An astronomical telescope consisting of an objective of focal length `60cm` and eye-piece of focal length `3 cm` is focused on the moon so that the final image is formed at least distance vision, i.e. `25 cm` from the eye-piece piece. Assuming the angular diameter of moon as `1//2^(@)` at the objective, calculate (a) angular size and (b) lenear size of image seen through the telescope.

Explanation

`f_(0) = 60cm, f_(e) = 3cm, D = 25cm`
`theta_(0)((1)/(2))^(@)`
Magnifying power of telescope
`m=- (f_(0))/(f_(e)) (1+(f_(e))/(D))`
`=- (60)/(3) (1+(3)/(25))`
`=- 20xx(28)/(25) =- 24`
`m = (theta)/(theta_(0))`
`theta = m theta_(0) = (22.4xx(1)/(2))^(@) = 11.2^(@)`
`= 11.2xx(pi)/(180) = 0.2 rad`
`theta = (I)/(25)`
`I = 25 theta = 25 xx 0.2 = 5cm `
`I:` size of final image which is formed at least distance of distinct vision.