Question

A $U$ -shaped wire is placed before a concave mirror having a radius of curvature $20cm$ as shown in the figure. Find the total length of the image.

• A. $20cm$
• B. $24cm$
• C. $18cm$
• D. $16cm$

Answer 1

Answer: (D)

For $AB\Rightarrow \frac{1}{v}+\frac{1}{u}=\frac{2}{R}$
$\frac{1}{v_{1}}=\frac{2}{- 20}+\frac{1}{15}=-\frac{1}{10}+\frac{1}{15}=\frac{- 3 + 2}{30}=-\frac{1}{30}\Rightarrow v_{1}=-30cm$
$m_{1}=-\frac{v}{u}=-\frac{\left(\right. - 30 \left.\right)}{- 15}=-2$
For $CD,\frac{1}{v_{2}}=\frac{1}{- 10}+\frac{1}{20}=\frac{- 2 + 1}{20}=-\frac{1}{20}\Rightarrow v_{2}=-20cm$
$m_{2}=-\frac{v}{u}=-\frac{\left(\right. - 20 \left.\right)}{- 20}=-1$
Total length $=2+10+4=16cm$