Question

A concave mirror produces three times magnified (enlarged) real image of object placed at 10 cm in front of it. Where is the image located?

Answer 1

Magnification produced by a spherical mirror is given by the relation,
$m=\frac{\text{Height of the image}}{\text{Height of the object}}$

$=-\frac{\text{Image distance}}{\text{Object distance}}$

$⇒ m=\frac{h_I}{h_o}=\frac{-v}{u}$
Let the height of the object,$h_o = h$
Then, height of the image,$h_I = −3h$ (Image formed is real)
$-\frac{3h}{h}=\frac{-v}{u}$
$⇒\frac{v}{u}=3.$
Object distance, u = −10 cm
v = 3 × (−10) = −30 cm
Here, the negative sign indicates that an inverted image is formed at a distance of 30 cm in front of the given concave mirror.