Question

The image formed by a convex mirror of focal length 20cm is a quarter of the object.What is the distance of the object from the mirror?​

Answer 1

HERE IS YOUR ANSWER DEAR

Answer 2

Given:

The image formed by a convex mirror of focal length 20cm is a quarter of the object.

To find:

Object distance ?

Calculation:

For a mirror , we know that :

$\sf{ \therefore \: magnification = \dfrac{h_{i}}{h_{o}} = - \dfrac{v}{u} }$

$\sf{ = > \dfrac{ \frac{1}{4}( h_{o})}{h_{o}} = - \dfrac{v}{u} }$

$\sf{ = > \dfrac{1}{4} = - \dfrac{v}{u} }$

$\sf{ = > v = - \dfrac{u}{4} }$

Now , applying Mirror Formula:

$\sf{ \therefore \: \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} }$

$\sf{ = > \: \dfrac{1}{20} = \dfrac{1}{( - \frac{u}{4} )} + \dfrac{1}{u} }$

$\sf{ = > \: \dfrac{1}{20} = - \dfrac{4}{u} + \dfrac{1}{u} }$

$\sf{ = > \: \dfrac{1}{20} = \dfrac{ - 4 + 1}{u} }$

$\sf{ = > \: \dfrac{1}{20} = \dfrac{ - 3}{u} }$

$\sf{ = > \: u = 20 \times ( - 3) }$

$\sf{ = > \: u = - 60 \: cm }$

So, object distance is 60 cm.