(a) A telescope has an objective of diameter 10 cm. What is its resolving power for λ = 550 nm, in radians and arcseconds? (b) A grating with 12,000 illuminated lines is used in second order at λ = 600 nm. Can it resolve the sodium doublet (589.0 nm and 589.6 nm)? Solution: (a) θ_min = 1.22λ/D = 1.22 × 550×10⁻⁹ / 0.10 = 6.71×10⁻⁶ rad. In arcseconds: × (180/π) × 3600 ≈ 1.38″. So it can just separate two stars 1.4 arcseconds apart. (b) Resolving power R = nN = 2 × 12,000 = 24,000. Required R for the doublet = λ/Δλ = 589.3/0.6 ≈ 982. Since 24,000 ≫ 982, yes — it resolves the doublet easily (smallest separable Δλ = 600/24,000 = 0.025 nm).