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physics
light and optics

Questions and Answers of Light and Optics

A point source of monochromatic light emitting a luminous flux Ф is positioned at the centre of a spherical layer of substance. The inside radius of the layer is a, the outside one is b. The
How many times will the intensity of a narrow X-ray beam of wavelength 20 pm decrease after passing through a lead plate of thickness d = 1.0 mm if the mass absorption coefficient for the given
A narrow beam of X-ray radiation of wavelength 62 pm penetrates an aluminum screen 2.6 cm thick. How thick must a lead screen be to attenuate the beam just as much? The mass absorption coefficients
Find the thickness of aluminum layer which reduces by half the intensity of a narrow monochromatic X-ray beam if the corresponding mass absorption coefficient is μ/p = 0.32 cm2/g.
How many 50%-absorption layers are there in the plate reducing the intensity of a narrow X-ray beam η = 50 times?
Making use of the spectral response curve for an eye (see Fig. 5.1), find: (a) The energy flux corresponding to the luminous flux of 1.0 lm at the wavelengths 0.51 and 0.64 μm; (b) The
A point isotropic source emits a luminous flux Ф = 10 lm with wavelength g = 0.59 μm. Find the peak strength values of electric and magnetic fields in the luminous flux at a distance r =
Find the mean illuminance of the irradiated part of an opaque sphere receiving (a) A parallel luminous flux resulting in illuminance Eo at the point of normal incidence; (b) Light from a point
Determine the luminosity of a surface whose luminance depends on direction as L = Lo cos θ, where θ is the angle between the radiation direction and the normal to the surface.
A certain luminous surface obeys Lambert's law. Its luminance is equal to L. Find: (a) The luminous flux emitted by an element AS of this surface into a cone whose axis is normal to the given
An illuminant shaped as a plane horizontal disc S = 100 cm2 in area is suspended over the centre of a round table of radius R = 1.0 m. Its luminance does not depend on direction and is equal to L =
A point source is suspended at a height h = 1.0 m over the centre of a round table of radius R = 1.0 m. The luminous intensity I of the source depends on direction so that illuminance at all points
A vertical shaft of light from a projector forms a light spot S = 100 cm2 in area on the ceiling of a round room of radius R = 2.0 m. The illuminance of the spot is equal to E = 1000 lx. The
A luminous dome shaped as a hemisphere rests on a horizontal plane. Its luminosity is uniform. Determine the illuminance at the centre of that plane if its luminance equals L and is independent of
A Lambert source has the Form of an infinite plane. Its luminance is equal to L. Find the illuminance of an area element oriented parallel to the given source.
An illuminant shaped as a plane horizontal disc of radius B = 25 cm is suspended over a table at a height h = 75 cm. The illuminance of the table below the centre of the illuminant is equal to Eo =
A small lamp having the form of a uniformly luminous sphere of radius R = 6.0 cm is suspended at a height h = 3.0 m above the floor. The luminance of the lamp is equal to L = 2.0.104 cd/m 2 and is
Write the law of reflection of a light beam from a mirror in vector form, using the directing unit vectors e and e' of the incident and reflected beams and the unit vector n of the outside normal to
Demonstrate that a light beam reflected from three mutually perpendicular plane mirrors in succession reverses its direction.
At what value of the angle of incident 01 is a shaft of light reflected from the surface of water perpendicular to the refracted shaft?
Two optical media have a plane boundary between them. Suppose θ1er is the critical angle of incidence of a beam and θ1 is the angle of incidence at which the refracted beam is perpendicular
A light beam falls upon a plane-parallel glass plate d = 6.0 cm in thickness. The angle of incidence is 0 = 60°. Find the value of deflection of the beam which passed through that plate.
A man standing on the edge of a swimming pool looks at a stone lying on the bottom. The depth of the swimming pool is equal to h. At what distance from the surface of water is the image of the stone
Demonstrate that in a prism with small refracting angle θ the shaft of light deviates through the angle α ≈ (n – 1) θ regardless of the angle of incidence, provided that the
A shaft of light passes through a prism with refracting angle θ and refractive index n. Let α be the diffraction angle of the shaft. Demonstrate that if the shaft of light passes through
The least deflection angle of a certain glass prism is equal to its refracting angle. Find the latter.
