Question

An object is placed in front of a concave mirror of radius of curvature is 30cm . The magnification is 1.5 then, what is the distance of object from concave mirror?​

Answer 1

Given that,

Radius of curvature of the concave mirror, R = 30 cm

Magnification, m = 1.5

To find,

The object distance.

Solution,

Radius of curvature = 2× focal length

Focal length = -15 cm (negative for concave mirror)

Magnification, $m=\dfrac{-v}{u}=1.5$

Mirror's formula :

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

Dividing both sides by v we get :

$1+\dfrac{v}{u}=\dfrac{v}{f}\\\\1-1.5=\dfrac{v}{-15}\\\\v=7.5\ cm$

So,

$m=\dfrac{-v}{u}\\\\u=\dfrac{-v}{m}\\\\u=\dfrac{-7.5}{1.5}\\\\u=-5\ cm$

So, the distance of object from concave mirror is 5 cm.