Exam 17: Wave Optics

A diffraction grating has 6.00 × 10³ lines per centimeter ruled on it. What is the angular separation between the second and the third orders on the same side of the central order when the grating is illuminated with a beam of light of wavelength 550 nm?

Light having a frequency in vacuum of 6.0 × 10¹⁴ Hz enters a liquid of refractive index 2.0. What is the frequency of the light in this liquid? (c = 3.0 × 10⁸ m/s)

When light of wavelength 450 nm falls on a single slit of width 0.30 mm, what is the angular width of the central bright region?

A soap bubble has an index of refraction of 1.33. What minimum thickness of this bubble will ensure maximum reflectance of normally-incident light having a wavelength of 530 nm?

What is the minimum thickness of a soap bubble film with refractive index 1.38 that results in a constructive interference in the reflected light if this film is illuminated by a beam of light of wavelength 610 nm?

Coherent light of wavelength 540 nm passes through a pair of thin slits that are 3.4 × $10 ^ { - 5 }$ m apart. At what angle away from the centerline does the second bright fringe occur?

A diffraction grating is to be used to find the wavelength of the emission spectrum of a gas. The grating spacing is not known, but light of a known wavelength of 632.8 nm is deflected by 43.2° in the second order by this grating. Light of the wavelength to be measured is deflected by 34.9° in the second order. What is the wavelength of the light that is to be measured?

A single thin slit forms a diffraction pattern when illuminated with monochromatic light. The fourth minimum of the pattern occurs at an angle of 32.0° away from the central maximum. At what angle does the fifth minimum occur?

Two very flat glass plates, 16 cm long, are in contact at one end and separated by 0.020 mm at the other end. The space between the plates is occupied by oil with index of refraction 1.45. The refractive index of the glass plates is 1.55. The plates are illuminated at normal incidence with monochromatic light, and fringes are observed. When the monochromatic light has a wavelength of 580 nm, how many bright fringes are visible in the pattern?

When light illuminates a diffraction grating with 7000 lines per centimeter, its second order maximum is at 62.4°. What is the wavelength of the light?

Light of the same wavelength passes through two diffraction gratings. One grating has 4000 lines/cm, and the other one has 6000 lines/cm. Which grating will spread the light through a larger angle in the first-order pattern?

Coherent light of wavelength 575 nm falls on a double-slit and the third-order bright fringe is seen at an angle of 6.5° away from the centerline. How far apart are the double slits?

A single slit, which is 0.0500 mm wide, is illuminated by light of 550 nm wavelength. What is the angular separation between the first two minima on either side of the central maximum?

A light beam with wavelength 500 nm is reflected constructively from a thin layer of oil having index of refraction 1.25. The oil floats on the top of water of index of refraction 1.33. What is the minimum thickness of the layer of oil?

Two radio antennas are 10 km apart on a north-south axis on high mountain tops at the seacoast. The antennas broadcast identical AM radio signals, in phase, at a frequency of 4.70 MHz. A steamship, 200 km offshore, travels toward the north at 15 km/h and passes east of the antennas. A radio on board the ship is tuned to the broadcast frequency. The reception of the radio signal on the ship is a maximum at a given instant. How much later until the next occurrence of maximum reception? (c = 3.00 × 10⁸ m/s)

What is the slit spacing of a diffraction grating necessary so that 600-nm light will produce a first order principal maximum at 25.0° away from the centerline?

Two beams of coherent light start out at the same point in phase and travel different paths to arrive at point P. If the maximum destructive interference is to occur at point P, the two beams must travel paths that differ by

A puddle of water has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the film. If the wavelength of light incident on the film is 560 nm and the indices of refraction of gasoline and water are 1.40 and 1.33, respectively, what must be the minimum thickness of the film to see a bright reflection?

An 18-mm-wide diffraction grating has rulings of 710 lines per millimieter. Monochromatic light of wavelength 506 nm wavelength is incident normally on the grating. What is the largest angle from the centerline at which an intensity maximum is formed?

Light having a wavelength in vacuum of 600 nm enters a liquid of refractive index 2.0. In this liquid, what is the wavelength of the light? (c = 3.0 × 10⁸ m/s)