suppose
In the Fizeau experiment on measurement of the velocity of light the distance between the gear wheel and the mirror is 1 = 7.0 kin, the number of teeth is z = 720. Two successive disappearances of light are observed at the following rotation velocities of the wheel: n1 = 283 rps and n2 = 313 rps.
A source of light moves with velocity v relative to a receiver, demonstrate that for v
One of the spectral lines emitted by excited He + ions has a wavelength λ = 410 nm. Find the Doppler shift ∆λ, of that line when observed at an angle 0 = 30° to the beam of moving ions possessing kinetic energy T = 10 MeV.
When a spectral line of wavelength λ = 0.59 pm is observed in the directions to the opposite edges of the solar disc along its equator, there is a difference in wavelengths equal to δλ = 8.0 pm. Find the period of the Sun's revolution about its own axis.
The Doppler Effect has made it possible to discover the double stars which are so distant that their resolution by means of a telescope is impossible. The spectral lines of such stars periodically become doublets indicating that the radiation does come from two stars revolving about their centre of
A plane electromagnetic wave of frequency wo falls normally on the surface of a mirror approaching with a relativistic velocity V. Making use of the Doppler formula, find the frequency of the reflected wave. Simplify the obtained expression for the case V
A radar operates at a wavelength λ = 50.0cm. Find the velocity of an approaching aircraft if the beat frequency between the transmitted signal and the signal reflected from the aircraft is equal to ∆v = 1.00 kHz at the radar location.
Taking into account that the wave phase wt – kx is an invariant, i.e. it retains its value on transition from one inertial frame to another determine how the frequency w and the wave number k entering the expression for the wave phase are transformed. Examine the unidimensional case.
How fast does a certain nebula recede if the hydrogen line λ = 434 nm in its spectrum is displaced by t30 nm toward longer wavelengths?
How fast should a car move for the driver to perceive a red traffic light (λ, ≈ 0.70μtm) as a green one (λ ≈ 0.55μm)?
An observer moves with velocity v1 = ½ c along a straight line. In front of him a source of monochromatic light moves with velocity v2 = ¾ c in the same direction and along the same straight line. The proper frequency of light is equal to wo. Find the frequency of light registered by the Observer.
One of the spectral lines of atomic hydrogen has the wavelength X =656.3 rim. Find the Doppler shift ∆λ of that line when observed at right angles to the beam of hydrogen atoms with kinetic energy T = 1.0 MeV (the transverse Doppler Effect)
A source emitting electromagnetic signals with proper frequency w0 = 3.0∙1010 s–1 moves at a constant velocity v = 0.80 c along a straight line separated from a stationary observer P by a distance l (Fig. 5.37). Find the frequency of the signals perceived by the observer at the moment when
A narrow beam of electrons passes immediately over the surface of a metallic mirror with a diffraction grating with period d = 2.0μm inscribed on it. The electrons move with velocity v, comparable to c, at right angles to the lines of the grating. The trajectory of the electrons can be seen in
A gas consists of atoms of mass m being in thermodynamic equilibrium at temperature T. Suppose wo is the natural frequency of light emitted by the atoms. (a) Demonstrate that the spectral distribution of the emitted light is defined by the formula I∞ = I0e–a(1 - ∞/w0)2. (Io is the
A plane electromagnetic wave propagates in a medium moving with constant velocity V
Aberration of light is the apparent displacement of stars attributable to the effect of the orbital motion of the Earth. The direction to a star in the ecliptic plane varies periodically, and the star performs apparent oscillations within an angle δθ = 41". Find the orbital velocity of
Demonstrate that the angle 0 between the propagation direction of light and the x axis transforms on transition from the reference frame K to K' according to the formula where β = V/c and V is the velocity of the frame K' with respect to the frame K. The x and x' axes of the reference frames
Find the aperture angle of a cone in which all the stars located in the semi-sphere for an observer on the Earth will be visible if one moves relative to the Earth with relativistic velocity V differing by 1.0% from the velocity of light. Make use of the formula of the foregoing problem.
Find the conditions under which a charged particle moving uniformly through a medium with refractive index n emits light (the Vavilov-Cherenkov effect). Find also the direction of that radiation. Consider the interference of oscillations induced by the particle at various moments of time.
Find the lowest values of the kinetic energy of an electron and a proton causing the emergence of Cherenkov's radiation in a medium with refractive index n = 1.60. For what particles is this minimum value of kinetic energy equal to Tmin = 29.6 MeV?
