Optics - Telescope

The angular separation of the two components of a double star is 8 microradians, and the light from the double star has a wavelength of 5500 angstroms. The smallest diameter of a telescope mirror that will resolve the double star is most nearly 

A. 1 mm
B. 1 cm
C. 10 cm
D. 1 m
E. 100 m

(GR9277 #68)

Solution:

Rayleigh telescope resolution limit: sin θ = 1.22 λ/D

D = 1.22 λ/sin θ = 1.22 (5500 × 10⁻¹⁰ m) / sin (8×10⁻⁶)

Since θ ≪, assume sin θ ~ θ

 D = (1.22 × 5.5 / 8) × 10³ × 10⁻¹⁰ × 10⁶ ≈ 10⁻¹ m = 10 cm

Answer: C