Worksheet: Two-Slit Interference

In this worksheet, we will practice calculating the positions of points of maximum and minimum intensity in interference patterns generated by double-slits.

Q1:

Light passes through a sheet in which there are two parallel narrow slits 12.8 Ξm apart. The light from the slits is incident on a screen parallel to the sheet, where a pattern of light and dark fringes is observed. A line ðŋ runs perpendicular to the surface of the sheet and the direction of the slits. The line ðŋ intersects the central bright fringe of the pattern on the screen. The angle between ðŋ and a line that intersects the center of the bright fringe closest to the central bright fringe is 3 . 0 9 ∘ . What is the wavelength of the light? Give your answer to three significant figures.

Q2:

Light with a wavelength of 636 nm passes through a sheet in which there are two parallel narrow slits. The light from the slits is incident on a screen parallel to the sheets, 1.08 m away, where a pattern of light and dark fringes is observed. A line ðŋ runs perpendicular to the surface of the sheet and the direction of the slits. The line ðŋ intersects the central bright fringe of the pattern on the screen. The distance on the screen from ðŋ to the center of the bright fringe nearest to the central bright fringe is 6.11 cm. What is the distance between the slits?

  • A 1 . 0 8 × 1 0 ïŠą ïŠŦ m
  • B 1 . 1 2 × 1 0 ïŠą ïŠŦ m
  • C 6 . 3 6 × 1 0 ïŠą ïŠŦ m
  • D 3 . 3 6 × 1 0 ïŠą ïŠŦ m
  • E 5 6 . 1 × 1 0 ïŠą ïŠŦ m

Q3:

Light with a wavelength of 625 nm passes through a sheet in which there are two parallel narrow slits. The light from the slits is incident on a screen parallel to the sheet, where a pattern of light and dark fringes is observed. A line ðŋ runs perpendicular to the surface of the sheet and the direction of the slits. The line ðŋ intersects the central bright fringe of the pattern on the screen. The angle between ðŋ and a line that intersects the center of the bright fringe closest to the central bright fringe is 2 . 6 7 ∘ . What distance separates the slits on the sheet? Give your answer to three significant figures.

Q4:

Light with a wavelength of 597 nm passes through a sheet in which there are two parallel narrow slits 7.64 Ξm apart. The light from the slits is incident on a screen parallel to the sheet, where a pattern of light and dark fringes is observed. A line ðŋ runs perpendicular to the surface of the sheet and the direction of the slits, intersecting the central bright fringe of the pattern on the screen. Two lines, line I and line II, intersect ðŋ at the position of the sheet. Line I intersects the center of the dark fringe closest to the central bright fringe and line II intersects the center of the bright fringe closest to the central bright fringe. What is the angle between line I and line II? Give your answer to three significant figures.

Q5:

Which of the following formulas correctly relates the angle 𝜃 at which light with a wavelength 𝜆 emerges from a pair of narrow slits separated by a distance 𝑑 to the order 𝑛 of a bright fringe of an interference pattern produced by the light on a screen?

  • A s i n 𝜃 = 𝑛 𝜆 𝑑
  • B 𝑑 𝜆 = 𝑛 𝜃 s i n
  • C s i n 𝜃 = 𝑑 𝑛 𝜆
  • D 𝑑 𝜃 = 𝑛 𝜆 s i n
  • E 𝑑 = 𝑛 𝜆 𝜃 s i n

Q6:

Light with a wavelength of 675 nm passes through a sheet in which there are two parallel narrow slits 10.5 Ξm apart. The light from the slits is incident on a screen parallel to the sheet, where a pattern of light and dark fringes is observed. A line ðŋ runs perpendicular to the surface of the sheet and the direction of the slits. The line ðŋ intersects the central bright fringe of the pattern on the screen. What is the angle between ðŋ and a line that intersects the center of the bright fringe closest to the central bright fringe? Give your answer to three significant figures.

Q7:

Light with a wavelength of 604 nm passes through a sheet in which there are two parallel narrow slits 9.44 Ξm apart. The light from the slits is incident on a screen parallel to the sheets, 1.25 m away, where a pattern of light and dark fringes is observed. A line ðŋ runs perpendicular to the surface of the sheet and the direction of the slits. The line ðŋ intersects the central bright fringe of the pattern on the screen. What is the distance on the screen from ðŋ to the center of the bright fringe nearest to the central bright fringe?

Q8:

Which of the following formulas correctly relates 𝜆 , the wavelength of light that emerges from a pair of narrow slits; 𝑠 , the separation between the slits; 𝑑 , the distance from the center of an interference pattern produced by the light on a screen; and 𝐷 , the distance from the slits to a bright fringe in the pattern of order 𝑛 ?

  • A 𝑠 = 𝑛 𝜆 𝐷 𝑑
  • B 𝑠 = 𝑛 𝜆 𝑑 𝐷
  • C 𝑠 = 𝜆 𝐷 𝑛 𝑑
  • D 𝑠 = 𝑛 𝜆 𝑑 𝐷
  • E 𝑠 = 𝑛 𝑑 𝐷 𝜆

Q9:

Light passes through a sheet in which there are two parallel narrow slits, 5.28 Ξm apart. The light from the slits is incident on a screen parallel to the sheets, 1.16 m away, where a pattern of light and dark fringes is observed. A line ðŋ runs perpendicular to the surface of the sheet and the direction of the slits. The line ðŋ intersects the central bright fringe of the pattern on the screen. The distance on the screen from ðŋ to the center of the dark fringe nearest to the central bright fringe is 4.77 cm. What is the wavelength of the light?

  • A 5 . 4 3 × 1 0 ïŠą ïŠŪ m
  • B 2 . 1 7 × 1 0 ïŠą  m
  • C 1 . 0 9 × 1 0 ïŠą  m
  • D 4 . 3 4 × 1 0 ïŠą  m
  • E 8 . 6 8 × 1 0 ïŠą  m

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