Question

The focal length of a concave mirror is $20cm$. Determine where an object must be placed to form an image magnified two times when the image is real

• A. $30cm$ from the mirror
• B. $10cm$ from the mirror
• C. $20cm$ from the mirror
• D. $15cm$ from the mirror

Answer 1

Answer: (B)

$10cm$ from the mirror

$\begin{array}{c}\text{By mirror formula:}\\ \Rightarrow \frac{1}{v}+\frac{1}{u}=\frac{1}{f}\end{array}$

as magnification $=m=-\left(\frac{v}{u}\right)$

$\Rightarrow 2=(-\frac{v}{u})$

as image is real

". both $v\&u$ have

same sign

$\therefore -2u=v$-(1)

$\begin{array}{c}f=-20cm\\ \text{as its concave}\\ \text{mirror}\end{array}$

$\begin{array}{cc}By\left(1\right)& \Rightarrow \frac{-1}{2u}+\frac{1}{u}=\frac{-1}{20}\\ \Rightarrow & \frac{1}{2u}=-\frac{1}{20}\end{array}$

$u=-10$cm

$\therefore$ object should

be placed $10cm$ from the

mirror.

Hence option 'B' is correct