In an astronomical telescope in normal adjustment a straight black line of length `L` is drawn on inside part of objective lens. The eye piece forms a real image of this line. The length of this image is `I`. The magnification of the telescope is

Options

A. `(L)/(I)`
B. `(L)/(I)+1`
C. `(L)/(I)-1`
D. `(L+I)/(L-I)`

Answer

A

Explanation

At normal adjustment `M=(f_(o))/(f_(e))` …`(i)`
and distance between lenses`=f_(o)+f_(e)`
Lateral magnification `(L)/(I)=(f_(o)+f_(e))/(v)` …`(ii)`
Using lens equation`(1)/(v)-(1)/(u)=(1)/(f)`
`implies(1)/(v)-(1)/(-(f_(o)+f_(e)))=(1)/(f_(e))`
`implies(1)/(v)=(f_(o))/(f_(e)(f_(o)+f_(e)))`
`rArr (f_(o))/(f_(e)) = (f_(o)+f_(e))/(v)` ...`(iii)`
Comparing equations (i), (ii) and (iii) `M=(f_(o))/(f_(e))=(L)/(I)`