Question

A convex mirror of focal length $10\text{cm}$ is shown in the figure. A linear object $\text{AB}=5\text{cm}$ is placed along the optical axis. Point $\text{A}$ is at a distance of $25\text{cm}$ from the pole of the mirror. The length of image of $\text{AB}$ is

• A. $2.5\text{cm}$
• B. $0.64\text{cm}$
• C. $0.75\text{cm}$
• D. $0.36\text{cm}$

Answer 1

The correct option is D $0.36\text{cm}$

Given:
For convex mirror,
focal length $\left(f\right)=10\text{cm};\text{AB}=5\text{cm}.$

For point $\text{A}$ :

$f=10\text{cm};u=-25\text{cm};v=v_A$

using mirror formula,

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

$\Rightarrow \frac{1}{v_A}-\frac{1}{25}=\frac{1}{10}$

$\frac{1}{v_A}=\frac{1}{10}+\frac{1}{25}=\frac{7}{50}$

$\Rightarrow v_A=\frac{50}{7}\text{cm}$

Similarly, for point $\text{B}$ :

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

$\frac{1}{v_B}-\frac{1}{30}=\frac{1}{10}\Rightarrow \frac{1}{v_B}=\frac{1}{30}+\frac{1}{10}=\frac{4}{30}$

$\Rightarrow v_B=\frac{30}{4}=\frac{15}{2}\text{cm}$

Length of the image $=v_B-v_A=\frac{15}{2}-\frac{50}{7}=\frac{105-100}{14}$

$\Rightarrow v_B-v_A=\frac{5}{14}=0.36\text{cm}$.

Hence, option $\left(b\right)$ is the correct answer.