The diameter of the moon is `3.5 xx 10^(3) km` and its distance from the earth is `3.8 xx 10^(5)km`. It is seen through a telescope having focal lengths of objective and eye-piece as `4m` and `10 cm` respectively. Calculate (a) magnifying power of telescope (b) length of telescope tube and (c) anngular size of image of moon.

Explanation

`f_(0) = 4m = 400cm, f_(e) = 10cm`
`(a) m=- (f_(0))/(f_(e)) =- (400)/(10) =- 40`
`(b) L = f_(0) +f_(e) = 400 +10 = 410cm = 4.1m`
`(c )` Angle subtended by moon
`theta_(0) = (3.5xx10^(3))/(3.8xx10^(5)) = (35)/(3800) rad`
`m=(theta)/(theta_(0))`
`theta = mtheta_(0) = 40 xx (35)/(3800) = 0.368rad`
`= (0.368xx(180)/(pi))^(0)`
`= 21^(@)`