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Worksheet: Single-Slit Diffraction

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:

A single-slit diffraction pattern for light with a wavelength πœ† = 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 center of the pattern is the center of the first dark fringe?

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

Q4:

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

Q5:

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

Q6:

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

Q7:

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 Γ— 1 0 βˆ’ 5 ∘
  • B 4 . 2 Γ— 1 0 βˆ’ 5 ∘
  • C 6 . 4 Γ— 1 0 βˆ’ 5 ∘
  • D 3 . 4 Γ— 1 0 βˆ’ 5 ∘
  • E 7 . 2 Γ— 1 0 βˆ’ 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 ∘

Q8:

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?

Q9:

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

Q10:

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.

Q11:

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 ∘ , βˆ’ 0 . 0 8 ∘
  • B 0 . 0 9 ∘ , βˆ’ 0 . 0 9 ∘
  • C 0 . 0 5 ∘ , βˆ’ 0 . 0 5 ∘
  • D 0 . 0 6 ∘ , βˆ’ 0 . 0 6 ∘
  • E 0 . 0 1 ∘ , βˆ’ 0 . 0 1 ∘

Q12:

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 Γ— 1 0 𝐼 βˆ’ 5 π‘œ
  • B 1 . 3 Γ— 1 0 𝐼 βˆ’ 5 π‘œ
  • C 1 . 9 Γ— 1 0 𝐼 βˆ’ 5 π‘œ
  • D 2 . 2 Γ— 1 0 𝐼 βˆ’ 5 π‘œ
  • E 2 . 6 Γ— 1 0 𝐼 βˆ’ 5 π‘œ

Q13:

Light of wavelength 6 . 0 0 Γ— 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 πœƒ can be expressed in terms of the intensity of the central maximum 𝐼  .

What is the intensity for πœƒ = 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 πœƒ = 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 πœƒ = 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 πœƒ = 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 πœƒ = 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 

Q14:

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.

Q15:

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 π‘œ
  • B 0 . 0 3 3 𝐼 π‘œ
  • C 0 . 0 6 7 𝐼 π‘œ
  • D 0 . 0 4 1 𝐼 π‘œ
  • E 0 . 0 7 5 𝐼 π‘œ

Q16:

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œ‹
  • D 1 ∢ 1
  • E 1 ∢ 4

Q17:

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

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 ∘ ?

Q18:

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.

Q19:

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

Q20:

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

Q21:

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.

Q22:

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

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

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

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

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

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

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

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

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

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

How wide is the central bright fringe on the screen?

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

Q23:

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.

Q24:

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?

Q25:

A single slit of width 1 8 5 0 nm is illuminated by normally incident light of wavelength 630 nm. Find the phase difference between waves from the top and the bottom of the slit to a point on a screen at a horizontal distance of 3.2 m and a vertical distance of 13.0 cm from the center.