Question

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. $10^6\,km$
• B. $10^8\,km$
• C. $10^{11}\,km$
• D. $10^{10}\,km$

Answer 1

Answer: (B)

We have, $\Delta \theta=\frac{0.61 \lambda}{9}=\frac{1}{ R }$
$1=\frac{ R }{9} 0.61 \times \lambda$
$=\frac{9.46 \times 10^{15} \times 10 \times 0.61 \times 600 \times 10^{-9}}{0.3}$
$=1.15 \times 10^{11} m$
$=1.115 \times 10^{8} km$