Question

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

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

Answer 1

Answer: (B)

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