JEE Mains · Physics · STD 12 - 10. Wave optics
Two stars are \(10\) light years away from the earth. They are seen through a telescope of objective diameter \(30\, cm\). The wavelength of light is \(600\, nm\). To see the stars just resolved by the telescope, the minimum distance between them should be ( \(1\) light year \(= 9.46 \times 10^{15}\, m\)) of the order of
- A \(10^8\,km\)
- B \(10^{10}\,km\)
- C \(10^{11}\,km\)
- D \(10^6\,km\)
Answer & Solution
Correct Answer
(A) \(10^8\,km\)
Step-by-step Solution
Detailed explanation
We know that \(\Delta \theta=\frac{1.22 \lambda}{D}=\frac{l}{R}\) The minimum distance between them \(l=\frac{9.46 \times 10^{15} \times 10 \times 1.22 \times 600 \times 10^{-9}}{0.3}\) \(=2308.24 \times 10^{8}\, \mathrm{m}\) \(\Rightarrow 2.308 \times 10^{8}\, \mathrm{km}\)
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