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

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

Solution:

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