Worksheet: Resolution of Wave Sources

In this worksheet, we will practice defining resolution of objects and relate their separations to gap widths that waves from the objects pass through.

Q1:

Two light sources emit light that passes through a narrow slit 1.89 μm wide. The angle between lines from each of the light sources that intersect at the center of the slit is 0.265 rad. What wavelength of light must the sources emit to be just resolvable according to the Rayleigh criterion from the diffraction patterns that they produce?

  • A2.50×10 m
  • B4.77×10 m
  • C1.00×10 m
  • D7.13×10 m
  • E4.95×10 m

Q2:

Two light sources emit light with a wavelength of 545 nm that passes through a narrow slit that is 4.33 μm wide. The light sources are just resolvable according to the Rayleigh criterion from the diffraction patterns produced. What is the angle between lines from each of the light sources that intersect at the center of the slit?

Q3:

Two light sources emit 482 nm wavelength light that passes through a narrow slit. The light sources are just resolvable according to the Rayleigh criterion from the diffraction patterns they produce. The angle between the lines from each of the light sources that intersect at the center of the slit is 0.177 rad. What is the width of the slit?

  • A1.04×10 m
  • B8.53×10 m
  • C3.32×10 m
  • D2.74×10 m
  • E5.45×10 m

Q4:

Two light sources emit 555 nm wavelength light that passes through a circular opening. The light sources are just resolvable according to the Rayleigh criterion from the diffraction patterns they produce. The angle between the lines from each of the light sources that intersect at the center of the opening is 0.221 rad. What is the diameter of the opening?

  • A1.01×10 m
  • B3.09×10 m
  • C2.06×10 m
  • D2.51×10 m
  • E5.55×10 m

Q5:

Two light sources emit light that passes through a circular opening 2.32 μm in diameter. The angle between lines from each of the light sources that intersect at the center of the opening is 0.325 rad. What wavelength of light must the sources emit to be just resolvable, according to the Rayleigh criterion, from the diffraction patterns that they produce?

  • A7.14×10 m
  • B9.20×10 m
  • C8.71×10 m
  • D6.07×10 m
  • E7.54×10 m

Q6:

Two light sources emit 625 nm wavelength light that passes through a circular opening 5.28 μm in diameter. The light sources are just resolvable according to the Rayleigh criterion by the diffraction patterns they produce. What is the angle between the lines from each of the light sources that intersect at the center of the opening?

Q7:

Two light sources emit 544 nm wavelength light that passes through a circular opening. The light sources are just resolvable according to the Rayleigh criterion. If the circular opening is replaced with a slit that has the same width as the circular opening, what wavelength of light must the light sources emit for them to be just resolvable from the diffraction patterns they produce?

Q8:

555 nm light from two point sources, source 1 and source 2, pass through a slit 975 nm wide. The light passing through the slits falls on a screen, as shown in the diagram, producing overlapping diffraction patterns. The central maximum of the diffraction pattern produced by each of the light sources has the same position on the screen as the first minimum of the pattern produced by the other light source. The sources of light are 2.55 mm behind the slit. What is the distance parallel to the screen between the light sources?

Q9:

The graph shows the change of power with position 𝑥 for two very close, equally bright light sources. The light from each source is symmetrically spread around the position of the center of the object, which is shown by the dashed line. The two light sources cannot be resolved as separate objects, as their light strongly overlaps. Which of the following graphs shows the two light sources at a separation where they are just resolvable as separate objects, according to the Rayleigh criterion? For each graph, the arrows on the 𝑥-axis indicate equal distances.

  • A
  • B
  • C
  • D
  • E

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