Question

in order to obtain a magnification of -2.0 with a concave mirror of focal length 12 cm and object will have to be placed at a distance

Answer 1

The object should be placed at a distance of 24 cm to from the lens (on the left side).

Answer 2

Given:

Magnification of -2.0 with a concave mirror of focal length 12 cm is required.

To find:

Object distance ?

Calculation:

In case of mirrors, magnification is written as:

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

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

$\sf\implies\: 2 = \dfrac{v}{u}$

$\sf\implies\: v = 2u$

Now, applying mirror formula:

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

$\sf \implies\: \dfrac{1}{ - 12} = \dfrac{1}{2u} + \dfrac{1}{u}$

$\sf \implies\: \dfrac{1}{ - 12} = \dfrac{1 + 2}{2u}$

$\sf \implies\: \dfrac{1}{ - 12} = \dfrac{3}{2u}$

$\sf \implies\: \dfrac{1}{ - 6} = \dfrac{3}{u}$

$\sf \implies\: u - 18 \: cm$

So, object distance is 18 cm before the mirror.