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 $AB\Rightarrow \frac{1}{v}+\frac{1}{u}=\frac{2}{R}$
$\frac{1}{v_1}=\frac{2}{-20}+\frac{1}{15}=-\frac{1}{10}+\frac{1}{15}=\frac{-3+2}{30}=-\frac{1}{30}\Rightarrow v_1=-30cm$
$m_1=-\frac{v}{u}=-\frac{(-30)}{-15}=-2$
For $CD,\frac{1}{v_2}=\frac{1}{-10}+\frac{1}{20}=\frac{-2+1}{20}=-\frac{1}{20}\Rightarrow v_2=-20cm$
$m_2=-\frac{v}{u}=-\frac{(-20)}{-20}=-1$
Total length $=2+10+4=16cm$