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

In This post you will get answer of Q.
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,

vA 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,

vB is object for lens C,

uC = 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

Solution Image

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