  Question

# How the focal length can be positive on left side of the same side of the object

Solution

## Please Draw a converging lens at mid point of x axis XX' and y axis YY'. that point is named O   OPTICAL CENTRE (O) Centre of lens,lies on principle axis. X’X is the principle axis here. According to SIGN CONVENTION Point to th left of O (OX’) is taken negative and to the right of O (OX) is considered positive. And OY is positive OY’ as negative . LENS FORMULA: 1/f=(1/v)-(1/u) where, f is focal length v is image distance from O u is object distance from O. Here since u is always negative as object lies to the left of O (OX’ axis). In a convex lens we get real inverted image on the opposite side of lens,Whenever object lies at or beyond F. v is positive,when u=f or u>f When object lies between F and O,image is virtual,erect on the same side where object is. v is negative,when u<f CASE I When u=f or u>f Lens formula is 1/f=(1/v)-(1/-u)=(1/v)+(1/u) when u=f or u>f f=(uv)/(u+v) Since both numerator denominator positive, therefore f is positive. CASE II When u less than f (u<f) 1/f=(1/-v) - (1/-u) f=(v-u)/(uv) Here v>u, since image is enlarged when object lies between F and O,(M>1) M=h’/h=v/u h and h’ length of object and image respectively. M=h’/h=v/u >1, THEREFORE v has to be greater than u. hence (v-u) is positive and (uv) also positive hence f is positive. Hence f is always positive for convex lens.(ACCORDING TO SIGN CONVENTION)  Suggest corrections   