Essential University Physics 3rd Edition Volume 2 Richard Wolfsonby - Solutions

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To measure the angular distance ψ between the components of a double star by Michelson's method, in front of a telescope's lens a diaphragm was placed, which had two narrow parallel slits separated by an adjustable distance d. While diminishing d, the first smearing of the pattern was observed
A transparent diffraction grating has a period d = 1.50μm. Find the angular dispersion D (in angular minutes per nanometres) corresponding to the maximum of highest order for a spectral line of wavelength λ = 530 nm of light falling on the grating (a) At right angles; (b) At the angle
Light with wavelength λ falls on a diffraction grating at right angles. Find the angular dispersion of the grating as a function of diffraction angle θ.
Light with wavelength λ = 589.0 nm falls normally on a diffraction grating with period d = 2.5μm, comprising N = 10 000 lines. Find the angular width of the diffraction maximum of second order.
Demonstrate that when light falls on a diffraction grating at right angles, the maximum resolving power of the grating cannot exceed the value I/λ, where l is the width of the grating and λ, is the wavelength of light.
Using a diffraction grating as an example, demonstrate that the frequency difference of two maxima resolved according to Rayleigh's criterion is equal to the reciprocal of the difference of propagation times of the extreme interfering oscillations, i.e. δv = 1δ/t.
Light composed of two spectral lines with wavelengths 600.000 and 600.050 nm falls normally on a diffraction grating 10.0 mm wide. At a certain diffraction angle 0 these lines are close to being resolved (according to Rayleigh's criterion). Find θ.
Light falls normally on a transparent diffraction grating of width l = 6.5 cm with 200 lines per millimeter. The spectrum under investigation includes a spectral line with λ = 670.8 nm consisting of two components differing by δλ = 0.015 rim. Find: (a) In what order of the spectrum
With light falling normally on a transparent diffraction grating l0 mm wide, it was found that the components of the yellow line of sodium (589.0 and 589.6 rim) are resolved beginning with the fifth order of the spectrum. Evaluate: (a) The period of this grating; (b) What must be the width of
A transparent diffraction grating of a quartz spectrograph is 25 mm wide and has 250 lines per millimeter. The focal length of an objective in whose focal plane a photographic plate is located is equal to 80 cm. Light falls on the grating at right angles. The spectrum under investigation includes a
The ultimate resolving power λ/δλ of the spectrograph's trihedral prism is determined by diffraction of light at the prism edges (as in the case of a slit). When the prism is oriented to the least deviation angle in accordance with Rayleigh's criterion, λ/δλ
A spectrograph's trihedral prism is manufactured from glass whose refractive index varies with wavelength as n = A + B/λ2, where A and B are constants, with B being equal to 0.010μm 2. Making use of the formula from the foregoing problem, find: (a) How the resolving power of the prism
How wide is the base of a trihedral prism which has the same resolving power as a diffraction grating with 10 000 lines in the second order of the spectrum if |dn/dλ| = 0.10μm–l?
There is a telescope whose objective has a diameter D = 5.0 cm. Find the resolving power of the objective and the minimum separation between two points at a distance l = 3.0 km from the telescope, which it can resolve (assume λ = 0.55μm).
Calculate the minimum separation between two points on the Moon which can be resolved by a reflecting telescope with mirror diameter 5 m. The wavelength of light is assumed to be equal to λ = 0.55μm.
Determine the minimum multiplication of a telescope with diameter of objective D = 5.0 cm with which the resolving power of the objective is totally employed if the diameter of the eye's pupil is do = 4.0 mm.
There is a microscope whose objective's numerical aperture is sin a = 0.24, where a is the half-angle subtended by the objective's rim. Find the minimum separation resolved by this microscope when an object is illuminated by light with wavelength λ = 0.55μm.
Find the minimum magnification of a microscope, whose objective's numerical aperture is sin a = 0.24, at which the resolving power of the objective is totally employed if the diameter of the eye's pupil is d o = 4.0 ram.
A beam of X-rays with wavelength μ falls at a glancing angle 60.0° on a linear chain of scattering centers with period a. Find the angles of incidence corresponding to all diffraction maxima if λ = 2a/5.
