Question

At what distance the object should be placed in front of a concave lens of focal length 20 cm so that the image will be formed at distance 10 cm from the lens? What is the magnification of the object?
[4 MARKS]

Answer 1

Lens formula: 1 Mark
Object distance: 2 Marks
Magnification: 1 Mark

In a concave lens, the image will be formed on the same side as that of the object.
Here Image distance, $v=-10$
Focal length, $f=-20cm$
Object distance, $u=?$
Using lens formula , $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
Or, $\frac{1}{u}=\frac{1}{v}-\frac{1}{f}$
Substituting given values we get, $\frac{1}{u}=\frac{1}{-10}-\frac{1}{-20}$
$\Rightarrow \frac{1}{u}=\frac{1}{-20}$
Hence, $u=-20cm$
Thus, the object should be kept at 20 cm from the concave lens on the left side of the lens.

Magnification$=\frac{v}{u}=\frac{-10}{-20}=\frac{1}{2}$