Two stars are 10 light years away from the earth. They are seen...

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 600nm. To see the stars just resolved by the telescope, the minimum distance between them should be

\left(1lightyear = 9.46 \times {10}^{15}m\right)

of the order of :

Options

A ${10}^{8}km$
B ${10}^{10}km$
C ${10}^{11}km$
D ${10}^{6}km$

Correct answer

A. ${10}^{8}km$

Step-by-step solution

l = \dfrac{R}{a}1 . 22 \times \lambda

and

a = 30cm

⇒ l = \dfrac{9.46 \times {10}^{15} \times 10 \times 1 . 22 \times 600 \times {10}^{- 9}}{0 . 3}

= 2.30 \times {10}^{11}m

⇒ 2.30 \times {10}^{8}km

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