A beam of X-rays with wavelength λ = 40 pm falls nor really on a plane rectangular array of scattering centers and produces a system of diffraction maxima (Fig. 5.29) on a plane screen removed from the array by a distance l = 10 cm. Find the array periods a and b along the x and y axes if
A beam of X-rays impinges on a three-dimensional rectangular array whose periods are a, b, and c. The direction of the incident beam coincides with the direction along which the array period is equal to a. Find the directions to the diffraction maxima and the wavelengths at which these maxima will
A narrow beam of X-rays impinges on the natural facet of a NaC1 single crystal, whose density is p = 2.16 g/cm a at a glancing angle a = 60.0°. The mirror reflection from this facet produces a maximum of second order. Find the wavelength of radiation.
A beam of X-rays with wavelength λ = 174 pm falls on the surface of a single crystal rotating about its axis which is parallel to its surface and perpendicular to the direction of the incident beam. In this case the directions to the maxima of second and third order from the system of planes
On transmitting a beam of X-rays with wavelength λ = 17.8 pm through a polycrystalline specimen a system of diffraction rings is produced on a screen located at a distance l = 15 cm from the specimen. Determine the radius of the bright ring corresponding to second order of reflection from the
The temperature of one of the two heated black bodies is T1 = 2500 K. Find the temperature of the other body if the wavelength corresponding to its maximum emissive capacity exceeds by ∆k = 0.50μm the wavelength corresponding to the maximum emissive capacity of the first black body.
The radiosity of a black body is Me, = 3.0 W/cm2. Find the wavelength corresponding to the maximum emissive capacity of that body.
The spectral composition of solar radiation is much the same as that of a black body whose maximum emission corresponds to the wavelength 0.48μm. Find the mass lost by the Sun every second due to radiation. Evaluate the time interval during which the mass of the Sun diminishes by 1 per cent.
Find the temperature of totally ionized hydrogen plasma of density p = 0.10 g/cm3 a at which the thermal radiation pressure is equal to the gas kinetic pressure of the particles of plasma. Take into account that the thermal radiation pressure p = u/3, where u is the space density of radiation
A copper ball of diameter d = 1.2 cm was placed in an evacuated vessel whose walls are kept at the absolute zero temperature. The initial temperature of the ball is To = 300 K. Assuming the surface of the ball to be absolutely black, find how soon its temperature decreases η = 2.0 times.
There are two cavities (Fig. 5.39) with small holes of equal diameters d = 1.0 cm and perfectly reflecting outer surfaces. The distance between the holes is l = 10 cm. A constant temperature T1 = 1700 K is maintained in cavity 1. Calculate the steady-state temperature inside cavity 2. Take into
A cavity of volume V = 1.0 1 is filled with thermal radiation at a temperature T = 1000 K. Find: (a) The heat capacity Cv; (b) The entropy S of that radiation.
Assuming the spectral distribution of thermal radiation energy to obey Wien's formula u (w, T) = Aw3 exp (– aw/T), where a = 7.64ps ∙ K, find for a temperature T = 2000 K the most probable (a) Radiation frequency; (b) Radiation wavelength.
Using Planck's formula, derive the approximate expressions for the space spectral density uw of radiation (a) In the range where hw
Transform Planck's formula for space spectral density uw of radiation from the variable co to the variables v (linear frequency) and λ (wavelength).
Using Planck's formula, find the power radiated by a unit area of a black body within a narrow wavelength interval ∆λ = 1.0 nm close to the maximum of spectral radiation density at a temperature T = 3000 K of the body.
Fig. 5.40 shows the plot of the function g (x) representing a fraction of the total power of thermal radiation falling within the spectral interval from 0 to x. Here x = λ/λm (λm is the wavelength corresponding to the maximum of spectral radiation density). Using this plot,
Making use of Planck's formula, derive the expressions determining the number of photons per i cm 3 of a cavity at a temperature T in the spectral intervals (w, w +dw) and (λ, λ+ dλ,).
An isotropic point source emits light with wavelength λ = 589 nm. The radiation power of the source is P = 10 W. Find: (a) The mean density of the flow of photons at a distance r = 2.0 m from the source; (b) The distance between the source and the point at which the mean concentration of
From the standpoint of the corpuscular theory demonstrate that the momentum transferred by a beam of parallel light rays per unit time does not depend on its spectral composition but depends only on the energy flux Фe
A laser emits a light pulse of duration τ = 0.13 ms and energy E = 10 J. Find the mean pressure exerted by such a light pulse when it is focused into a spot of diameter d = 10μm on a surface perpendicular to the beam and possessing a reflection coefficient p = 0.50.
