# Problems in General Physics → Optics → Diffraction of Light

 5.98. A point source of light with wavelength λ = 0.50 μm is located at a distance a = 100 cm in front of a diaphragm with round aperture of radius r = 1.0 mm. Find the distance b between the diaphragm and the observation point for which the number of Fresnel zones in the aperture equals k = 3. Free solution >> 5.99. 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 screen are equal to a = 100 cm and b = 125 cm. Determine the wavelength of light if the intensity maximum at the centre of the diffraction pattern of the screen is observed at r1 = 1.00 mm and the next maximum at r2 = 1.29 mm. Free solution >> 5.100. 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) is equal to the first Fresnel zone; to the internal half of the first zone; (b) was made equal to the first Fresnel zone and then half of it was closed (along the diameter)? Free solution >> 5.101. 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 equal to after (a) half of the disc (along the diameter) was removed; (b) half of the external half of the first Fresnel zone was removed (along the diameter)? Free solution >> 5.107. 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 η = 3.0 times. Find the new distance b' at which the screen should be positioned to obtain the diffraction pattern similar to the previous one but diminished η times. Free solution >> 5.109. 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 length of the zone plate. Free solution >> 5.121. Light with wavelength λ = 0.50 μm falls on a slit of width b = 10 μm at an angle θ0 = 30° to its normal. Find the angular position of the first minima located on both sides of the central Fraunhofer maximum. Free solution >> 5.124. 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 is equal to (a) two; (b) three. Free solution >> 5.128. Light with wavelength 530 nm falls on a transparent diffraction grating with period 1.50 μm. Find the angle, relative to the grating normal, at which the Fraunhofer maximum of highest order is observed provided the light falls on the grating (a) at right angles; (b) at the angle 60° to the normal. Free solution >> 5.136. Light with wavelength λ = 589.0 nm falls normally on a diffraction grating with period d = 2.5 μm, comprising N = 10000 lines. Find the angular width of the diffraction maximum of second order. Free solution >> 5.139. 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 θ these lines are close to being resolved (according to Rayleigh's criterion). Find θ. Free solution >> 5.140. Light falls normally on a transparent diffraction grating of width l = 6.5 cm with 200 lines per millimetre. The spectrum under investigation includes a spectral line with λ = 670.8 nm consisting of two components differing by δλ = 0.015 nm. Find: (a) in what order of the spectrum these components will be resolved; (b) the least difference of wavelengths that can be resolved by this grating in a wavelength region λ ≈ 670 nm. Free solution >> 5.156. 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 specimen. Determine the radius of the bright ring corresponding to second order of reflection from the system of planes with interplanar distance d = 155 pm. Free solution >>