Exam 34: Wave and Particle Optics

Two sources of light illuminate a double slit simultaneously.One has wavelength 570 nm and the second has an unknown wavelength.The m = 5 bright fringe of the unknown wavelength overlaps the M = 4 bright fringe of the light of 570 nm wavelength.What is the unknown wavelength?

A radio telescope 200 m in diameter is used to investigate sources emitting a 21-cm wavelength wave.What is the minimum angular separation of the sources that can be resolved by this system?

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)

If an x-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 20° with a set of planes in a crystal causing first order constructive interference,at what angle will the second order line appear?

A gas of helium atoms (each of mass 6.65 × 10^-27 kg)are at room temperature of 20.0°C.What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10^-34 J • s,the Boltzmann constant is 1.38 × 10^-23 J/K)

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?

A single slit,which is 0.050 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?

In a double-slit experiment,the slit separation is 2.0 mm,and two wavelengths,750 nm and 900 nm,illuminate the slits simultaneously. A screen is placed 2.0 m from the slits. At what distance from the central maximum on the screen will a bright fringe from one pattern first coincide with a bright fringe from the other?

A He-Ne laser,which produces light of wavelength 632.8 nm,is used to calibrate a diffraction grating. If the first-order maximum occurs at 20.5° from the central spot,what is the distance between the slits of the grating?

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?

Certain planes of a crystal of halite have a spacing of 0.399 nm.The crystal is irradiated by a beam of x-rays.First order constructive interference occurs when the beam makes an angle of 20° with the planes.What is the wavelength of the x-rays?

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 is the minimum thickness of the film to see a bright reflection?

A light beam shines through a thin slit and illuminates a distant screen.The central bright fringe on the screen is 1.00 cm wide,as measured between the dark fringes that border it on either side.Which of the following actions would decrease the width of the central bright fringe? (There may be more than one correct choice.)

A certain astronomical telescope has a diameter of 5.60 m.Considering only the limitation due to diffraction,what is the minimum angle of resolution for this telescope at a wavelength of 620 nm?

A diffraction grating is to be used to find the wavelength of the light in the emission spectrum of a gas.The grating spacing is not known,but a light having a known wavelength of 632.8 nm is deflected by 43.2° away from the central maximum in the second order by this grating.Light of the wavelength to be measured is deflected by 48.2° away from the central maximum in the second order.What is the wavelength of this light?

In a photoelectric effect experiment,electrons emerge from a copper surface with a maximum kinetic energy of 1.10 eV when light shines on the surface.The work function of copper is 4.65 eV.Which one of the following values is closest to the wavelength of the light? (h = 6.626 × 10^-34 J • s,c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A slit of width 0.010 mm has light of frequency 5.0 × 10¹⁴ Hz passing through it onto a screen 60 cm away.How wide is the central maximum? (c = 3.00 × 10⁸ m/s)

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)

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (m_el = 9.11 × 10^-31 kg,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10^-19 J)

In the two-slit experiment,monochromatic light of frequency 5.00 × 10¹⁴ Hz passes through a pair of slits separated by 2.20 × 10^-5 m.(c = 3.00 × 10⁸ m/s) (a)At what angle away from the central bright spot does the third bright fringe past the central bright spot occur? (b)At what angle does the second dark fringe occur?