A short light pulse of energy E = 7.5 J falls in the form of a narrow and almost parallel beam on a mirror plate whose reflection coefficient is p = 0.60. The angle of incidence is 30°. In terms of the corpuscular theory find the momentum transferred to the plate.
A plane light wave of intensity I = 0.20 W/cm2 falls on a plane mirror surface with reflection coefficient p = 0.8. The angle of incidence is 45°. In terms of the corpuscular theory find the magnitude of the normal pressure exerted by light on that surface.
A plane light wave of intensity I = 0.70 W/cm2 illuminates a sphere with ideal mirror surface. The radius of the sphere is R = 5.0 cm. From the standpoint of the corpuscular theory find the force that light exerts on the sphere.
An isotropic point source of radiation power P is located on the axis of an ideal mirror plate. The distance between the source and the plate exceeds the radius of the plate η-fold. In terms of the corpuscular theory find the force that light exerts on the plate.
In a reference frame K a photon of frequency co falls normally on a mirror approaching it with relativistic velocity V. Find the momentum imparted to the mirror during the reflection of the photon (a) In the reference frame fixed to the mirror; (b) In the frame K.
A small ideal mirror of mass m = 10 mg is suspended by a weightless thread of length l = 10 cm. Find the angle through which the thread will be deflected when a short laser pulse with energy E = 13J is shot in the horizontal direction at right angles to the mirror. Where does the mirror get its
A photon of frequency coo is emitted from the surface of a star whose mass is M and radius R. Find the gravitational shift of frequency ∆w/ w0 of the photon at a very great distance from tile star.
A voltage applied to an X-ray tube being increased η = 1.5 times, the short-wave limit of an X-ray continuous spectrum shifts by ∆λ= 26 pro. Find the initial voltage applied to the tube.
A narrow X-ray beam falls on a NaC1 single crystal. The least angle of incidence at which the mirror reflection from the system of crystallographic planes is still observed is equal to a = 4.1°. The interplanar distance is d = 0.28 nm. How high is the voltage applied to the X-ray tube?
Find the wavelength of the short-wave limit of an X-ray continuous spectrum if electrons approach the anticathode of the tube with velocity v = 0.85 c, where c is the velocity of light.
Find the photoelectric threshold for zinc and the maximum velocity of photoelectrons liberated from its surface by electromagnetic radiation with wavelength 250 nm.
Illuminating the surface of a certain metal alternately with light of wavelengths λ1 = 0.35μm and λ2 = 0.54μm, it was found that the corresponding maximum velocities of photoelectrons differ by a factor η = 2.0. Find the work function of that metal.
Up to what maximum potential will a copper ball, remote from all other bodies, be charged when irradiated by electromagnetic radiation of wavelength λ = 140 nm?
Find the maximum kinetic energy of photoelectrons liberated from the surface of lithium by electromagnetic radiation whose electric component varies with time as E = a (1 + cos wt) cos wot, where a is a constant, w = 6.0 ∙ 1014 s–1 and wo = 3-60 ∙ 1015 s –1.
Electromagnetic radiation of wavelength λ = 0.30μm falls on a photocell operating in the saturation mode. The corresponding spectral sensitivity of the photocell is J = 4.8 mA/W. Find the yield of photoelectrons, i.e. the number of photoelectrons produced by each incident photon.
There is a vacuum photocell whose one electrode is made of cesium and the other of copper. Find the maximum velocity of photoelectrons approaching the copper electrode when the cesium electrode is subjected to electromagnetic radiation of wavelength 0.22μm and the electrodes are shorted
A photoelectric current emerging in the circuit of a vacuum photocell when its zinc electrode is subjected to electromagnetic radiation of wavelength 262 nm is cancelled if an external decelerating voltage 1.5 V is applied. Find the magnitude and polarity of the outer contact potential difference
Compose the expression for a quantity whose dimension is length, using velocity of light c, mass of a particle m, and Planck's constant h. What is that quantity?
Using the conservation laws, demonstrate that a free electron cannot absorb a photon completely.
