Worksheet: Diffraction Gratings

In this worksheet, we will practice calculating the positions of principal maxima of intensity in diffraction patterns generated by diffraction gratings.

Q1:

A diffraction grating is 12.5 cm long. The slits of the grating are perpendicular to its length. Light of wavelength 625 nm passes through the whole length of the grating. There is an angle of 6 5 . 3 from a line that intersects the center of the grating and the center of the diffraction pattern to a line that intersects the center of the grating and the first-order principal maximum of the diffraction pattern. What is the number of slits in the diffraction grating?

  • A 3 . 6 3 × 1 0
  • B 1 . 8 2 × 1 0
  • C 9 . 1 0 × 1 0
  • D 6 . 2 0 × 1 0
  • E 1 . 2 5 × 1 0

Q2:

There are 250 slits per millimeter along the length of a diffraction grating. Light of wavelength 550 nm passes through the grating. How many principal maxima are contained in the diffraction pattern produced?

Q3:

Light of wavelength 𝜆 passes through a diffraction grating that has slits separated by a distance 𝑑 . The light falls on a screen where a diffraction pattern is produced. Which of the following formulas correctly relates 𝑑 and 𝜆 to the angle 𝜃 from a line that intersects the center of the grating and the center of the diffraction pattern to a line that intersects the center of the grating and a principal maximum of the diffraction pattern of order 𝑚 ?

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

Q4:

White light, consisting of all wavelengths between 400 nm and 700 nm, passes through a diffraction grating and falls onto a screen. The angle 𝜃 is the angle from a line that intersects the center of the grating and the center of the diffraction pattern to a line that intersects the center of the grating and the first-order principal maximum of red light. The angle 𝜃 is the angle from a line that intersects the center of the grating and the center of the diffraction pattern to a line that intersects the center of the grating and the first-order principal maximum of violet light. If 𝜃 is 4 . 5 , find 𝜃 .

Q5:

Monochromatic light passes through a set of equal-width narrow slits that are evenly spaced. The light then falls onto a screen perpendicular to the slits. The diagram shows the intensity distribution of light across the length of the screen. The dashed curve represents the outline of the central maximum of the intensity distribution that is produced by the light passing through only one of the slits, while all the other slits are covered. How many slits did the light pass through?

Q6:

Monochromatic light passes through a set of equal-width narrow slits that are evenly spaced. The light then falls onto a screen perpendicular to the slits. The diagram shows the intensity distribution of light across the length of the screen. The dashed curve represents the outline of the central maximum of the intensity distribution that is produced by the light passing through only one of the slits, while all the other slits are covered. How many slits did the light pass through?

Q7:

Light that contains various wavelengths passes through a diffraction grating and falls onto a screen. 𝜃 is the angle from a line that intersects the center of the grating and the center of the diffraction pattern to a line that intersects the center of the grating and the first-order principal maximum for the longest wavelength of the light. 𝜃 is the angle from a line that intersects the center of the grating and the center of the diffraction pattern to a line that intersects the center of the grating and the first-order principal maximum for the shortest wavelength of the light. 𝜃 is 8 . 2 and 𝜃 is 5 . 5 . Find the ratio of the longest wavelength of the light passing through the grating to the shortest wavelength. Give your answer to two significant figures.

Q8:

Light that contains various wavelengths passes through a diffraction grating and falls onto a screen. 𝜃 = 5 . 2 is the angle from a line that intersects the center of the grating and the center of the diffraction pattern to a line that intersects the center of the grating and the first-order principal maximum for the longest wavelength of the light. 𝜃 = 2 . 3 is the angle from a line that intersects the center of the grating and the center of the diffraction pattern to a line that intersects the center of the grating and the first-order principal maximum for the shortest wavelength of the light. There are 333 slits per millimeter on the diffraction grating. What is the difference between the longest and shortest wavelengths present in the diffracted light?

  • A 1.1 nm
  • B 150 nm
  • C 300 nm
  • D 1.5 nm
  • E 120 nm

Q9:

Monochromatic light passes through a set of equal-width narrow slits that are evenly spaced. The light then falls onto a screen perpendicular to the slits. The diagram shows the intensity distribution of light across the length of the screen. The dashed curve represents the outline of the central maximum of the intensity distribution that is produced by the light passing through only one of the slits, while all the other slits are covered. How many slits did the light pass through?

Q10:

Monochromatic light passes through a set of equal-width narrow slits that are evenly spaced. The light then falls onto a screen perpendicular to the slits. The diagram shows the intensity distribution of light across the length of the screen. The dashed curve represents the outline of the central maximum of the intensity distribution that is produced by the light passing through only one of the slits, while all the other slits are covered. How many slits does the light pass through?

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