Problems in General Physics → Optics → Interference of Light
5.72. A plane light wave falls on Fresnel mirrors with an angle α = 2.0' between them. Determine the wavelength of light if the width of the fringe on the screen Δx = 0.55 mm.
5.74. 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 wavelength of light if the width of the fringe on the screen is Δx = 0.55 mm.
5.76. 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 the diaphragm. By what distance and in which direction will these fringes be displaced when one of the slits is covered by a glass plate of thickness h = 10 μm?
5.77. 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 = 589 nm, 1 and 2 are identical tubes with air of length l = 10.0 cm each, D is a diaphragm with two slits. After the air in tube 1 was replaced with ammonia gas, the interference pattern on the screen Sc was displaced upward by N = 17 fringes. The refractive index of air is equal to n = 1.000277. Determine the refractive index of ammonia gas.
5.79. 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 light to be coloured yellow (λ = 0.60 μm) most intensively?
5.80. Find the minimum thickness of a film with refractive index 1.33 at which light with wavelength 0.64 μm experiences maximum reflection while light with wavelength 0.40 μm is not reflected at all. The incidence angle of light is equal to 30°.
5.81. 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' = sqrt(n), where n is the refractive index of the glass. In this case the amplitudes of electromagnetic oscillations reflected from both coated surfaces are equal. At what thickness of that coating is the glass reflectivity in the direction of the normal equal to zero for light with wavelength λ?
5.87. The convex surface of a plano-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 mm. Watching the given ring, the lens was gradually removed from the plate by a distance Δh = 5.0 μm. What has the radius of that ring become equal to?
5.88. At the crest of a spherical surface of a plano-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 the lens's convex surface is equal to R = 150 cm. Find the radius of the sixth bright ring when observed in reflected light with wavelength λ = 655 nm.
5.89. A plano-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 equal to d1 = 1.00 mm and d2 = 1.50 mm. Find the wavelength of light.