Question

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

• A. $0.36\text{cm}$
• B. $0.75\text{cm}$
• C. $0.64\text{cm}$
• D. $0.25\text{cm}$

Answer 1

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

For image of point $A$: $\frac{1}{v_A}+\frac{1}{u_A}=\frac{1}{f}$

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

$\frac{1}{v_A}=\frac{1}{10}+\frac{1}{25}=\frac{5+2}{50}=\frac{7}{50}$

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

For B: $\frac{1}{v_B}+\frac{1}{u_B}=\frac{1}{f}$

$\frac{1}{v_B}-\frac{1}{30}=\frac{1}{10}$

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

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

Now,
Length of the image $=v_B-v_A=\frac{15}{2}-\frac{50}{7}=0.36\text{cm}$