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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)

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