(a) A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece of focal length 1.0 cm is used, what is the angular magnification of the telescope?
(b) If this telescope is used to view the Moon, what is the diameter of the image of the Moon formed by the objective lens? The diameter of the Moon is `3.48 xx 10^(6) m` and the radius of lunar orbit is `3.8 xx 10^(6) m.`

Explanation

Given, focal length of objective, `f_(o)=15m`
Focal length of eyepiece, `f_(e)=1cm=10^(-2)m`
Angular magnification `=(f_(o))/(f_(e))=(15)/(0.01)=1,500`
(b) Given, diameter of the Moon, `d=3.48xx10^(6)m`
Radius of lunar orbit, `r=3.8xx10^(8)`
Let `theta` be the angle substended by the diameter of the Moon. Then,
`theta=(d)/(r )=(3.48xx10^(6))/(3.8xx10^(8))`
If `theta.` is the angle subtended by the image, then
`theta.=(d_(i))/(f_(o))=(d_(i))/(15)`
Where `d_(i)` is the size of image
Since `theta=theta.`
`rArr" (d_(i))/(15)=(3.48xx10^(6))/(3.8xx10^(8))`
`rArr" "d_(i)=13.74cm`