Question

A concave lens has a focal length of 15 cm. At what distance should the object be from the lens placed so that it forms an image 10 cm from the lens? Also find the magnification. [3 MARKS]

Answer 1

Lens formula: 1 Mark
object distance: 1 Mark
magnification: 1 Mark

A concave lens always forms a virtual, erect image on the same side as the object.

Image distance, $v=-10cm$

Focal length, $f=-15cm$

Object distance, $u=$ ?

Using the len's formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ we get

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

$u=-30cm$

Thus, the object should be placed at 30 cm from the lens.
Object and the image are on the same side of the lens

Magnification, $m=\frac{v}{u}=\frac{-10}{-30}=0.33$

The positive sign shows that the image is erect and virtual. The size of the image is one - third of that object.