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physics
light and optics

Questions and Answers of Light and Optics

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
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
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
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
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
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
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
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
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
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
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.
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,
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 =
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
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
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
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
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
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
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
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
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
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 =
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
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
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
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 =
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
(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
(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
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"
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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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