Worksheet: Single-Slit Diffraction

In this worksheet, we will practice calculating light intensities of different wavelengths at variable angles relative to a single-slit's transmission axis.

Q1:

A single slit of width 0.20 mm is illuminated by light of 400 nm wavelength. The diffracted light falls on a screen. In the pattern formed on the screen, the second minimum of the diffracted light is a distance of 2.5 mm from the central maximum. What is the distance between the slit and the screen?

Q2:

Calculate the wavelength of light that produces its first minimum at an angle of 3 6 . 9 when falling on a single slit of width 1.00 μm.

Q3:

At what angle is the first minimum for 550-nm light falling on a single slit of width 1.00 μm?

Q4:

A microwave of an unknown wavelength is incident on a single slit of width 6.0 cm. The angular width of the central peak is found to be 2 5 . Find the wavelength.

Q5:

A single slit of width 3.9 μm is illuminated by light of wavelength 589 nm. Find the light intensity at an angle of 1 5 to the central axis of the transmitted light, expressing the intensity in terms of the intensity of the central maximum.

  • A 0 . 0 5 0 𝐼 𝑜
  • B 0 . 0 3 3 𝐼 𝑜
  • C 0 . 0 6 7 𝐼 𝑜
  • D 0 . 0 4 1 𝐼 𝑜
  • E 0 . 0 7 5 𝐼 𝑜

Q6:

A single slit of width 0.10 mm is illuminated by light of wavelength 576 nm. Find the light intensity at an angle of 1 0 to the central axis of the transmitted light, expressing the intensity in terms of the intensity of the central maximum.

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

Q7:

Find the wavelength of light that has its third minimum at an angle of 4 8 . 6 when it falls on a single slit of width 3.00 μm.

Q8:

Suppose that the central peak of a single-slit diffraction pattern is so wide that the first minima can be assumed to occur at angular positions of ± 9 0 . For this case, what is the ratio of the slit width to the wavelength of the light?

  • A 1 2
  • B 1 2
  • C 1 𝜋
  • D 1 1
  • E 1 4

Q9:

If the separation between the first and the second minima of a single-slit diffraction pattern is 6.00 mm, what is the distance between the screen and the slit? The light wavelength is 500 nm and the slit width is 0.160 mm.

Q10:

A single-slit diffraction pattern for light with a wavelength 𝜆 = 5 8 9 n m is projected onto a screen that is 1.00 m away from a slit of width 0.25 mm.

How far from the centre of the pattern is the centre of the first dark fringe?

  • A 2.1 mm
  • B 1.8 mm
  • C 2.8 mm
  • D 2.4 mm
  • E 3.3 mm

How far from the centre of the pattern is the centre of the second dark fringe?

  • A 4.7 mm
  • B 4.0 mm
  • C 3.3 mm
  • D 2.4 mm
  • E 5.5 mm

Q11:

Monochromatic light of wavelength 530 nm passes through a horizontal single slit of width 1.5 μm in an opaque plate. A screen of dimensions 2 . 0 × 2 . 0 m m is 1.2 m away from the slit.

What is the angle with respect to the centre of the diffraction pattern of the first minimum of intensity observed?

  • A ± 1 3
  • B ± 1 0
  • C ± 1 5
  • D ± 2 0
  • E ± 1 7

What is the angle with respect to the centre of the diffraction pattern of the second minimum of intensity observed?

  • A ± 4 4
  • B ± 4 1
  • C ± 3 8
  • D ± 3 0
  • E ± 4 7

What is the angle with respect to the centre of the diffraction pattern of the first maximum of intensity observed?

  • A ± 9 . 0
  • B ± 2 . 6
  • C 0
  • D ± 5 . 0
  • E ± 7 . 7

What is the angle with respect to the centre of the diffraction pattern of the second maximum of intensity observed?

  • A ± 3 1
  • B ± 3 5
  • C ± 2 8
  • D ± 2 0
  • E ± 2 4

What is the angle with respect to the centre of the diffraction pattern of the third maximum of intensity observed?

  • A ± 5 5
  • B ± 3 3
  • C ± 2 0
  • D ± 6 0
  • E ± 6 7

How wide is the central bright fringe on the screen?

  • A 75 cm
  • B 110 cm
  • C 64 cm
  • D 89 cm
  • E 93 cm

How wide is the first bright fringe on the screen that is separated from the central bright fringe by a dark fringe?

  • A 110 cm
  • B 71 cm
  • C 62 cm
  • D 99 cm
  • E 88 cm

Q12:

How many times the wavelength 𝜆 of a wave is the minimum width of a single slit that will produce a diffraction pattern containing a first minimum?

How many times the wavelength 𝜆 of a wave is the minimum width of a single slit that will produce a diffraction pattern containing 50 minima?

How many times the wavelength 𝜆 of a wave is the minimum width of a single slit that will produce a diffraction pattern containing 1 0 0 0 minima?

