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 3.09∘. 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?

  • A56.1×10ïŠąïŠŦ m
  • B1.12×10ïŠąïŠŦ m
  • C3.36×10ïŠąïŠŦ m
  • D6.36×10ïŠąïŠŦ m
  • E1.08×10ïŠąïŠŦ 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 2.67∘. 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?

  • A𝑑=𝑛𝜆𝜃sin
  • Bsin𝜃=𝑛𝜆𝑑
  • C𝑑𝜃=𝑛𝜆sin
  • D𝑑𝜆=𝑛𝜃sin
  • Esin𝜃=𝑑𝑛𝜆

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?

  • A𝑠=𝑛𝜆𝑑𝐷
  • B𝑠=𝜆𝐷𝑛𝑑
  • C𝑠=𝑛𝜆𝐷𝑑
  • D𝑠=𝑛𝑑𝐷𝜆
  • E𝑠=𝑛𝜆𝑑𝐷

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?

  • A8.68×10ïŠąïŠ­ m
  • B4.34×10ïŠąïŠ­ m
  • C5.43×10ïŠąïŠŪ m
  • D1.09×10ïŠąïŠ­ m
  • E2.17×10ïŠąïŠ­ m

Q10:

Light with a wavelength of 563 nm passes through a sheet in which there are two parallel narrow slits 8.38 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. How many bright fringes will be present on a screen that can extend, without limit, either side of ðŋ?

Q11:

Light with a wavelength of 588 nm passes through a sheet in which there are two parallel narrow slits, 12.6 Ξm apart. The light from the slits is incident on a screen parallel to the sheet, 1.52 m away, where a pattern of light and dark fringes is observed. The screen is 2.24 m long and its center is aligned with the midpoint between the slits in the sheet. How many bright fringes are observed on the screen?

Q12:

Light of two different wavelengths 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 distance on the screen from ðŋ to the center of the dark fringe nearest to the central bright fringe is 5.55 cm. The distance on the screen from ðŋ to the center of the dark fringe nearest to the central bright fringe is 7.25 cm. What is the ratio of the longer-wavelength light to that of the shorter-wavelength light?

Q13:

An interference pattern produced by two slits separated by 9.87 Ξm is shown in the diagram. The pattern appears on a screen 33.3 cm in front of the slits. What is the wavelength of the light that passes through the slits?

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.