Question

obtain
the equivalent focal length of combination of thin
lenses placed in Contact
​

Answer 1

For the image formed by the first lens 'A' we get

$\longrightarrow \bold{ \frac{1}{v_1} - \frac{1}{u } = \frac{1}{f_1} }$

let this be equation (1)

For the image formed by the second lens 'B' we get

$\longrightarrow \bold{ \frac{1}{v} - \frac{1}{v_1 } = \frac{1}{f_2} }$

let this be equation (2)

By adding equation (1) and (2) we get

$\longrightarrow \bold{ \frac{1}{v} - \frac{1}{u} = \frac{1}{f_1} + \frac{1}{f_2} }$

If the two lens system is regarded as equivalent to a single lens of focal length 'f' then we have

$\longrightarrow \bold{ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} }$

So we get

$\longrightarrow \pink { \boxed { \frac{1}{f_1} + \frac{1}{f_2} = \frac{1}{f} }}$

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