Question

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

• A. $10\text{cm}$
• B. $2.5\text{cm}$
• C. $1\text{cm}$
• D. $0.5\text{cm}$

Answer 1

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


For point $\text{A}:$

$u=-30\text{cm};f=-10\text{cm}$

Using mirror formula

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

$\Rightarrow \frac{1}{v}=\frac{1}{-10}-\frac{1}{(-30)}$

$\Rightarrow v=-15\text{cm}$

For point $\text{B}:$

$u^{\prime }=-35\text{cm};f=-10\text{cm}$

Again using mirror formula

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

$\Rightarrow \frac{1}{v^{\prime }}=\frac{1}{-10}-\frac{1}{(-35)}$

$\Rightarrow v^{\prime }=-14\text{cm}$

Therefore, size of the image
$\left|A^{\prime }{B}^{\prime }\right|=|v-v^{\prime }|=|-15-(-14)|$

$\Rightarrow \left|A^{\prime }{B}^{\prime }\right|=1\text{cm}$

$\begin{array}{c}Ans.\left(a\right)\end{array}$