Worksheet: Single-Slit Diffraction

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

Q1:

Light of wavelength 475 nm passes through a slit 8.25 Ξm in width and falls onto a screen 4.6 cm in front of the slit, producing a diffraction pattern that has its central maximum at a point directly in front of the slit. The angle 𝜃 that light in the diffraction pattern makes with the line passing through the center of the slit and the center of the diffraction pattern is small enough for sin𝜃≃𝜃. What is the width of the central maximum of the pattern? Answer to two significant figures.

Q2:

Light of wavelength 550 nm passes through a slit 7.55 Ξm in width and falls onto a screen 12.5 cm in front of the slit, producing a diffraction pattern that has its central maximum at a point directly in front of the slit. The angle 𝜃 that light in the diffraction pattern makes with the line passing through the center of the slit and the center of the diffraction pattern is small enough for sin𝜃≃𝜃. What is the distance from the central maximum of the diffraction pattern to the first minimum of the pattern?

Q3:

Light of wavelength 𝜆 passing through a narrow slit of width ð‘Ī falls on a screen where a diffraction pattern is produced. Which of the following formulas correctly relates 𝜆 and ð‘Ī to the angle 𝜃 from a line that intersects the center of the slit and the center of the diffraction pattern to a line that intersects the center of the slit and a minimum of the diffraction pattern of order 𝑚?

  • Að‘Ī𝜃=𝑚𝜆sin
  • B𝜆𝜃=𝑚ð‘Īsin
  • Cð‘Ī=𝑚𝜆𝜃sin
  • D𝑚𝜃=ð‘Ī𝜆sin
  • Esin𝜃=ð‘Ī𝑚𝜆

Q4:

Light passes through a narrow slit and falls onto a screen in front of the slit, producing a diffraction pattern that has its central maximum at a point directly in front of the slit. The angle 𝜃 from a line that intersects the center of the slit and the center of the diffraction pattern to a line that intersects the center of the slit and the second order minimum of the diffraction pattern is 0.24∘. What is the ratio of the width of the slit to the wavelength of the light? Give your answer to two significant figures.

Q5:

Light of wavelength 630 nm passes through a narrow slit and falls onto a screen 15 cm in front of the slit, producing a diffraction pattern that has its central maximum at a point directly in front of the slit. The distance from the central maximum of the diffraction pattern to the first minimum of the pattern is 18 mm. The angle 𝜃 that light in the diffraction pattern makes with the line passing through the center of the slit and the center of the diffraction pattern is small enough for sin𝜃≃𝜃. What is the width of the slit?

Q6:

Light of wavelength 636 nm passes through a slit and falls onto an indefinitely extendable screen in front of the slit, producing a diffraction pattern that has its central maximum at a point directly in front of the slit. No minima are observed in the diffraction pattern for any length that the screen is extended to. What is the greatest possible width of the slit?

Q7:

Light passes through a slit 9.4 Ξm in width and falls onto a screen 42 cm in front of the slit, producing a diffraction pattern that has its central maximum at a point directly in front of the slit. The angle 𝜃 that light in the diffraction pattern makes with the line passing through the center of the slit and the center of the diffraction pattern is small enough for sin𝜃≃𝜃. The distance from the central maximum of the diffraction pattern to the second minimum of the pattern is 23 mm. What is the wavelength of the light?

Q8:

Light of wavelength 400 nm passes through a slit 15.0 Ξm in width and falls onto a screen 12.5 cm in front of the slit, producing a diffraction pattern that has its central maximum at a point directly in front of the slit. The angle 𝜃 that light in the diffraction pattern makes with the line passing through the center of the slit and the center of the diffraction pattern is small enough for sin𝜃≃𝜃. The position of the first minimum of the diffraction pattern is marked on the screen. The light source is then replaced with a source that emits light of wavelength 700 nm.

How far would the screen need to be moved perpendicularly to the line that passes through the center of the slit for the first minimum of the new diffraction pattern to be at the position of the mark made on the screen? Answer to three significant figures.

  • A5.83 mm
  • B3.60 mm
  • C5.00 mm
  • D2.50 mm
  • E9.17 mm

The original 400 nm wavelength light source is again used, replacing the new light source. How far would the screen now need to be moved parallel to the line that passes through the center of the slit for the first minimum of the diffraction pattern to be at the position of the mark made on the screen? Answer to three significant figures.

  • A71.4 mm
  • B34.1 mm
  • C219 mm
  • D93.8 mm
  • E125 mm

Q9:

Light of wavelength 420.0 nm passes through a slit 25.00 Ξm in width and falls onto a screen 33.00 cm in front of the slit, producing a diffraction pattern that has its central maximum at a point directly in front of the slit. The angle 𝜃 is the angle from a line that intersects the center of the slit and the center of the diffraction pattern to a line that intersects a minimum of the diffraction pattern. There is a difference between the distance 𝑑 from the center of the diffraction pattern to the center of the tenth minimum of the diffraction pattern when the small angle approximation that sin𝜃≃𝜃 is used and when it is not used. The difference between the values of 𝑑 obtained with and without using the small angle approximation is Δ𝑑.

Find Δ𝑑. Answer to four significant figures.

Find the ratio of Δ𝑑 to the width of the slit. Answer to four significant figures.

Find the ratio of Δ𝑑 to the wavelength of the light. Answer to four significant figures.

Q10:

Light of wavelength 𝜆 passing through a narrow slit of width ð‘Ī falls on a screen a distance 𝑆 from the slit, where a diffraction pattern is produced. The angle 𝜃 that light in the diffraction pattern makes with the line passing through the center of the slit and the center of the diffraction pattern is small enough for sin 𝜃≃𝜃. Which of the following formulas correctly relates 𝜆, ð‘Ī, 𝑆, and the distance 𝑑 from the center of the diffraction pattern to the center of a minimum of the diffraction pattern of order 𝑚?

  • A𝑑=𝑚𝑆𝜆ð‘Ī
  • B𝑑=𝑆ð‘Ī𝑚𝜆
  • C𝑑=𝑚𝜆𝑆ð‘Ī
  • D𝑑=𝑚𝜆ð‘Ī𝑆
  • E𝑑=𝑆𝜆𝑚ð‘Ī

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