Question

The object $AB$ is placed on the axis of a concave mirror of focal length $10\text{cm}$. End $A$ of the object is $30\text{cm}$ from the mirror. Find the length of the image if the length of the object is $5\text{cm}$.

• A. $1\text{cm}$
• B. $2\text{cm}$
• C. $3\text{cm}$
• D. $4\text{cm}$

Answer 1

The correct option is A $1\text{cm}$

For end $A$,
$u=-30\text{cm}$
$f=-10\text{cm}$
So, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}-\frac{1}{30}=\frac{-1}{10}$
$\Rightarrow \frac{1}{v}=\frac{-1}{15}$
$\Rightarrow v=-15\text{cm}$
Similarly, for end $B$,
$u=-(30+5)=-35\text{cm}$
$f=-10\text{cm}$
So, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}-\frac{1}{35}=\frac{-1}{10}$
$\Rightarrow \frac{1}{v}=\frac{-1}{14}$
$\Rightarrow v=-14\text{cm}$
Now, size of image $=|-15-(-14)|=1\text{cm}$