Question

Where should an object be placed, with reference to a concave mirror of radius 180 cm, to form a real image having half its linear dimensions?​

Answer 1

Given:

Real image is formed having half linear dimensions as compared to the object. Radius of curvature of mirror is 180 cm

To find:

Object Distance from the mirror

Concept:

Since the image is said to be real and diminished , it can also be considered as inverted. So we need to introduce a negative sign for object height during calculation.

Calculation:

$\therefore \: \dfrac{h_{i}}{h_{0}} = - \dfrac{v}{u}$

$= > \: \dfrac{ (- \frac{h_{0}}{2} )}{h_{0}} = - \dfrac{v}{u}$

$= > \: \dfrac{ - 1}{2} = - \dfrac{v}{u}$

$= > v = \dfrac{u}{2}$

Radius of curvature = 180 cm

Therefore , focal length = 180/2 = 90 cm

Applying Mirror Formula:

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

$= > \: \dfrac{1}{( - 90)} = \dfrac{2}{u} + \dfrac{1}{u}$

$= > \: \dfrac{1}{( - 90)} = \dfrac{2 + 1}{u}$

$= > \: \dfrac{1}{( - 90)} = \dfrac{3}{u}$

$= > u = - 270 \: cm$

So final answer:

Object has to be placed 270 cm before the mirror.