A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convec lens if the image is equal to the size of the object ? Also, find power of the lens.

Explanation

`{:("Concave lens","Object","Image"),(f=?,h,h.=-h),(,u=?,v=+50cm),("Power "=?,,"Nature of image = Real, magnified"):}`
Since the image size is equal to the object size, the object is placed at `C_(1)(i.e., 2F_(1))` and the image is formed at `C_(2)(i.e., 2F_(2))`. The magnitude of the object distance is equal to image distance i.e., u = v
Applying the New Cartesian sign, u is - ve, v is + ve
Magnification (m) `=(h.)/(h)`
`m=((-h))/((h))=-1`
The negative sign of m shows that the image is inverted and real and that the image is formed below the principal axis.
Magnification `(m)=(v)/(u)`
`-1=(50)/(u)`,
`u=-50 cm`
The needle is placed at a distance of 50 cm on the left side of the convex lens.
Lens formula `(l)/(v)=(l)/(u)=(l)/(f)`
`(l)/(f)=(l)/(50)-(l)/((-50))=(1+l)/((50)), (1)/(f)=(2)/(50)=(1)/(25)`,
`f=25cm=+0.25 m`
Power of lens `(P)=(l)/("Focal length of the lens in metre (f)")`
`P=(1)/(f)=(1)/(0.25)=+4D`
Power of the convex lens `=+4D`