Question

A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.

Answer 1

Focal length of concave lens (OF1), $f = −15\ cm$
Image distance, $v = −10\ cm$
According to the lens formula,
$\frac 1v-\frac 1u=\frac 1f$

$\frac 1u=\frac 1v-\frac 1f$

$\frac 1u=-\frac {1}{10}-\frac {1}{(-15)}$

$\frac 1u=-\frac {1}{10}+\frac {1}{15}$

$\frac 1u=-\frac {5}{150}$
$u=-30\ cm$
The negative value of u indicates that the object is placed $30\ cm$ in front of the lens. This is shown in the following ray diagram.