Question

the concave lens is used to form an image which is 1/4 of the size of an object .if the distance of the image from from lens is X ,the distance of the object from the lense is​

Answer 1

OBJECT DISTANCE IS -4X

Given:

• Concave lens produces an image which is one fourth the size of an object.

• Distance of image from lens is X

To find:

• Object distance ?

Calculation:

For image formation by lens, the formula for magnification is given as :

$mag. = \dfrac{ h_{i} }{ h_{o} } = \dfrac{v}{u}$

$\implies \dfrac{ h_{i} }{ h_{o} } = \dfrac{v}{u}$

• Putting the value of image size as ¼ of object size .

• Also, value of v as -X. This is because concave lenses will always produce virtual images .

$\implies \dfrac{ \frac{1}{4} \times h_{o} }{ h_{o} } = \dfrac{ - X}{u}$

$\implies \dfrac{ 1}{ 4 } = \dfrac{ - X}{u}$

$\implies u = - 4X$

So, object distance is -4X.