Question

Two concave mirrors facing each others are placed at a separation of 20 cm with their principal axis separated by 3 cm. Distance of the image from the axis of $M_1$ and $M_2$ respectively is (Take paraxial rays approximation)

• A. 1.5 cm
• B. 2.5 cm
• C. 3.5 cm
• D. 4.5 cm

Answer 1

Answer: (A)

1.5 cm

$\begin{array}{c}\text{For}{M}_1\\ \frac{1}{v}+\frac{1}{-15}=\frac{1}{-10}\left(\text{mirror formula}\right)\\ \begin{array}{c}\frac{1}{v}=\frac{1}{15}-\frac{1}{10}\\ v=-30cm\end{array}\\ \text{For}{m}_2\\ \frac{1}{v}+\frac{1}{10}=\frac{1}{10}\end{array}$

$\begin{array}{c}v=-5cm\\ m=-\frac{v}{u}=-\left(\frac{-5}{10}\right)=\frac{1}{2}\\ \Rightarrow \frac{h_i}{h_0}=\frac{1}{2}\\ h_{\phi }=\frac{3}{2}=1.5cm\end{array}$