(a) Two stars are 0.5 arcseconds apart. Can a 10 cm telescope (λ = 550 nm) resolve them? What about a 1 m telescope? (b) A microscope objective has NA = 1.25. What is the smallest resolvable separation with green light (λ = 550 nm)? With violet light (λ = 400 nm)? Step 1: θ_min = 1.22λ/D = 1.22 × 550×10⁻⁹/0.10 = 6.71×10⁻⁶ rad. Convert: × (180/π) × 3600 ≈ 1.38 arcseconds. The stars at 0.5″ are NOT resolved by the 10 cm scope — they merge. Step 2: For D = 1 m: θ_min = 0.138″ < 0.5″ → resolved. Ten times the aperture, ten times sharper — the observatory argument in one number. Step 3: d_min = λ/(2NA) = 550 nm/(2×1.25) = 220 nm. With violet: 400/2.5 = 160 nm. Shorter wavelength resolves finer detail — one reason UV microscopes exist, and why electron microscopes (λ ~ picometres) see atoms.