Question

A gain telescope in an observatory has an objective of focal length $19m$ and an eye-piece of focal length $1.0cm$. What is the diameter of the image of moon formed by the objective in normal adjustment? The diameter of moon is $3.5\times {10}^{6}m$ and the radius of the lunar orbit round the earth is $3.8\times {10}^{8}m.$

• A. $10cm$
• B. $12.5cm$
• C. $15cm$
• D. $17.5cm$

Answer 1

The correct option is D $17.5cm$

$f_0=19m{f}_e=0.01m$

Lens formula at objective lens

$\begin{array}{cc}\frac{1}{f}& =\frac{1}{v}-\frac{1}{u}\\ \frac{1}{19}& =\frac{1}{v}-\frac{1}{3.8\times {10}^8}\\ & v\simeq 19cm\end{array}$

Given diameter of $moon=3.5\times {10}^6$

Image diameter $=\frac{3.5\times {10}^6}{3.8\times {10}^8}\times 19cm$

$=17.5cm$