Question

If an object of 10 cm height is placed at a distance of 36 cm from a concave mirror of focal length 12 cm, find the position, nature and height of image.

Answer 1

Step1: Applying Mirror Formula

Object distance $u=-36cm$

Focal length of concave mirror $f=-12cm$

Using mirror formula : $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Or $\frac{1}{v}+\frac{1}{-36}=\frac{1}{-12}$

$⟹v=-18cm$,

Since image position is negative, i.e. image is on the same side of object, which is real space, therefore the image is real.

Step2: Finding Height using Magnification

Magnification $\frac{h_i}{h_o}=\frac{-v}{u}$

Or $\frac{h_i}{10}=\frac{-(-18)}{-12}$

$⟹h_i=-15cm$

Negative height implies that the image is inverted.

Hence, a real and inverted image of height 15 cm is formed at a distance of 18 cm in front of the mirror.