Question

an object of height 10 cm is placed before a convex mirror of focal length to 250 cm if the height of the image is 5 cm and the object distance is?​

Answer 1

Given:

An object of height 10 cm is placed before a convex mirror of focal length to 250 cm The height of the image is 5 cm.

To find:

Object distance?

Calculation:

As per magnification of mirror:

$\rm \: \dfrac{ h_{i}}{h_{o}} = - \dfrac{v}{u}$

$\rm \implies\: \dfrac{5}{10} = - \dfrac{v}{u}$

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

$\rm \implies\:v = - \dfrac{u}{2}$

Now, applying Mirror Formula:

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

$\rm \implies \dfrac{1}{250} = - \dfrac{2}{u} + \dfrac{1}{u}$

$\rm \implies \dfrac{1}{250} = \dfrac{ - 2 + 1}{u}$

$\rm \implies \dfrac{1}{250} = \dfrac{ - 1}{u}$

$\rm \implies \: u = - 250 \: cm$

So, object distance is -250 cm.