Question

the image formed by a concave mirror is twice the size of the object.thevfocal length of the mirror is 20cm.the distance of the object from the mirror is ​

Answer 1

OBJECT DISTANCE IS 10 cm.

Given:

• Size of image is twice the size of object.
• Focal length = 20 cm
• It is a concave mirror

To find:

Distance of object from mirror ?

Calculation:

We know that , magnification of a mirror is:

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

$\implies 2= - \dfrac{v}{u}$

$\implies v = - 2u$

Now, applying MIRROR FORMULA:

$\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$

$\implies \dfrac{1}{ - 20} = \dfrac{1}{ - 2u} + \dfrac{1}{u}$

$\implies - \dfrac{1}{20} = \dfrac{ - 1 + 2}{ 2u}$

$\implies - \dfrac{1}{20} = \dfrac{ 1}{ 2u}$

$\implies u = - 10 \: cm$

So, object distance is 10 cm.