A gaint refrecting telescope at an observatory has an objective lens of focal length `15 m`. If an eye piece lens of focal length `1 cm` is used, find the angular magnification of the telescope.
If this telescope is used to view the moon, what is the diameter of image of moon formed by objective lens ? The diameter of the moon is `3.42 xx 10^6 m` and radius of lunar orbit is `3.8 xx 10^8 m`.

Explanation

`f_(0)=15m, f_(c)=10^(-2)m`
(a) Angular magnification of the telescope `=(f_(0))/(f_(e))=-(15)/(10^(-2))=-1500`
(b) Let `d` be the diameter of the image Angle subtended by image `=(d)/(f_(0))=(d)/(15)`
Angle subtended by diameter of moon `=(3.48xx16^(6)M)/(3.8xx10^(8)M)`
Equating `(d)/(15)=(3.48xx10^(6)M)/(3.8xx10^(8)M)`
On simplification , `d=13.73 cm`