Question

Q)A diverging mirror of radius of curvature 60 cm forms an image which is ¾ th the height of the object. Find the object and image positions.

Answer 1

Given:

A diverging mirror of radius of curvature 60 cm forms an image which is ¾ th the height of the object.

To find:

• Object and image distance

Calculation:

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

$\implies \dfrac{ \frac{3}{4} h_{o}}{h_{o}} = - \dfrac{v}{u}$

$\implies \dfrac{3}{4} = - \dfrac{v}{u}$

$\implies - \dfrac{3u}{4} = v$

Now, applying Mirror Formula:

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

$\implies \dfrac{1}{30} = \dfrac{4}{ - 3u} + \dfrac{1}{u}$

$\implies \dfrac{1}{30} = \dfrac{ - 4 + 3}{ 3u}$

$\implies u = - 10 \: cm$

$\implies v= 7.5 \: cm$

So, object distance is 10 cm and image distance is 7.5 cm.