Find the minimum and maximum deflection angles for a light ray passing through a glass prism with refracting angle θ = 60°.
A trihedral prism with refracting angle 60° provides the least deflection angle 37° in air. Find the least deflection angle of that prism in water.
A light ray composed of two monochromatic components passes through a trihedral prism with refracting angle θ = 60°. Find the angle Ace between the components of the ray after its passage
Using Fermat's principle derives the laws of deflection and refraction of light on the plane interface between two media.
By means of plotting find:(a) The path of a light ray after reflection from a concave and convex spherical mirrors (see Fig. 5.4, where F is the focal point, 00' is the optical axis);(b) The
Determine the focal length of a concave mirror if: (a) with the distance between an object and its image being equal to l = 15 cm, the transverse magnification β = – 2.0; (b) In a certain
A point source with luminous intensity I0 = 100 cd is positioned at a distance s = 20.0 cm from the crest of a concave mirror with focal length f = 25.0 cm. Find the luminous intensity of the
Proceeding from Fermat's principle derive the refraction formula for paraxial rays on a spherical boundary surface of radius B between media with refractive indices n and n'.
A parallel beam of light falls from vacuum on a surface enclosing a medium with refractive index n (Fig. 5.6). Find the shape of that surface, x (r), if the beam is brought into focus at the point F
A point source is located at a distance of 20 cm from the front surface of a symmetrical glass biconvex lens. The lens is 5.0 cm thick and the curvature radius of its surfaces is 5.0 cm. How far
An object is placed in front of convex surface of a glass piano-convex lens of thickness d = 9.0 cm. The image of that object is formed on the plane surface of the lens serving as a screen. Find: (a)
Find the optical power and the focal lengths (a) Of a thin glass lens in liquid with refractive index no = 1.7 if its optical power in air is Ф0 = 5.0 D; (b) Of a thin symmetrical biconvex
By means of plotting find:(a) The path of a ray of light beyond thin converging and diverging lenses (Fig. 5.7, where 00' is the optical axis, F and F' are the front and rear focal points);(b) The
A thin converging lens with focal length f = 25 cm projects the image of an object on a screen removed from the lens by a distance l=5.0 m. Then the screen was drawn closer to the lens by a distance
A source of light is located at a distance l = 90 cm from a screen, A thin converging lens provides the sharp image of the source when placed between the source of light and the screen at two
A thin converging lens is placed between an object and a screen whose positions are fixed. There are two positions of the lens at which the sharp image of the object is formed on the screen. Find the
A thin converging lens with aperture ratio D: f = 1: 3.5 (D is the lens diameter, f is its focal length) provides the image of a sufficiently distant object on a photographic plate. The object
How does the luminance of a real image depend on diameter D of a thin converging lens if that image is observed? (a) Directly; (b) On a white screen backscattering according to Lambert's law?
There are two thin symmetrical lenses: one is converging, with refractive index n1 = 1.70 and the other is diverging with refractive index n2 = 1.51. Both lenses have the same curvature radius of
Determine the focal length of a concave spherical mirror which is manufactured in the form of a thin symmetric biconvex glass lens one of whose surfaces is silvered. The curvature radius of the lens
Figure 5.9 illustrates an aligned system consisting of three thin lenses. The system is located in air. Determine:(a) The position of the point of convergence of a parallel ray incoming from the left
A Galilean telescope of 10-fold magnification has the length of 55 cm when adjusted to infinity. Determine: (a) The focal lengths of the (telescope's objective and ocular; (b) By what distance the
Find the magnification of a Keplerian telescope adjusted to infinity if the mounting of the objective has a diameter D and the image of that mounting formed by the telescope's ocular has a diameter d.
