Two stars are separated by an angle of 3 × 10−5 radians. What is the diameter of the smallest telescope can resolve the two stars using visible light (λ = 600 nanometers)? (ignore any effect due to Earth’s atmosphere)
A. 1 mm
B. 2.5 cm
C. 10 cm
D. 2.5 m
E. 10 m
(GR0177 #13)
Solution:
Rayleigh telescope resolution limit: sin θ = 1.22 λ/D
Since θ ≪, assume sin θ ~ θ
D = 1.22λ/θ
λ = 600 nanometers = 600 × 10−9 mD = 1.22(600×10−9)/(3×10−5) = 2.44 × 10-2 m ≈ 2.5 cm
Answer: B
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