Question

Calculate the distance of an object of height h from a concave mirror of radius of curvature 20 cm, so as to obtain a real image of magnification 2. Find the location of the image also.

Answer 1

Given: Radius of curvature of mirror = 20 cm

 ∴ Focal length of mirror, f = −10 cm

Since the image is real,
Magnification of image, m = −2

${\displaystyle m=-\frac{v}{u}}$

${\displaystyle \Rightarrow -2=-\frac{v}{u}}$

${\displaystyle \Rightarrow v=2u}$

Using mirror formula,

${\displaystyle \frac{1}{f}=\frac{1}{v}+\frac{1}{u}=\frac{1}{2u}+\frac{1}{u}=\frac{3}{2u}}$

${\displaystyle \Rightarrow u=\frac{3}{2}f=\frac{3}{2}\times (-10)=-15cm}$

∴v=2u=−30 cm

Therefore, the distance of the object is 15 cm in front of the mirror and the position of the image is 30 cm in front of the mirror.