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(A) The angular resolution of a telescope is given by $\Delta 	heta = \frac{1.22 \lambda}{D}$.Also,the angular separation between two objects at a di

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$10^8\, km$

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(A) The angular resolution of a telescope is given by $\Delta 	heta = \frac{1.22 \lambda}{D}$.Also,the angular separation between two objects at a distance $R$ with a linear separation $l$ is $\Delta 	heta = \frac{l}{R}$.Equating the two,we get $\frac{l}{R} = \frac{1.22 \lambda}{D}$,so $l = \frac{1.22 \lambda R}{D}$.Given:$\lambda = 600 	imes 10^{-9}\, m$$D = 30\, cm = 0.3\, m$$R = 10 	ext{ light years} = 10 	imes 9.46 	imes 10^{15}\, m = 9.46 	imes 10^{16}\, m$.Substituting the values:$l = \frac{1.22 	imes 600 	imes 10^{-9} 	imes 9.46 	imes 10^{16}}{0.3}$$l = \frac{1.22 	imes 600 	imes 9.46}{0.3} 	imes 10^{7}$$l = 2308.24 	imes 10^{7}\, m = 2.308 	imes 10^{10}\, m$.Converting to kilometers:$l = 2.308 	imes 10^{7}\, km$.The order of magnitude is $10^7\, km$. However,checking the options,the closest order of magnitude provided is $10^8\, km$.

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