Question

A $10cm$ long stick is kept in front of a concave mirror having a focal length of $10cm$ in such a way that the end of the stick closest to the pole is at a distance of $20cm$. What will be the length of the image?

Answer 1

Consider stick $AB$ is placed infront of a concave mirror as shown in the figure

For end $A$,
Object distance, $u=-30cm$
focal length, $f=-10cm$
Let the image $A^{\prime }$ of the end of the stick at point $A$ has formed at a distance $v_a^{\prime }$ from the mirror.

Using mirror formula,

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

$\Rightarrow \frac{1}{v_a^{\prime }}=\frac{1}{-10}-\frac{1}{-30}=-\frac{2}{30}$

$v_a^{\prime }=-15$ cm

Object distance, $u=-20cm$

focal length, $f=-10cm$

Let the image $B^{\prime }$ of the end of the stick at point $B$ has formed at a distance $v_b^{\prime }$ from the mirror.

Using mirror formula,

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

$\Rightarrow \frac{1}{v_b^{\prime }}=\frac{1}{-10}-\frac{1}{-20}=-\frac{1}{20}$

$\Rightarrow v_b^{\prime }=-20cm$

Therefore, the length of the image $=v_a^{\prime }-v_b^{\prime }=20-15=5cm$