Question

Diameter of the moon is $3.5\times {10}^{3}km$ and its distance from the earth is $3.8\times {10}^{5}km$. It is seen by a telescope whose objective and eyepiece have focal lengths $4m$ and $10cm$ respectively. The angular diameter of the image of the moon is (assume final image is at infinity)

• A. $0.36radian$
• B. $0.009radian$
• C. $0.011radian$
• D. $0.022radian$

Answer 1

The correct option is A $0.36radian$


Angular diameter of the moon
$\theta \approx \frac{3500}{3.8\times {10}^5}=0.009radian$
Angular magnification $m=-\frac{f_o}{f_e}=\frac{-400}{10}=-40$
Hence, angular diameter of the image ${\theta }^{\prime }=m\times \theta$
$=40\times 0.009=0.36radian$