A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm

Question

A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $5 \times 10^{- 7}$ radian. The value of R is ______ cm. [2026]

Smart Achievers · Accepted Answer

(2)

$θ = 5 \times 10^{- 7} radian$

$λ = 500 \times 10^{- 9} m$

$θ = \frac{1.22 λ}{R}$

$R = \frac{1.22 λ}{θ} = 1.22 m = 122 cm$

Solution

Q.
A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $5 \times 10^{- 7}$ radian. The value of R is ______ cm. [2026]

1 61

2 122

3 244

4 305

Ans.
(2)

$θ = 5 \times 10^{- 7} radian$

$λ = 500 \times 10^{- 9} m$

$θ = \frac{1.22 λ}{R}$

$R = \frac{1.22 λ}{θ} = 1.22 m = 122 cm$

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