A telescope with an objective of diameter R is used to observe a distant star emitting light of wavelength 500 nm. The required angular resolution is 5×10⁻⁷ rad. Using the Rayleigh criterion θ = 1.22λ /R, what is R in centimetres?
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Question

A telescope with an objective of diameter R is used to observe a distant star emitting light of wavelength 500 nm. The required angular resolution is 5×10⁻⁷ rad. Using the Rayleigh criterion θ = 1.22λ /R, what is R in centimetres?

Options

G1 Physics · Accepted Answer

Using the Rayleigh criterion, θ = 1.22λ ÷ R. Therefore, R = 1.22λ ÷ θ. Substitute: λ = 500×10⁻⁹ m, θ = 5×10⁻⁷ rad. Thus, R = 1.22×500×10⁻⁹ ÷ (5×10⁻⁷) = 1.22 m = 122 cm. Correct option: B.