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 1015 m) of the order of :

Wave Optics PYQ — JEE Main 2016 · 10 Apr · Shift 1 · Q51 with Solution

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Correct answer: B

For a circular objective, the minimum angular separation for just resolution is

\theta_{\min} = 1.22\,\frac{\lambda}{D}

Given:

So,

\theta_{\min} = 1.22\times \frac{600\times 10^{-9}}{0.30}

= 1.22\times 2\times 10^{-6} = 2.44\times 10^{-6}\text{ rad}

Each star is $10$ light years away.

Using $1$ light year $= 9.46\times 10^{15}\text{ m}$ ,

L = 10\times 9.46\times 10^{15} = 9.46\times 10^{16}\text{ m}

For small angles,

\theta \approx \frac{s}{L}

Hence minimum separation,

s = L\theta_{\min}

s = 9.46\times 10^{16} \times 2.44\times 10^{-6}

s \approx 23.08\times 10^{10} = 2.308\times 10^{11}\text{ m}

2.308\times 10^{11}\text{ m} = 2.308\times 10^{8}\text{ km}

So the required minimum distance is of the order of

10^8\text{ km}

Therefore, the correct option is B.