Question

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

• A. $1 / 14 \,cm$
• B. $5 / 14 \,cm$
• C. $3 / 14 \,cm$
• D. $4 / 14 \,cm$

Answer 1

Answer: (B)

For point $B, u=-25\, cm , f=+10\, cm$
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
or, $\frac{1}{v}-\frac{1}{25}=\frac{1}{10}$
or, $\frac{1}{v}=\frac{1}{10}+\frac{1}{25}$
or, $\frac{1}{v}=\frac{5+2}{50} v=\frac{50}{7}$
For point $A, u^{\prime}=-30 \,cm , f^{\prime}=10 \,cm$
$\frac{1}{v^{\prime}}+\frac{1}{u^{\prime}}=\frac{1}{f^{\prime}} $
or, $ \frac{1}{v^{\prime}}-\frac{1}{30}=\frac{1}{10}$
or, $\frac{1}{v^{\prime}}=\frac{1}{30}+\frac{1}{10}=\frac{1+3}{30}=\frac{4}{30}$
$v^{\prime}=\frac{30}{4}=\frac{15}{2} cm$
$A^{\prime} B^{\prime}=\frac{15}{2}-\frac{50}{7}=\frac{5}{14} cm$