Question

An object $20cm$ from a convex lens forms a virtual image $15cm$ behind the lens. The focal length of the lens is

• A. 8.5 cm
• B. $\frac{30}{7}cm$
• C. $\frac{90}{7}cm$
• D. $\frac{60}{7}cm$

Answer 1

The correct option is D

$\frac{60}{7}cm$

Taking new Cartesian sign conventions,

image distace, $v=+15cm$

object distance, $u=-20cm$

Using lens formula,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{15}-\frac{1}{-20}=\frac{1}{f}$
$\Rightarrow \frac{4+3}{60}=\frac{1}{f}\Rightarrow f=\frac{60}{7}cm$