Q13:

Equal intensities of 550 nm and 600 nm wavelength light are incident on a slit of width 1.8 μm. Find the separation of the 𝑚 = 1 bright spots for the two wavelengths on a screen 30.0 cm away.

Q14:

A doorway of width 1.0 m acts as an aperture that diffracts both light and sound.

What is the angular position of the first minimum in the diffraction pattern of 600-nm light passing through the doorway?

  • A 5 . 0 × 1 0 5
  • B 4 . 2 × 1 0 5
  • C 6 . 4 × 1 0 5
  • D 3 . 4 × 1 0 5
  • E 7 . 2 × 1 0 5

What is the angular position of the first minimum in the diffraction pattern of 440-Hz-frequency sound passing through the doorway at a speed of 343 m/s?

  • A 5 1
  • B 3 9
  • C 2 7
  • D 1 5
  • E 4 4

Q15:

Light of wavelength 6 . 0 0 × 1 0 m is diffracted by a single slit of width 0.025 mm. The diffracted light is incident on a screen 2.0 m from the slit. The intensity of the light in the diffraction pattern for different values of the diffraction angle 𝜃 can be expressed in terms of the intensity of the central maximum 𝐼 .

What is the intensity for 𝜃 = 0 . 5 0 .

  • A 0 . 7 4 𝐼
  • B 0 . 6 8 𝐼
  • C 0 . 7 7 𝐼
  • D 0 . 6 3 𝐼
  • E 0 . 8 1 𝐼

What is the intensity for 𝜃 = 1 . 0 .

  • A 0 . 1 1 𝐼
  • B 0 . 2 5 𝐼
  • C 0 . 2 0 𝐼
  • D 0 . 1 5 𝐼
  • E 0 . 3 1 𝐼

What is the intensity for 𝜃 = 1 . 5 .

  • A 0 . 0 0 5 3 𝐼
  • B 0 . 0 0 1 8 𝐼
  • C 0 . 0 0 6 7 𝐼
  • D 0 . 0 0 2 5 𝐼
  • E 0 . 0 0 3 7 𝐼

What is the intensity for 𝜃 = 3 . 0 .

  • A 0 . 0 0 6 2 𝐼
  • B 0 . 0 1 2 𝐼
  • C 0 . 0 0 8 7 𝐼
  • D 0 . 0 0 2 8 𝐼
  • E 0 . 0 0 4 3 𝐼

What is the intensity for 𝜃 = 1 0 . 0 .

  • A 0 . 0 0 1 3 𝐼
  • B 0 . 0 0 1 1 𝐼
  • C 0 . 0 0 0 9 8 𝐼
  • D 0 . 0 0 0 8 8 𝐼
  • E 0 . 0 0 1 5 𝐼

Q16:

An aircraft maintenance technician walks past a tall hangar door that acts like a single slit for sound entering the hangar. Outside the door, on a line perpendicular to the opening in the door, a jet engine makes a 600-Hz sound. At what angle with the door will the technician observe the first minimum in sound intensity if the vertical opening is 0.800 m wide and the speed of sound is 340 m/s?

Q17:

A single slit produces its first minimum for 633-nm-wavelength light at an angle of 2 8 . 0 .

How wide is the slit?

  • A 1 . 6 2 × 1 0 m
  • B 1 . 1 8 × 1 0 m
  • C 1 . 8 4 × 1 0 m
  • D 1 . 3 5 × 1 0 m
  • E 2 . 0 9 × 1 0 m

At what angle will the second minimum be?

Q18:

A slit is 3.00 μm wide. At what angle does the slit produce a first-order minimum for 410 nm wavelength light?

Q19:

A slit is 4.00 μm wide. At what angle does the slit produce a third-order minimum for 700 nm wavelength light?

Q20:

Find the width of a single slit that produces a second-order minimum at 5 3 . 7 for 650 nm wavelength light.

Q21:

Find the wavelength of light that produces a third-order minimum at 6 8 . 2 0 when passing through a slit with a width of 6.000 μm.

Q22:

Light passing through a single slit produces a second-order minimum at an angle of 1 5 . 3 .

At what angle is the third-order minimum produced?

At what angle is the first-order minimum produced?

Q23:

Light of wavelength 450 nm passes through a slit of width 0.32 mm.

What is the angular position of the second-order minimum in the diffraction pattern produced?

What is the angular width of the central peak of the diffraction pattern?

  • A 0 . 0 8 , 0 . 0 8
  • B 0 . 0 9 , 0 . 0 9
  • C 0 . 0 5 , 0 . 0 5
  • D 0 . 0 6 , 0 . 0 6
  • E 0 . 0 1 , 0 . 0 1

Q24:

Red light of wavelength 630 nm in air from a helium-neon laser is incident on a single slit of width 0.0400 mm. The entire apparatus is immersed in water of refractive index 1.33. Determine the angular width of the central peak.

Q25:

630 nm wavelength light falls onto a slit of width 25.3 μm.

Find the angle of the second-order diffraction minimum produced.

What slit width would produce a second-order diffraction minimum angle of 7 7 . 8 ?

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