Find the kinetic energy of electrons emitting light in a medium with refractive index n = 1.50 at an angle 0 = 30° to their propagation direction.
A plane light wave falls normally on a diaphragm with round aperture opening the first N Fresnel zones for a point P on a screen located at a distance b from the diaphragm. The wavelength of light is equal to λ. Find the intensity of light Io in front of the diaphragm if the distribution of
A point source of light with wavelength λ = 0.50μm is located at a distance a = 100cm in front of a diaphragm with round aperture of radius r = 1.0 mm. Find the distance b between the diaphragm and the observation point for which the number of Fresnel zones in the aperture equals k = 3.
A diaphragm with round aperture, whose radius r can be varied during the experiment, is placed between a point source of light and a screen. The distances from the diaphragm to the source and the screen are equal to a = 100cm and b = 125 cm. Determine the wavelength of light if the intensity
A plane monochromatic light wave with intensity I0 falls normally on an opaque screen with a round aperture. What is the intensity of light I behind the screen at the point for which the aperture (a) Is equal to the first Fresnel zone; to the internal half of the first zone; (b) Was made equal to
A plane monochromatic light wave with intensity I0 falls normally on an opaque disc closing the first Fresnel zone for the observation point P. What did the intensity of light I at the point P become equal to after (a) Half of the disc (along the diameter) was removed; (b) Half of the external half
A plane monochromatic light wave with intensity I0 falls normally on the surfaces of the opaque screens shown in Fig. 5.20. Find the intensity of light I at a point P(a) Located behind the corner points of screens 1-3 and behind the edge of half-plane 4;(b) For which the rounded-off edge of screens
A plane light wave with wavelength λ = 0.60μm falls normally on a sufficiently large glass plate having a round recess on the opposite side (Fig. 5.2i). For the observation point P that recess corresponds to the first one and a half Fresnel zones. Find the depth h of the recess at which
A plane light wave with wavelength λ and intensity Io falls normally on a large glass plate whose opposite side serves as an opaque screen with a round aperture equal to the first Fresnel zone for the observation point P. In the middle of the aperture there is a round recess equal to half the
A plane light wave with wavelength λ – 0.57μm falls normally on a surface of a glass (n = 1.60) disc which shuts one and a half Fresnel zones for the observation point P. What must the minimum thickness of that disc be for the intensity of light at the point P to be the highest? Take
A plane light wave with wavelength λ = 0.54μm goes through a thin converging lens with focal length f = 50 cm and an aperture stop fixed immediately after the lens, and reaches a screen placed at a distance b = 75 cm from the aperture stop. At what aperture radii has the centre of the
A plane monochromatic light wave falls normally on a round aperture. At a distance b = 9.0 m from it there is a screen showing a certain diffraction pattern. The aperture diameter was decreased η = 3.0 times. Find the new distance b' at which the screen should be positioned to obtain the
(a) The image dimension g' on the plate if the transverse dimension of the source is y = 6.0 mm; (b) The minimum height of irregularities, covering the surface of the ball at random, at which the ball obstructs light. Note. As calculations and experience show, that happens when the height of
A point source of monochromatic light is positioned in front of a zone plate at a distance a = 1.5 m from it. The image of the source is formed at a distance b = 1.0 m from the plate. Find the focal length of the zone plate.
A plane light wave with wavelength λ = 0.60μm and intensity Io falls normally on a large glass plate whose side view is shown in Fig. 5.22. At what height h of the ledge will the intensity of light at points located directly below be?(a) Minimum;(b) Twice as low as Io (the losses due to
A plane monochromatic light wave falls normally on an opaque half-plane. A screen is located at a distance b = 100 cm behind the half-plane. Making use of the Cornu spiral (Fig. 5.19), find: (a) The ratio of intensities of the first maximum and the neighbouring minimum; (b) The wavelength of
A plane light wave with wavelength 0.60μm falls normally on a long opaque strip 0.70 mm wide. Behind it a screen is placed at a distance 100 cm. Using Fig. 5.19, find the ratio of intensities of light in the middle of the diffraction pattern and at the edge of the geometrical shadow.
