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Two stars distant two light years are just resolved by a telescope. The diameter of the telescope lens is 0.25 m. If the wavelength of light used in 5000A0, then the minimum distance between the stars is
Asked by sirib942254 | 04 Aug, 2021, 08:30: PM

Angular resolution of telescope Δθ = (1.22 λ ) / D  , where λ is the wavelength of light and D is diameter of lens

Δθ = (1.22 × 5000 × 10-8 ) / 0.25 = 2.44 × 10-4 rad

Δθ is the smallest possible angle subtended by two stars at far away distance .

If d is the far away distance , the distance s between the stars is given as

s = d × Δθ

1 light year = 9.461 ×1015 m

Hence if far away distance is 2 light years , then distance s between two stars is given as

s = 2 × 9.461 × 1015 × 2.44 × 10-4 = 4.617 × 1012 m
Answered by Thiyagarajan K | 04 Aug, 2021, 10:22: PM

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