To determine the angular location of the first minimum in the diffraction pattern of a circular aperture, we can use the formula for the angular position of the first minimum:
θ = 1.22 * (λ / D)
where: θ is the angular position of the first minimum, λ is the wavelength of the light, D is the diameter of the circular aperture.
Given: Wavelength (λ) = 630 nm = 630 × 10^(-9) m Diameter (D) = 0.4 mm = 0.4 × 10^(-3) m
Let's substitute these values into the formula:
θ = 1.22 * (λ / D) = 1.22 * (630 × 10^(-9) m / 0.4 × 10^(-3) m) = 1.22 * (1.575 × 10^(-6) / 4 × 10^(-4)) = 1.22 * (1.575 × 10^(-6) / 4 × 10^(-4)) = 1.22 * 3.9375 × 10^(-3) ≈ 4.80 × 10^(-3) radians
Therefore, the angular location of the first minimum in the diffraction pattern is approximately 4.80 × 10^(-3) radians.