Question

Four identical lenses are kept one beside the other on the same optical as shown in the figure. The right surface of rightmost lens is silvered. Focal length of lens is 20 cm and radius of silvered is 20 cm. The focal length of the combined system is

• A. 2 cm
• B. -2 cm
• C. 5 cm
• D. -5 cm

Answer 1

The correct option is B -2 cm

$\begin{array}{cc}\text{for net focus of lenses}a,b,c\&d\text{we use formula}& \\ \frac{1}{F_{net}}=\frac{1}{f_a}+\frac{1}{f_b}+\frac{1}{f_c}+\frac{1}{f_d}=\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}=\frac{4}{20}=\frac{1}{5}& =F_{net}=5cm\end{array}$

for net focus of the systern we use formula

$\frac{1}{F_{\text{net}}}=\frac{-2}{f_{\text{lens}}}+\frac{a_2}{R_{\text{mirror}}}=\frac{-2}{5}+\frac{2}{(-20)}$

$F_{\text{net}}=-2cm$

Hence $B^{\prime }$ is correct