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)
Practice Questions
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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)
30°
60°
45°
15°
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°.
Questions & Step-by-step Solutions
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Q
Q: 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)
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°.
Steps: 7
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.