On passing through a telescope a flux of light increases its intensity η = 4.0 ∙ l04 a times. Find the angular dimension of a distant object if its image formed by that telescope has an
A Keplerian telescope with magnification Γ = 15 was submerged into water which filled up the inside of the telescope. To make the system work as a telescope again within the former dimensions,
At what magnification F of a telescope with a diameter of the objective D = 6.0 cm is the illuminance of the image of an object on the retina not less than without the telescope? The pupil diameter
The optical powers of the objective and the ocular of a microscope are equal to 100 and 20 D respectively. The microscope magnification is equal to 50. What will the magnification of tile microscope
A microscope has a numerical aperture sin a – 0.12, where a is the aperture angle subtended by the entrance pupil of tile microscope. Assuming the diameter of an eye’s s pupil to be equal to do =
Find the positions of the principal planes, the focal and nodal points of a thin biconvex symmetric glass lens with curvature radius of its surfaces equal to R = 7.50 cm. There is air on one side of
An optical system is located in air. Let OO' be its optical axis, F and F' are the front and rear focal points, H and H' are the front and rear principal planes, P and P' are the conjugate points. By
Suppose F and F' are the front and rear focal points of an optical system, and H and H' are its front and rear principal points, by means of plotting find the position of the image, S' of the point S
A telephoto lens consists of two thin lenses, the front converging lens and the rear diverging lens with optical powers Ф1 = + 10 D and Ф2 = – 10 D. Find: (a) The focal length and the
Calculate the positions of the principal planes and focal points of a thick convex-concave glass lens if the curvature radius of the, convex surface is equal to R1 = 10.0 cm and of the concave
An aligned optical system consists of two thin lenses with focal lengths f1 and f2, the distance between the lenses being equal to d. The given system has to be replaced by one thin lens which, at
A system consists of a thin symmetrical converging glass lens with the curvature radius of its surfaces R = 38 cm and a plane mirror oriented at right angles to the optical axis of the lens. The
At what thickness will a thick convex-concave glass lens in air (a) Serve as a telescope provided the curvature radius of its convex surface is ∆R = 1.5 cm greater than that of its concave
Find the positions of the principal planes, the focal length and the sign of the optical power of a thick convex-concave glass lens (a) Whose thickness is equal to d and curvature radii of the
A telescope system consists of two glass balls with radii R1 = 5.0 cm and R2 = 1.0cm. What are the distance between the centers of the balls and the magnification of the system if the bigger ball
Two identical thick symmetrical biconvex lenses are put close together. The thickness of each lens equals the curvature radius of its surfaces, i.e. d = R = 3.0cm. Find the optical power of this
A ray of light propagating in an isotropic medium with refractive index n varying gradually from point to point has a curvature radius p determined by the formula 1/p = ∂/∂N(In n). Where
Find the curvature radius of a ray of light propagating in a horizontal direction close to the Earth's surface where the gradient of the refractive index in air is equal to approximately 3.10–8
Demonstrate that when two harmonic oscillations are added, the time-averaged energy of the resultant oscillation is equal to the sum of the energies of the constituent oscillations, if both of them
By means of plotting find the amplitude of the oscillation resulting from the addition of the following three oscillations of the same direction:
A certain oscillation results from the addition of coherent oscillations of the same direction ∑K = a cos [wt + (k – 1) фl, where k is the number of the oscillation (k = i, 2, ..., N),
A system illustrated in Fig. 5.12 consists of two coherent point sources 1 and 2 located in a certain plane so that their dipole moments are oriented at right angles to that plane. The sources are
A stationary radiating system consists of a linear chain of parallel oscillators separated by a distance d, with the oscillation phase varying linearly along the chain. Find the time dependence of
In Lloyd's mirror experiment (Fig. 5.13) a light wave emitted directly by the source S (narrow slit) interferes with the wave reflect ed from a mirror M. As a result, an interference fringe pattern
Two coherent plane light waves propagating with a divergence angle ψ
Figure 5.14 illustrates the interference experiment with Fresnel mirrors. The angle between the mirrors is a = 12', the distances from the mirrors' intersection line to the narrow slit S and the
A plane light wave falls on Fresnel mirrors with an angle a = 2.0' between them. Determine the wavelength of light if the width of the fringe on the screen ∆x = 0.55 mm.