A plane monochromatic light wave falls normally on a long rectangular slit behind which a screen is positioned at a distance b = 60 cm. First the width of the slit was adjusted so that in the middle of the diffraction pattern the lowest minimum was observed. After widening the slit by ∆h =
A plane light wave with wavelength λ = 0.65μm falls normally on a large glass plate whose opposite side has a long rectangular recess 0.60 mm wide. Using Fig. 5.19, find the depth h of the recess at which the diffraction pattern on the screen 77 cm away from the plate has the maximum
A plane light wave with wave length λ = 0.65μm falls normally on a large glass plate whose opposite side has a ledge and an opaque strip of width a = 0.30 mm (Fig. 5.23). A screen is placed at a distance b = 110 cm from the plate. The height h of the ledge is such that the intensity of
A plane monochromatic light wave of intensity Io falls normally on an opaque screen with a long slit having a semicircular cut on one side (Fig. 5.24). The edge of the cut coincides with the boundary line of the first Fresnel zone for the observation point P. The width of the slit measures 0.90 of
A plane monochromatic light wave falls normally on an opaque screen with a long slit whose shape is shown in Fig. 5.25. Making use of Fig. 5.19, find the ratio of intensities of light at points 1, 2, and 3 located behind the screen at equal distances from it. For point 3 the rounded-off edge of the
A plane monochromatic light wave falls normally on an opaque screen shaped as a long strip with a round hole in the middle. For the observation point P the hole corresponds to half the Fresnel zone, with the hole diameter being η = 1.07 times less than the width of the strip. Using Fig. 5.19,
Light with wavelength k falls normally on a long rectangular slit of width b. Find the angular distribution of the intensity of light in the case of Fraunhofer diffraction, as well as the angular position of minima.
Making use of the result obtained in the foregoing problem find the conditions defining the angular position of maxima of the first, the second, and the third order.
Light with wavelength λ = 0.50μm falls on a slit of width b = 10μm at an angle θ0 = 30° to its normal. Find the angular position of the first minima located on both sides of the central Fraunhofer maximum.
A plane light wave with wavelength λ = 0.60μm falls normally on the face of a glass wedge with refracting angle Θ =15°. The opposite face of the wedge is opaque and has a slit of width b = 10μm parallel to the edge. Find: (a) The angle A0 between the directions to the
A monochromatic beam falls on a reflection grating with period d = 1.0 mm at a glancing angle αo = 1.0% When it is diffracted at a glancing angle α = 3.0° a Fraunhofer maximum of second order occurs. Find the wavelength of light.
Draw the approximate diffraction pattern originating in the case of the Fraunhofer diffraction from a grating consisting of three identical slits if the ratio of the grating period to the slit width is equal to (a) Two; (b) Three.
With light falling normally on a diffraction grating, the angle of diffraction of second order is equal to 45° for a wavelength λ1 = 0.65μm. Find the angle of diffraction of third order for a wave length λ2 = 0.50μm.
Light with wavelength 535 nm falls normally on a diffraction grating, find its period if the diffraction angle 35°corresponds to one of the Fraunhofer maxima and the highest order of spectrum is equal to five.
Find the wavelength of monochromatic light falling normally on a diffraction grating with period d = 2.2μm if the angle between the directions to the Fraunhofer maxima of the first and the second order is equal to ∆0 = 75°.
Light with wavelength 530 nm falls on a transparent diffraction grating with period 1.50μm, find the angle, relative to the grating normal, at which the Fraunhofer maximum of highest order is observed provided the light falls on the grating (a) At right angles; (b) At the angle 60° to the
Light with wavelength λ = 0.60μm falls normally on a diffraction grating inscribed on a plane surface of a piano-convex cylindrical glass lens with curvature radius R = 20cm. The period of the grating is equal to d = 6.0μm. Find the distance between the principal maxima of first
A plane light wave with wavelength λ = 0.50μm falls normally on the face of a glass wedge with an angle O = 30. On the opposite face of the wedge a transparent diffraction grating with period d = 2.00μm is inscribed, whose lines are parallel to the wedge's edge. Find the angles that
A plane light wave with wavelength λ falls normally on a phase diffraction grating whose side view is shown in Fig. 5.26. The grating is cut on a glass plate with refractive index n. Find the depth h of the lines at which the intensity of the central Fraunhofer maximum is equal to zero. What
Figure 5.27 illustrates an arrangement employed in observations of diffraction of light by ultrasound. A plane light wave with wavelength λ = 0.55μm passes through the water-filled tank T in which a standing ultrasonic wave is sustained at a frequency v = 4.7 MHz. As a result of

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