Question

Find the position of final image from first lens.If the focal length of each lens is $10cm$.

• A. 40 cm
• B. 50 cm
• C. 45 cm
• D. 55 cm

Answer 1

Answer: (B)

Refraction from lens A,
From lens formula,
$\frac{1}{V_A}-\frac{1}{u_A}=\frac{1}{f_A}$
$\frac{1}{V_A}=\frac{1}{f_A}+\frac{1}{u_A}$
$\frac{1}{V_A}=\frac{1}{10}-\frac{1}{40}$
$V_A=\frac{40}{3}$ cm
Refraction from lens B,
v_A is object for lens B,
$u_B=30-\frac{40}{3}=\frac{50}{3}$ cm
So, $\frac{1}{v_B}-\frac{1}{u_B}=\frac{1}{f_B}$
$\frac{1}{v_B}+\frac{3}{50}=\frac{1}{10}$
$\frac{1}{v_B}=\frac{1}{10}-\frac{3}{50}$
$\frac{1}{v_B}=\frac{2}{50}$
$v_B=25$ cm
Refraction from lens C,
v_B is object for lens C,
u_C = 30 - 25 = 5 cm
$\frac{1}{v_C}=\frac{1}{f_C}+\frac{1}{u_C}\Rightarrow \frac{1}{v_C}=\frac{1}{10}-\frac{1}{5}\Rightarrow \frac{1}{v_C}=\frac{-1}{10}$
$v_c=-10$ cm
Final image distance from lens C is 10 cm towards lens B. So the final image distance from lens A is,
= 20 + 30 = 50 cm