A lens of diameter 5.0 cm and focal length f = 25.0 cm was cut along the diameter into two identical halves. In the process, the layer of the lens a = 1.00 mm in thickness was lost. Then the halves
The distances from a Fresnel biprism to a narrow slit and a screen are equal to a = 25 cm and b = 100 cm respectively. The refracting angle of the glass biprism is equal to θ = 20'. Find the
A plane light wave with wavelength λ = 0.70μm falls normally on the base of a biprism made of glass (n = 1.520) with refracting angle θ = 5.0°. Behind the biprism (Fig. 5.15) there is
A plane monochromatic light wave falls normally on a diaphragm with two narrow slits separated by a distance d = 2.5 mm. A fringe pattern is formed on a screen placed at a distance l = 100 cm behind
Figure 5.16 illustrates an interferometer used in measurements of refractive indices of transparent substances. Here S is a narrow slit illuminated by monochromatic light with wavelength λ =
An electromagnetic wave falls normally on the boundary between two isotropic dielectrics with refractive indices n1 and n2. Making use of the continuity condition for the tangential components, E and
A parallel beam of white light falls on a thin film whose refractive index is equal to n = 1.33. The angle of indices is θ1 = 52°. What must the film thickness be equal to for the reflected
Find the minimum thickness of a film with refractive index 1.33 at which light with wavelength 0.64μm experiences maximum reflection while light with wavelength 0.40μm is not reflected at
To decrease light losses due to reflection from the glass surface the latter is coated with a thin layer of substance whose refractive index n' = √n, where n is the refractive index of the
Diffused monochromatic light with wavelength λ = 0.60μm falls on a thin film with refractive index n = 1.5. Determine the film thickness if the angular separation of neighbouring maxima
Monochromatic light passes through an orifice in a screen Sc (Fig. 5.17) and being reflected from a thin transparent plate P produces fringes of equal inclination on the screen. The thickness of the
A plane monochromatic light wave with wavelength λ falls on the surface of a glass wedge whose faces form an angle a
Light with wavelength λ = 0.55μm from a distant point source falls normally on the surface of a glass wedge. A fringe pattern whose neighbouring maxima on the surface of the wedge are
The convex surface of a piano-convex glass lens comes into contact with a glass plate. The curvature radius of the lens's convex surface is R, the wavelength of light is equal to λ, Find the
The convex surface of a piano-convex glass lens with curvature radius R = 40 cm comes into contact with a glass plate. A certain ring observed in reflected light has a radius r = 2.5 ram. Watching
At the crest of a spherical surface of a piano-convex lens there is a ground-off plane spot of radius r0 = 3.0 mm through which the lens comes into contact with a glass plate. The curvature radius of
A piano-convex glass lens with curvature radius of spherical surface R = 12.5 cm is pressed against a glass plate. The diameters of the tenth and fifteenth dark Newton's rings in reflected light are
Two piano-convex thin glass lenses are brought into contact with their spherical surfaces. Find the optical power of such a system if in reflected light with wavelength λ, = 0.60μm the
Two thin symmetric glass lenses, one biconvex and the other biconcave, are brought into contact to make a system with optical power Ф = 0.50 D. Newton's rings are observed in reflected light
The spherical surface of a piano-convex lens comes into contact with a glass plate. The space between the lens and the plate is filled up with carbon dioxide. The refractive indices of the lens,
In a two-beam interferometer the orange mercury line composed of two wavelengths λ1 = 576.97nm and λ2 = 579.03 nm is employed. What is the least order of interference at which the sharpness
In Michelson's interferometer the yellow sodium line composed of two wavelengths λ1 = 589.0 nm and λ2 = 589.6 nm was used. In the process of translational displacement of one of the mirrors
When a Fabry-Perot etalon is illuminated by monochromatic light with wavelength λ an interference pattern, the system of concentric rings, appears in the focal plane of a lens (Fig. 5.18). The
A plane monochromatic wave of natural light with intensity Io falls normally on a screen composed of two touching Polaroid half-planes. The principal direction of one Polaroid is parallel, and of the

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