Question

Find the magnification and nature of the image when point $O$ is $30cm$ behind the mirror.

• A. $2$ (Virtual, Inverted)
• B. $3$ (Real, Inverted)
• C. $5$ (Real, Erect)
• D. $2$ (Virtual, Erect)

Answer 1

The correct option is A $2$ (Virtual, Inverted)

For this situation, object will be virtual as shown in the figure.

Here, $u=+10cm$ and

$f=+20cm$.

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

So, $\frac{1}{v}+\frac{1}{+10}=\frac{1}{+20}\Rightarrow i.e.,v=-20cm$

i.e., the image will be at a distance of $20cm$ in front of the mirror and will be real, erect and enlarged with

$m=\frac{-v}{u}$

$m=\frac{-(-20)}{10}=+2$.

(b.) For this situation also, object will be virtual as shown in the figure.

Here, $u=+30cm$

And $f=+20cm$

$\frac{1}{v}+\frac{1}{+30}=\frac{1}{+20}i.e.,v=+60cm$

i.e., the image will be at a distance of $60cm$ behind the mirror and will be virtual, inverted, and enlarged with $m=(-60/30)=-2$.