Exam 28: Sources of Magnetic Field

Double-slit interference: In a two-slit experiment, the slit separation is 3.00 × m. The interference pattern is recorded on a flat screen-like detector that is 2.00 m away from the slits. If the seventh bright fringe on the detector is 10.0 cm away from the central fringe, what is the wavelength of the light passing through the slits?

Diffraction grating: What is the angular separation of the two second-order spectral lines having wavelengths 417 nm and 388 nm using a diffraction grating having 456 lines/mm?

Double-slit interference: Two radio antennas are 120 m apart on a north-south line, and they radiate in phase at a frequency of 3.4 MHz. All radio measurements are made far from the antennas. If the east-west reference line passes midway between the two antennas, what is the smallest angle from the antennas, measured north of east, at which constructive interference of two radio waves occurs? (c = 3.00 × 10⁸ m/s)

Diffraction grating: In a diffraction grating experiment, light of 600 nm wavelength produces a first-order maximum 0.350 mm from the central maximum on a distant screen. A second monochromatic source produces a third-order maximum 0.870 mm from the central maximum when it passes through the same diffraction grating. What is the wavelength of the light from the second source?

Thin films: A soap bubble, when illuminated with light of frequency 5.11 × 10¹⁴ Hz, appears to be especially reflective. If it is surrounded by air and if its index of refraction is 1.35, what is the thinnest thickness the soap film can be? (c = 3.00 × 10⁸ m/s)

Thin films: Two extremely flat glass plates, 10.0 cm wide, touch at one end but are separated by a thin wire at the other end, forming a wedge. Light with a wavelength of 450 nm shines almost perpendicularly on the glass and forms fringes which are 1.80 mm apart. What is the diameter of the wire?

Single-slit diffraction: A single slit forms a diffraction pattern with monochromatic light. The 4th minimum of the pattern occurs at an angle of 35° from the central maximum. How many bright bands are on each side of the central maximum?

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

Resolving power: If the diameter of a radar dish is doubled, what happens to its resolving power assuming that all other factors remain unchanged?

Single-slit diffraction: In the figure, a slit 0.30 mm wide is illuminated by light of wavelength 426 nm. A diffraction pattern is seen on a screen 2.8 m from the slit. What is the linear distance on the screen between the first diffraction minima on either side of the central diffraction maximum?

Resolving power: If the headlights on a car are separated by 1.3 m, how far down the road can they be resolved if the angular resolution of the eye is 5.0 × 10^-4 rad and the person has excellent vision?

Diffraction grating: A metallic sheet has a large number of slits, 5.0 mm wide and 20 cm apart, and is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. If the microwave wavelength is 6.0 cm, what is the largest angle away from the central maximum at which an intensity maximum occurs.

Diffraction grating: A metallic sheet has a large number of slits, 5.0 mm wide and 20 cm apart, and is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. What is the smallest microwave frequency for which only the central maximum occurs? (c = 3.00 × 10⁸ m/s)

Single-slit diffraction: If the fifth order minimum in the diffraction pattern of a thin slit is at 40° from the central maximum, what is the highest order minimum in the pattern?

Intensity of double-slit pattern: Light passes through a pair of very thin parallel slits. The resulting interference pattern is viewed far from the slits at various angles θ relative to the centerline coming outward from the midpoint between the slits. The central bright fringe is at θ = 0°. If the central bright fringe has intensity I₀, what is the intensity of the next bright fringe on either side of it?

Thin films: Light of frequency 6.00 × 10¹⁴ Hz illuminates a soap film (n = 1.33) having air on both sides of it. When viewing the film by reflected light, what is the minimum thickness of the film that will give an interference maximum when the light is incident normally on it? (c = 3.00 × 10⁸ m/s)

Single-slit diffraction: A laser beam passes through a thin slit. When the pattern is viewed on a screen 1.25 m past the slit, you observe that the fifth-order dark fringes occur at ±2.41 cm from the central bright fringe. The entire experiment is now performed within a liquid, and you observe that each of the fifth-order dark fringes is 0.790 cm closer to the central fringe than it was in air. What is the index of refraction of this liquid?

Double-slit interference: Light from a 600 nm source goes through two slits 0.080 mm apart. What is the angular separation of the two first order maxima occurring on a screen 2.0 m from the slits?

X-ray diffraction: If an X-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 30° with a set of planes in a crystal causing first order constructive interference, what is the plane spacing?

Diffraction grating: A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, what is the highest order maximum that will appear?