Problems in General Physics → Optics → Photometry and Geometrical Optics
5.1. Making use of the spectral response curve for an eye (see Fig. 5.1), find:
5.2. A point isotropic source emits a luminous flux Φ = 10 lm with wavelength λ = 0.59 μm. Find the peak strength values of electric and magnetic fields in the luminous flux at a distance r = 1.0 m from the source. Make use of the curve illustrated in Fig. 5.1.
5.3. Find the mean illuminance of the irradiated part of an opaque sphere receiving
5.4. Determine the luminosity of a surface whose luminance depends on direction as L = L0 cos θ, where θ is the angle between the radiation direction and the normal to the surface.
5.5. A certain luminous surface obeys Lambert's law. Its luminance is equal to L. Find:
5.6. 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 = 1.6*104 cd/m2. At what height over the table should the illuminant be suspended to provide maximum illuminance at the circumference of the table? How great will that illuminance be? The illuminant is assumed to be a point source.
5.7. 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 of the table is the same. Find the function I(θ), where θ is the angle between the radiation direction and the vertical, as well as the luminous flux reaching the table if I(0) = I0 = 100 cd.
5.9. 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 direction.
5.10. 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.
5.11. An illuminant shaped as a plane horizontal disc of radius R = 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 E0 = 70 lx. Assuming the source to obey Lambert's law, find its luminosity.
5.12. 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/m2 and is independent of direction. Find the illuminance of the floor directly below the lamp.
5.16. Two optical media have a plane boundary between them. Suppose θ1cr is the critical angle of incidence of a beam and θ1 is the angle of incidence at which the refracted beam is perpendicular to the reflected one (the beam is assumed to come from an optically denser medium). Find the relative refractive index of these media if sin θ1cr/sin θ1 = η = 1.28.
5.17. A light beam falls upon a plane-parallel glass plate d=6.0 cm in thickness. The angle of incidence is θ = 60°. Find the value of deflection of the beam which passed through that plate.
5.21. The least deflection angle of a certain glass prism is equal to its refracting angle. Find the latter.
5.24. A light ray composed of two monochromatic components passes through a trihedral prism with refracting angle θ = 60°. Find the angle Δα between the components of the ray after its passage through the prism if their respective indices of refraction are equal to 1.515 and 1.520. The prism is oriented to provide the least deflection angle.
5.33. Find the optical power and the focal lengths
5.34. By means of plotting find:
5.35. 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 Δl = 18 cm. By what distance should the object be shifted for its image to become sharp again?
5.37. 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 transverse dimension of the object if at one position of the lens the image dimension equals h' = 2.0 mm and at the other, h" = 4.5 mm.
5.42. Figure 5.9 illustrates an aligned system consisting of three thin lenses. The system is located in air. Determine:
5.52. 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 means of plotting find: