University of Central Florida (UCF) PHY2054 General Physics with Calculus II Practice Exam

Two point sources become just resolvable when the peak of one image falls on the first dark ring of the diffraction pattern from a circular aperture. That diffraction pattern is an Airy disk, and the angle to the first minimum of that pattern is approximately 1.22 times the wavelength divided by the aperture diameter. Hence the minimum resolvable angular separation is Δθ ≈ 1.22 λ / D. Here λ is the light’s wavelength and D is the aperture diameter. The constant 1.22 comes from the mathematics of the circular aperture’s diffraction pattern. The other expressions either misplace the factor, use the wrong minimum (e.g., a second minimum), or invert the ratio, which would not reflect how diffraction sets the limit on resolution.