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 s i n 𝜃 ≃ 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 s i n 𝜃 ≃ 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 ?

  • A 𝑚 𝜃 = ð‘Ī 𝜆 s i n
  • B ð‘Ī 𝜃 = 𝑚 𝜆 s i n
  • C ð‘Ī = 𝑚 𝜆 𝜃 s i n
  • D s i n 𝜃 = ð‘Ī 𝑚 𝜆
  • E 𝜆 𝜃 = 𝑚 ð‘Ī s i n

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 . 2 4 ∘ . 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 s i n 𝜃 ≃ 𝜃 . What is the width of the slit?

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