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physics
light and optics

Questions and Answers of Light and Optics

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
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
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
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
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
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
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
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 =
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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.
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
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
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
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
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)
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
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
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
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
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
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
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
(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
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
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
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)
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
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
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
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
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
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,
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,
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
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
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
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
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
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
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
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
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
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
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
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
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

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