Question

a convex lens has a focal length of 20cm .find the position of the object for which the image will be half the size of the object.​

Answer 1

Explanation:

Given f=20cm

m=1/2

but,m=-v/u

1/2=-v/u

v=-u/2

1/v=-2/u

We know 1/f=1/u+1/v

=1/20=1/u-2/u

=-1/u=1/20

=u=-20

The answer is 20 cm behind the lens.

Answer 2

• Given :-

Focal length. = 20cm

Object distance = -u ( object distance is always negative sign )

Image distance = half of object distance= (-u/2)

• To find

★ THE POSITION OF OBJECT

now according to lens formula

$\boxed{\sf \dfrac{1}{f}= \dfrac{1}{v}-\dfrac{1}{u}}$

$\sf \ \ \dfrac{1}{v} = \dfrac{1}{\dfrac{-u}{2}}= \dfrac{-2}{u}\\ \\ \longmapsto\sf \dfrac{1}{f}= \dfrac{1}{v}-\dfrac{1}{u}\\ \\ \longmapsto\sf \dfrac{1}{20}= \dfrac{-2}{u} -\dfrac{-1}{u}\\ \\ \longmapsto\sf \dfrac{1}{20}= \dfrac{-2+1}{u}\\ \\ \longmapsto\sf \dfrac{u}{20}= -1 \\ \\ \longmapsto\sf u= 20\times (-1)\\ \\ \longmapsto\sf u= -20 cm$

Object distance = -20cm

Image distance = half of object distance

=> u/2 =-20/2= -10cm

So the position of image is behind the lens ! because the sign is (-ve) .

Negative side indicate that object is placed at left side of the lens .