Worksheet: Multiple-Slit Interference

In this worksheet, we will practice calculating the light intensities of different wavelengths at variable angles relative to the transmission axis of multiple slits.

Q1:

For a three-slit interference pattern, find the ratio of the peak intensities of a secondary maximum to a principal maximum.

  • A 1 3
  • B 1 2
  • C 1 6
  • D 1 9
  • E 1 8

Q2:

Eight slits equally separated by 0.149 mm are uniformly illuminated by a monochromatic light at 𝜆 = 5 2 3 n m . What is the angular width of the central principal maximum on a screen 2.35 m away?

Q3:

Light of wavelength 500 nm falls normally on 50 slits that are 2 . 5 × 1 0 3 mm wide and spaced 5 . 0 × 1 0 3 mm apart. How many interference fringes lie in the central peak of the diffraction pattern?

Q4:

Ten narrow slits are equally spaced 0.25 mm apart and illuminated with yellow light of wavelength 580 nm.

What is the angular position of the third principal maximum?

What is the angular position of the fourth principal maximum?

What is the separation of the third and fourth principal maxima on a screen 2.0 m from the slits?

  • A 9 . 4 × 1 0 3 m
  • B 2 . 9 × 1 0 3 m
  • C 4 . 6 × 1 0 3 m
  • D 6 . 2 × 1 0 3 m
  • E 7 . 9 × 1 0 3 m

Q5:

The angular width of the central fringe of the interference pattern of some slits illuminated by 730 nm wavelength light varies as the number of slits is varied.

Find the angular width when 25 slits per millimeter are used.

Find the angular width when 55 slits per millimeter are used.

Q6:

A monochromatic light of frequency 6 . 5 × 1 0 1 4 Hz falls on eight slits separated from each other by 0.038 mm. What is the distance between the first-order and third-order maxima of the interference pattern produced on a screen that is 1.3 m from the slits?

Q7:

Ten slits equally separated from each other by 0.132 mm are uniformly illuminated by a monochromatic light of wavelength 534 nm. What is the ratio of the intensity of a secondary maximum to that of the principal maximum in the interference pattern produced?

Q8:

Forty-one narrow slits are equally spaced and separated by 0.290 mm. The slits are illuminated by blue light of wavelength 400 nm. The twenty-fifth secondary maximum of the interference pattern produced is observed.

What is the angular position of this maximum?

What is the ratio of the peak intensity of this maximum to that of the primary maximum?

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