Question

The magnification of an object placed in front of a convex lens of focal length $20\text{cm}$ is $+2$. To obtain a magnification of $-2$, the object has to be moved by a distance equal to:

• A. $10\text{cm}$
• B. $30\text{cm}$
• C. $20\text{cm}$
• D. $40\text{cm}$

Answer 1

The correct option is C $20\text{cm}$

From the formula of magnification,
$m=\frac{v}{u}=2$
$v=2u$

Using lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{2u}-\frac{1}{u}=\frac{1}{+20}$
$u=-10\text{cm}$

New magnification,
$m^{\prime }=\frac{v^{\prime }}{u^{\prime }}=-2$
$v^{\prime }=-2u^{\prime }$

Again, using lens formula,
$\frac{1}{v^{\prime }}-\frac{1}{u^{\prime }}=\frac{1}{f}$
$\frac{1}{-2u^{\prime }}-\frac{1}{u^{\prime }}=\frac{1}{+20}$
$u^{\prime }=-30\text{cm}$

Distance by which object moved,
$d=|u^{\prime }-u|$
$d=|-30-(-10)|$
$d=20\text{cm}$