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