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What is the angle of diffraction for the first minimum in a single-slit diffract

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Question: What is the angle of diffraction for the first minimum in a single-slit diffraction pattern if the slit width is 0.5 mm and the wavelength of light is 500 nm? (2023)

Options:

  1. 30°
  2. 60°
  3. 45°
  4. 15°

Correct Answer: 45°

Exam Year: 2023

Solution:

The angle for the first minimum is given by sin θ = λ/a, where a is the slit width. Thus, sin θ = 500 nm / 0.5 mm = 0.001, leading to θ ≈ 30°.

What is the angle of diffraction for the first minimum in a single-slit diffract

Practice Questions

Q1
What is the angle of diffraction for the first minimum in a single-slit diffraction pattern if the slit width is 0.5 mm and the wavelength of light is 500 nm? (2023)
  1. 30°
  2. 60°
  3. 45°
  4. 15°

Questions & Step-by-Step Solutions

What is the angle of diffraction for the first minimum in a single-slit diffraction pattern if the slit width is 0.5 mm and the wavelength of light is 500 nm? (2023)
  • Step 1: Identify the given values. The slit width (a) is 0.5 mm and the wavelength of light (λ) is 500 nm.
  • Step 2: Convert the slit width from millimeters to nanometers for consistency. 0.5 mm = 500,000 nm.
  • Step 3: Use the formula for the angle of the first minimum in single-slit diffraction: sin θ = λ / a.
  • Step 4: Substitute the values into the formula: sin θ = 500 nm / 500,000 nm.
  • Step 5: Calculate the value: sin θ = 0.001.
  • Step 6: Find the angle θ by taking the inverse sine (arcsin) of 0.001.
  • Step 7: Use a calculator to find θ ≈ 0.0573 degrees, which is approximately 0.06 degrees.
  • Single-Slit Diffraction – Understanding the diffraction pattern produced by a single slit and the conditions for minima.
  • Wavelength and Slit Width Relationship – Applying the relationship between wavelength, slit width, and angle of diffraction to find the first minimum.
  • Trigonometric Functions in Physics – Using the sine function to relate the angle of diffraction to the wavelength and slit width.
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