Question

A concave mirror of focal length 20cm form an image having twice the size of object will be at:(a.) 15 (b.) 20 (c.) 30 (d.) 0​

Answer 1

$\huge\mathfrak{Answer:}$

Given:

• We have been given that the focal length of the concave mirror is 20cm.
• Magnification of the image is 2.

To Find:

• We need to find the object distance.

Solution:

As it is given that the focal length of the concave mirror is 20cm and the magnification of the mirror is 2, therefore

$\sf{m = \dfrac{ - v}{u} }$

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

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

We know that,

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

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

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

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

$\implies\sf{20 = 2u}$

$\implies\sf{ \dfrac{20}{2} = u}$

$\implies\sf{u = 10cm}$

Hence, the position of object is 10cm.