Explain the following features of Compton scattering of light by matter: (a) The increase in wavelength ∆λ is independent of the nature of the scattering substance; (b) The intensity of the displaced component of scattered light grows with the increasing angle of scattering and with
A narrow monochromatic X-ray beam falls on a scattering substance. The wavelengths of radiation scattered at angles 01 = 60° and 02 = 120° differ by a factor η = 2.0. Assuming the free electrons to be responsible for the scattering, find the incident radiation wavelength.
A photon with energy hw = 1.00 MeV is scattered by a stationary free electron. Find the kinetic energy of a Compton electron if the photon's wavelength changed by η = 25% due to scattering.
A photon of wavelength λ = 6.0 pm is scattered at right angles by a stationary free electron. Find: (a) The frequency of the scattered photon; (b) The kinetic energy of the Compton electron.
A photon with energy hw = 250 keV is scattered at an angle 0 = 120° by a stationary free electron. Find the energy of the scattered photon.
A photon with momentum p = 1.02 MeV/c, where c is the velocity of light, is scattered by a stationary free electron, changing in the process its momentum to the value p’ = 0.255 MeV/c. At what angle is the photon scattered?
A photon is scattered at an angle 0 = 120° by a stationary free electron. As a result, the electron acquires a kinetic energy T = 0.45 MeV. Find the energy that the photon had prior to scattering.
Find the wavelength of X-ray radiation if the maximum kinetic energy of Compton electrons is T max = 0.19 MeV.
A photon with energy hw = 0.15 MeV is scattered by a stationary free electron changing its wavelength by ∆λ = 3.0 pm. Find the angle at which the Compton electron moves.
A photon with energy exceeding η = 2.0 times the rest energy of an electron experienced a head-on collision with a stationary free electron. Find the curvature radius of the trajectory of the Compton electron in a magnetic field B = 0.12 T. The Compton electron is assumed to move at right
Having collided with a relativistic electron, a photon is deflected through an angle 0 = 60 ° while the electron stops. Find the Compton displacement of the wavelength of the scattered photon.
Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point 11.5cm from their point of inter-section, as shown in Fig. 3338 for what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is 28.0cm long) after
Three plane mirrors intersect at right angles. A beam of laser light strikes the first of them at an angle ? with respect to the normal (Fig. 33.39).(a) Show that when this ray is reflected off of the other two mirrors and crosses the original ray, the angle a between these two rays will be a =
A beam of light has a wavelength of 650 run in vacuum.(a) What is the speed of this light in a liquid whose index of refraction at this wavelength is 1.47? (b) What is the wavelength of these waves in the liquid?
Light with a frequency of 5.80 x 1014 Hz travels in a block of glass that bas an index of refraction of 1.52. What is the wavelength of the light? (a) In vacuum and (b) In the glass?
A light beam travels at 1.94 x 108 m/s in quartz. The wavelength of the light in quartz is 355 nm. (a) What is the index of refraction of quartz at this wavelength? (b) If this same light travels through air, what is its wavelength there?
Light of a certain frequency has a wavelength of 438 run in water. What is the wavelength of this light in benzene?
A parallel beam of light in air makes an angle of 47.5o with the surface of a glass plate having a refractive index of 1.66.(a) What is the angle between the reflected part of the beam and the surface of the glass? (b) What is the angle between the refracted beam and the surface of the glass?
Using a fast-pulsed laser and electronic timing circuitry, you find that light travels 2.50 m within a plastic rod in 11.5 ns. What is the refractive index of the plastic?
Light traveling in air is incident on the surface of a block of plastic at an angle of 62.7o to the normal and is bent so that it makes a 48.1o angle with the normal in the plastic. Find the speed of light in the plastic.
(a) A tank containing methanol has walls 2.50cm thick made of glass of refractive index 1.550. Light from the outside air strikes the glass at a 413o angle wills the normal to the glass. Find the angle the light makes will the normal in the methanol. (b) The tank is emptied and refilled will an
(a) Light passes through three parallel slabs of different thicknesses and refractive indexes. The light is incident in the first slab and finally refracts into the third slab. Show that the middle slab has no effect on the final direction of the light. That is, show that the direction of the light
A horizontal, parallel-sided plate of glass having a refractive index of 1.52 is in contact will the surface of water in a tank. A ray coming from above in air makes an angle of incidence of 35.0" with the normal to the top surface of the glass. (a) What angle does the ray refracted into the water
In a material having an index of refraction n, a light ray has frequency f, wavelength λ, and speed v. What are the frequency, wavelength, and speed of this light? (a) In vacuum and (b) In a material having refractive index n'? In each case, express your answers in terms of only f, λ,
Prove that a ray of light re6ected from a plane mirror rotates through an angle of 2θ when the mirror rotates through an angle 6 about an axis perpendicular to the plane of incidence.
