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In a single-slit diffraction pattern, what is the angle for the first minimum if

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Question: In a single-slit diffraction pattern, what is the angle for the first minimum if the slit width is 0.5 mm and the wavelength of light is 600 nm?

Options:

  1. 30°
  2. 60°
  3. 45°
  4. 15°

Correct Answer: 45°

Solution: 

For single-slit diffraction, the first minimum occurs at sin θ = λ/a. Here, sin θ = 600 x 10^-9 m / 0.5 x 10^-3 m = 0.0012, θ ≈ 0.0698 rad ≈ 4°.

In a single-slit diffraction pattern, what is the angle for the first minimum if

Practice Questions

Q1
In a single-slit diffraction pattern, what is the angle for the first minimum if the slit width is 0.5 mm and the wavelength of light is 600 nm?
  1. 30°
  2. 60°
  3. 45°
  4. 15°

Questions & Step-by-Step Solutions

In a single-slit diffraction pattern, what is the angle for the first minimum if the slit width is 0.5 mm and the wavelength of light is 600 nm?
  • Step 1: Identify the given values. The slit width (a) is 0.5 mm, which is 0.5 x 10^-3 m, and the wavelength of light (λ) is 600 nm, which is 600 x 10^-9 m.
  • Step 2: Use the formula for the angle of the first minimum in single-slit diffraction, which is sin θ = λ/a.
  • Step 3: Substitute the values into the formula: sin θ = (600 x 10^-9 m) / (0.5 x 10^-3 m).
  • Step 4: Calculate the value: sin θ = 600 x 10^-9 / 0.5 x 10^-3 = 0.0012.
  • Step 5: Find the angle θ by taking the inverse sine (arcsin) of 0.0012: θ = arcsin(0.0012).
  • Step 6: Use a calculator to find θ in radians: θ ≈ 0.0698 rad.
  • Step 7: Convert the angle from radians to degrees: θ ≈ 0.0698 rad × (180/π) ≈ 4°.
  • Single-Slit Diffraction – The phenomenon where light spreads out after passing through a narrow slit, creating a pattern of light and dark bands.
  • Minima Calculation – Understanding how to calculate the angles at which minima occur in a diffraction pattern using the formula sin θ = λ/a.
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