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?
30°
60°
45°
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°.
