Question

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$1/2^{\circ }$from the earth. Due to atmosperic fluctations , eye can't resolve objects smaller than $1$ arc minute

Answer 1

Given, At 1 A.U. distance, sun's angular diameter from earth=${\left(\frac{1}{2}\right)}^{\circ }$

Angular diameter of the sun like star at a distance of 2 parsec$=\frac{\frac{1}{2}}{2\times 2\times {10}^{-5}}$

$={(\frac{1}{8}\times {10}^{-5})}^{\circ }=(\frac{1}{8}\times {10}^{-5})\times 60min$

$7.5\times {10}^{-5}$arcmin

When we see through a telescopewith 100 magnification, the angulat diameter of the star$=100\times 7.5\times {10}^{-3}$arcmin.
Due to atmospheric fluctuation,eye cannot resolve smaller that 1 arcmin.
So, angular size of unlike tar appears as 1 arcmin.

Final answer: 1 arcmin