For a single-slit diffraction pattern, the first minimum occurs when sin θ1 = λ/d. With d = 0.20 mm and λ = 500 nm, estimate θ1.

For a single-slit diffraction pattern, the first minimum occurs when sin θ1 = λ/d. With d = 0.20 mm and λ = 500 nm, estimate θ1.

• A. θ1 ≈ 0.143°
• B. θ1 ≈ 0.286°
• C. θ1 ≈ 1.43°
• D. θ1 ≈ 0.0143°

Answer: (A)

In a single-slit diffraction pattern, the minima occur when the path difference across the slit gives destructive interference, which is described by a sin θ = m λ. For the first minimum, take m = 1, so sin θ1 = λ/d. Plug in the values: d = 0.20 mm = 2.0 × 10^-4 m and λ = 500 nm = 5.0 × 10^-7 m. This gives sin θ1 = (5.0 × 10^-7) / (2.0 × 10^-4) = 2.5 × 10^-3 = 0.0025. Because the angle is small, sin θ ≈ θ in radians, so θ1 ≈ 0.0025 rad. Converting to degrees: 0.0025 rad × (180/π) ≈ 0.143 degrees. Thus θ1 ≈ 0.143°, which matches the estimated value.

In a single-slit diffraction pattern, the minima occur when the path difference across the slit gives destructive interference, which is described by a sin θ = m λ. For the first minimum, take m = 1, so sin θ1 = λ/d.

Plug in the values: d = 0.20 mm = 2.0 × 10^-4 m and λ = 500 nm = 5.0 × 10^-7 m. This gives sin θ1 = (5.0 × 10^-7) / (2.0 × 10^-4) = 2.5 × 10^-3 = 0.0025.

Because the angle is small, sin θ ≈ θ in radians, so θ1 ≈ 0.0025 rad. Converting to degrees: 0.0025 rad × (180/π) ≈ 0.143 degrees.

Thus θ1 ≈ 0.143°, which matches the estimated value.