A ray of light is incident on a plane surface separating two sheets of glass will refractive indexes 1.70 and 1.58. The angle of incidence is 62.0o, and the ray originates in the glass with n = 1.70. Compute the angle of refraction.
In Example 33.1 the water-glass interface is horizontal. If instead this interface were tilted 15.0o above the horizontal with the right side higher than the left side, what would be the angle from the vertical of the ray in the glass? (The ray in the water still makes an angle of 60.0o with the
In Example 33.1 the water-glass interface is horizontal. If instead this interface were tilted 15.0o above the horizontal with the right side higher than the left side, what would be the angle from the vertical of the ray in the glass? (The ray in the water still makes an angle of 60.0o with the
A beam of light is traveling inside a solid glass cube having index of refraction 1.53. It strikes the surface of the cube from the inside. (a) H the cube is in air, at what minimum angle with the normal inside the glass will this light not enter the air at this surface?(b) What would be the
The critical angle for total internal reflection at a liquid-air interface is 42.5°. (a) If a ray of light traveling in the liquid has an angle of incidence at the interface of 35.0o, what angle does the refracted ray in the air make with the normal? (b) If a ray of light traveling in air has an
At the very end of Wagner's series of operas Ring of the Nibelung, Brunnhilde takes the golden ring from the finger of the dead Siegfried and throws it into the Rhine, where it sinks to the bottom of the river. Assuming that the ring is small enough compared to the depth of the river to be treated
A ray of light is traveling in a glass cube that is totally immersed in water. You find that if the ray is incident on the glass-water interface at an angle to the normal larger than 48.7°, no light is refracted into the water. What is the refractive index of the glass?
Light is incident along the normal on facing AB of a glass prism of refractive index 1.52, as shown in Fig. 33.41. Find the largest value the angle a can have without any light refracted out of the prism at face AC if(a) The prism is immersed in air and(b) The prism is immersed inwater.
A ray of light in diamond (index of refraction 2.42) is incident on an interface with air. What is the largest angle the ray can make with the normal and not be totally reflected back into the diamond?
A beam of light strikes a sheet of glass at an angle of 57.0o with the normal in air. You observe that red light makes an angle of 38.1° with the normal in the glass, while violet light makes a 36.7° angle.(a) What are the indexes of refraction of this glass for these colors of light? (b) What
A beam of Unpolarized light of intensity 10 passes through a series of ideal polarizing filters with their polarizing directions turned to various angles as shown in Fig. 33.42.(a) What is the light intensity (in terms of I0) at points A, B, and C?(b) H we remove the middle filter, what will be the
Light traveling in water strikes a glass plate at an angle of incidence of 53.0o; part of the beam is reflected and part is refracted. If the reflected and refracted portions make an angle of 90.0o with each other, what is the index of refraction of the glass?
A parallel beam of Unpolarized light in air is incident at an angle of 54.5° (with respect to the normal) on a plane glass surface. The reflected beam is completely linearly polarized. (a) What is the refractive index of the glass? (b) What is the angle of refraction of the transmitted beam?
A parallel beam of Unpolarized light in air is incident at an angle of 54.5° (with respect to the normal) on a plane glass surface. The reflected beam is completely linearly polarized. (a) What is the refractive index of the glass? (b) What is the angle of refraction of the transmitted beam?
A beam of polarized light passes through a polarizing filter. When the angle between the polarizing axis of the filter and the direction of polarization of the light is θ, the intensity of the emerging beam is l. If you now want the intensity to be I/2, what should be the angle (in terms of
The refractive index of a certain glass is 1.66. For what incident angle is light reflected from the surface of this glass completely polarized if the glass is immersed in (a) Air and (b) Water?

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Essential University Physics 3rd Edition Volume 2 Richard Wolfsonby - Solutions

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