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Consider a sunlike star at a distance of 2 parsecs. When it is seen through a telescope with 100 magnification, what should be the angular size of the star? Sun appears to be (1/2)° from the earth. Due to atmospheric fluctuations, eye can’t resolve objects smaller than 1 arc minute.
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Solution
The angle of the sun's diameter `(1/2)^circ` is subtended by 1 A.U. since the distance from the sun increases angle subtended in the same ratio.
Now, 2 x 10^{5} A.U. will from an angle of θ = `(1/(4 xx 10^5))^circ`, since the diameter is the same angle subtended on earth by 1 parsec will be same.
If the sunlike star is at 2 parsec the angle becomes half = (1.25 × 10^{–6})°
Thus, angle = 75 × 10^{–6} min
When it is seen with a telescope that has a magnification of 100, the angle formed will be 7.5 × 10^{–3} min, viz., less than a minute.
Hence, it can't be observed by a telescope.
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