Question

The diameter of moon is $3.5\times {10}^3$ km and its distance from the earth is $3.8\times {10}^{8}km$ it is seen by a telescope having focal lengths of objective and eye piece as 4 m and 10 cm respectively. the diameter of the image of the moon is nearly

• A. $2^0$
• B. ${20}^0$
• C. ${40}^0$
• D. ${50}^0$

Answer 1

The correct option is B ${20}^0$

Angle subtended by moon on object

${\theta }_0=\frac{3.5\times {10}^3}{3.8\times {10}^5}=9.2\times {10}^{-3}rad$

$={(9.2\times {10}^{-3}\times \frac{{180}^0}{\pi })}^o\approx {0.5}^o$

$|m|=\frac{f_0}{f_e}=\frac{400}{10}=40$

$m=\frac{\theta }{{\theta }_0}\Rightarrow 40=\frac{\theta }{(0.5{)}^o}$

$\theta ={20}^o$