34. Wave Optics

A single slit is illuminated by coherent monochromatic light at $680\mathrm{nm}.$ On a screen $2.9\mathrm{m}$ behind the slit, a central bright spot is observed to have a width of $39\mathrm{mm}.$ What is the width of the single slit?

A carbon dioxide laser produces  electromagnetic waves, which pass through a circular aperture with diameter $1.0\mathrm{ mm}.$ What is the approximate width of the laser beam when it strikes a target $3.0\mathrm{ m}$ away?

A single slit is illuminated by coherent monochromatic light at $680\mathrm{nm}$. On a screen $\mathrm{2..9}\mathrm{m}$ behind the slit, a central bright spot is observed to have a width of $39\mathrm{mm}$. What is the width of the single slit?

A single slit experiment is conducted in air using a laser at $532\mathrm{nm}$ and a slit width of $20\mathrm{\mu }\mathrm{m}$. What happens to the fringe spacing if the entire experiment is conducted in water?

A single slit experiment is conducted in air using a laser at $532\mathrm{nm}$ and a slit width of $20\mathrm{\mu }\mathrm{m}$. What happens to the fringe spacing if the slit width is decreased while the distance to the screen and wavelength remain constant?

Parallel rays of green mercury light with a wavelength of 546 nm pass through a slit covering a lens with a focal length of 60.0 cm. In the focal plane of the lens, the distance from the central maximum to the first minimum is 8.65 mm. What is the width of the slit?

Light of wavelength 585 nm falls on a slit 0.0666 mm wide. (a) On a very large and distant screen, how many totally dark fringes (indicating complete cancellation) will there be, including both sides of the central bright spot? Solve this problem without calculating all the angles! (Hint: What is the largest that sin u can be? What does this tell you is the largest that m can be?) (b) At what angle will the dark fringe that is most distant from the central bright fringe occur?

Diffraction occurs for all types of waves, including sound waves. High-frequency sound from a distant source with wavelength 9.00 cm passes through a slit 12.0 cm wide. A microphone is placed 8.00 m directly in front of the center of the slit, corresponding to point O in Fig. 36.5a . The microphone is then moved in a direction perpendicular to the line from the center of the slit to point O. At what distances from O will the intensity detected by the microphone be zero?

A series of parallel linear water wave fronts are traveling directly toward the shore at 15.0 cm/s on an otherwise placid lake. A long concrete barrier that runs parallel to the shore at a distance of 3.20 m away has a hole in it. You count the wave crests and observe that 75.0 of them pass by each minute, and you also observe that no waves reach the shore at +-61.3 cm from the point directly opposite the hole, but waves do reach the shore everywhere within this distance. (a) How wide is the hole in the barrier?

A series of parallel linear water wave fronts are traveling directly toward the shore at 15.0 cm/s on an otherwise placid lake. A long concrete barrier that runs parallel to the shore at a distance of 3.20 m away has a hole in it. You count the wave crests and observe that 75.0 of them pass by each minute, and you also observe that no waves reach the shore at +-61.3 cm from the point directly opposite the hole, but waves do reach the shore everywhere within this distance. (b) At what other angles do you find no waves hitting the shore?

Monochromatic light of wavelength 580 nm passes through a single slit and the diffraction pattern is observed on a screen. Both the source and screen are far enough from the slit for Fraunhofer diffraction to apply. (a) If the first diffraction minima are at +-90.0°, so the central maximum completely fills the screen, what is the width of the slit? (b) For the width of the slit as calculated in part (a), what is the ratio of the intensity at u = 45.0° to the intensity at u = 0?

A slit 0.240 mm wide is illuminated by parallel light rays of wavelength 540 nm. The diffraction pattern is observed on a screen that is 3.00 m from the slit. The intensity at the center of the central maximum (u = 0°) is 6.00 x 10^-6 W/m2. (a) What is the distance on the screen from the center of the central maximum to the first minimum?

A slit 0.240 mm wide is illuminated by parallel light rays of wavelength 540 nm. The diffraction pattern is observed on a screen that is 3.00 m from the slit. The intensity at the center of the central maximum (u = 0°) is 6.00 x 10^-6 W/m2. (b) What is the intensity at a point on the screen midway between the center of the central maximum and the first minimum?

Monochromatic light of wavelength 592 nm from a distant source passes through a slit that is 0.0290 mm wide. In the resulting diffraction pattern, the intensity at the center of the central maximum (u = 0°) is 4.00x10-5 W/m2. What is the intensity at a point on the screen that corresponds to u = 1.20°?

A single-slit diffraction pattern is formed by monochromatic electromagnetic radiation from a distant source passing through a slit 0.105 mm wide. At the point in the pattern 3.25° from the center of the central maximum, the total phase difference between wavelets from the top and bottom of the slit is 56.0 rad. (a) What is the wavelength of the radiation?

A single-slit diffraction pattern is formed by monochromatic electromagnetic radiation from a distant source passing through a slit 0.105 mm wide. At the point in the pattern 3.25° from the center of the central maximum, the total phase difference between wavelets from the top and bottom of the slit is 56.0 rad. (b) What is the intensity at this point, if the intensity at the center of the central maximum is I0?